RELIABILITY ANALYSIS OF TACTICAL UNMANNED AERIAL
VEHICLE (UAV)
A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY
BY
YILMAZ KOÇ
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
AEROSPACE ENGINEERING
DECEMBER 2017
Approval of the thesis:
RELIABILITY ANALYSIS OF TACTICAL UNMANNED AERIAL
VEHICLE (UAV)
submitted by YILMAZ KOÇ in partial fulfillment of the requirements for the
degree of Master of Science in Aerospace Engineering Department, Middle East
Technical University by,
Prof. Dr. Gülbin Dural Ünver _____________________
Dean, Graduate School of Natural and Applied Sciences
Prof. Dr. Ozan Tekinalp _____________________
Head of Department, Aerospace Engineering
Prof. Dr. Nafiz Alemdaroğlu _____________________
Supervisor, Aerospace Engineering Dept., METU
Prof. Dr. Barış Sürücü _____________________
Co-Supervisor, Statistics Dept., METU
Examining Committee Members:
Prof. Dr. Serkan Özgen _____________________
Aerospace Engineering Dept., METU
Prof. Dr. Nafiz Alemdaroğlu _____________________
Aerospace Engineering Dept., METU
Prof. Dr. Altan Kayran _____________________
Aerospace Engineering Dept., METU
Prof. Dr. Birdal Şenoğlu _____________________
Statistics Dept., Ankara University
Prof. Dr. Barış Sürücü _____________________
Statistics Dept., METU
Date: 26/12/2017
iv
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced
all material and results that are not original to this work.
Name, Last name: Yılmaz KOÇ
Signature:
v
ABSTRACT
RELIABILITY ANALYSIS OF TACTICAL UNMANNED AERIAL
VEHICLE (UAV)
KOÇ, Yılmaz
M. Sc., Department of Aerospace Engineering
Supervisor: Prof. Dr. Nafiz Alemdaroğlu
Co-Supervisor: Prof. Dr. Barış Sürücü
December 2017, 105 pages
To design cost effective and reliable products are considered to be important to be
competitive in the Aerospace Industry. Reliability is therefore, taken as an integral
part of the design process. Reliability, which is a kind of design parameter that
affects cost and system safety, shall be taken into account in early phases of design
process due to difficulties facing during changes in design at the later phases.
Reliability of Tactical UAVs can be evaluated by reliability testing but these tests are
very expensive and difficult. Because of the difficulties in reliability testing, in early
design phases reliability can be evaluated by using reliability methods.
In the scope of this thesis work, simulation study is performed to make reliability
prediction for METU Tactical UAV. Two different approaches are used to calculate
reliability characteristics for systems of METU Tactical UAV. The approaches
applied during simulation study are; firstly, items failure characteristics (i.e. failure
rate) are taken as a constant and thus exponential distribution is used as probability
distribution model. Second approach was that simulated time to failure data having
Weibull distribution characteristic is derived and it is determined to show how
vi
predicted reliability changes if it is assumed to be exponentially distributed. Within
the context of this simulation study, graphical methods i.e. Quantile-Quantile plotting
and probability-probability plotting were conducted to find the best distribution
model. Three-parameter Weibull distribution is taken as primary model to assess
simulated data and unknown parameters of Weibull distribution for which Goodness
- of - Fit Tests have been applied is estimated by using Maximum Likelihood and
Least Square Estimation. This simulation study is conducted to emphasis the effect
of assumption on distribution model, which represent the simulated data.
Keywords: Mission Reliability, Reliability Predictions, Tactical UAV. Exponential
Distribution
vii
ÖZ
TAKTİK İNSANSIZ HAVA ARACININ (İHA) GÜVENİLİRLİK ANALİZİ
KOÇ, Yılmaz
Yüksek Lisans, Havacılık ve Uzay Mühendisliği Bölümü
Danışman: Prof. Dr. Nafiz Alemdaroğlu
Yardımcı Danışman: Prof. Dr. Barış Sürücü
Aralık 2017, 105 sayfa
Piyasada rekabetçi olabilmek için maliyet etkin ve güvenilir ürünler tasarlamak çok
önemlidir. Bu amaçla güvenilirliğin tasarım sürecinin bir parçası olarak ele alınması
gerekmektedir. Bu nedenle, ilerleyen aşamalarda tasarımda değişiklik yapmak zor
olduğundan maliyet ve güvenliği etkileyen güvenilirlik erken tasarım aşamalarında
dikkate alınmalıdır.
Taktik İnsansız Hava Araçlarının (İHA) güvenilirliği güvenilirlik testleri ile
değerlendirilebilir fakat bu testler maliyetli ve zordur. Güvenilirlik testlerindeki
zorluklar nedeni ile erken tasarım aşamalarında güvenilirlik, güvenilirlik kestirimi
sonuçları ile değerlendirilebilir.
Bu çalışmada, Taktik İnsansız Hava Aracı için güvenilirlik analizi
gerçekleştirilmiştir. Taktik İnsansız Hava Aracı sistemlerinin ve elemanlarının
güvenilirlik analizleri iki farklı yaklaşım kullanılmış; birinci yaklaşımda elemanların
hata karakteristiğinin sabit kabul edildiği ve analizlerde üstel dağılımı kullanılarak
görev güvenilirliği hesaplanmıştır. İkincil yaklaşımda Weibull dağılım
karakteristiğine sahip olan arıza zamanlarının üstel dağılım özelliği göstermediği
durumlarda, uygun dağılım modeli belirleyerek görev güvenilirliği hesaplanmıştır.
Simülasyon çalışması kapsamında, grafiksel metotlar uygulanmış ve veri setine en
viii
uygun dağılım modeli belirlenmiştir. Üç parametreli Weibull model seçilmiş ve
bilinmeyen parametreleri MLE ve LSE yöntemleriyle hesaplanmış ve GOF testleri
uygulanmıştır. Bu çalışma kapsamında iki yaklaşım arasındaki meydana gelen
güvenilirlik farkları elde edilmiş ve karşılaştırılmıştır.
Anahtar Kelimeler: Görev Güvenilirliği, Lojistik Güvenilirlik, Güvenilirlik Testi,
Güvenilirlik Tahmini, Taktik İnsansız Hava Aracı (İHA).
ix
ACKNOWLEDGMENTS
The author wishes to express his grateful appreciation and thanks to his advisor, Prof.
Dr. Nafiz Alemdaroğlu for his continuous support and valuable guidance throughout
the study. The guidance and cooperation of Co-Supervisor Prof. Dr. Barış Sürücü,
are also appreciated.
The author would like to thank to his parents Mrs. Fatma Koç and Mr. Arslan Koç, to
his sister Mrs. Yeşim Koç, and to his friends Duygu Sarıkaya, Serhat Akgün and
Ufuk Başlamışlı for their support, encouragement, patience and understanding
throughout the course of his studies.
x
TABLE OF CONTENTS
ABSTRACT .......................................................................................................... v
ACKNOWLEDGMENTS .................................................................................... ix
TABLE OF CONTENTS ...................................................................................... x
LIST OF TABLES .............................................................................................. xii
LIST OF FIGURES ............................................................................................ xvi
CHAPTERS
1. INTRODUCTION ........................................................................................ 1
1.1 Introduction to UAVs .................................................................................... 1
1.2 Reliability ...................................................................................................... 3
1.3 Scope of the Research .................................................................................. 11
2. RELIABILITY MATHEMATICS ............................................................. 13
2.1 Distributions ................................................................................................ 13
2.2 Graphical Methods ....................................................................................... 20
2.3 Parameter Estimation ................................................................................... 23
2.4 Reliability Modeling .................................................................................... 26
3. OVERVIEW OF METU TACTICAL UAV AND ITS SYSTEM
RELIABILITY .................................................................................................... 33
3.1 METU Tactical UAV ................................................................................... 33
3.2 Mission Profile of METU Tactical UAV ..................................................... 34
xi
3.3 Systems of METU Tactical UAV ................................................................ 36
3.4 Component and System Reliability of UAV ............................................... 50
4. SIMULATION STUDY AND RELIABILITY COMPARISONS ........... 59
4.1 Reliability Estimation .................................................................................. 59
4.2 Estimation of Three-parameter Weibull Distribution Parameters ............... 60
4.3 Systems Reliability Based on Weibull Distribution .................................... 74
4.4 Reliability Comparisons .............................................................................. 75
5. CONCLUSIONS AND FUTURE WORK ................................................ 77
5.1 Conclusions ................................................................................................. 77
5.2 Future Work ................................................................................................ 79
REFERENCES.................................................................................................... 81
APPENDICES
A. TIME TO FAILURE DATA ..................................................................... 89
B. QUANTILE-QUANTILE PLOTS .......................................................... 101
C. CURRICULUM VITAE ......................................................................... 105
xii
LIST OF TABLES
TABLES
Table 3.1: Main Technical Specification of the UAV ............................................... 34
Table 3.2: Flight Phases of METU Tactical UAV Flight and Their Durations ......... 36
Table 3.3: Item and Components of Landing Gears .................................................. 39
Table 3.4: Items and Components of Electrical System ............................................ 41
Table 3.5: Components of Ice Protection System ...................................................... 43
Table 3.6: Items and Components of Propulsion System .......................................... 44
Table 3.7: Items and Components of Fuel System ..................................................... 45
Table 3.8: Items and Components of Lighting System .............................................. 46
Table 3.9: Items and Components of Communication System .................................. 46
Table 3.10: Items and Components of Automatic Flight Control System ................. 49
Table 3.11: Items in Mission System ......................................................................... 49
Table 3.12: Landing Gear System Reliability Data ................................................... 51
Table 3.13: Electrical System Reliability Data .......................................................... 51
Table 3.14: Ice Protection System Reliability Data ................................................... 51
Table 3.15: Propulsion System Reliability Data ........................................................ 52
Table 3.16: Fuel System Reliability Data .................................................................. 52
Table 3.17: Lighting System Reliability Data ............................................................ 52
Table 3.18: Communication System Reliability Data ................................................ 52
Table 3.19: AFCS Reliability Data ............................................................................ 53
Table 3.20: Mission Systems Reliability Data ........................................................... 53
Table 3.21: Reliabilities of systems ........................................................................... 58
xiii
Table 4.1: Estimated Parameters of Exponential Data for Landing Gear System,
where sample size (n=20) .......................................................................................... 61
Table 4.2: Estimated Parameters of Exponential Data for Electrical System, where
sample size (n=20) ..................................................................................................... 62
Table 4.3: Estimated Parameters of Exponential Data for Ice Protection System,
where sample size (n=20) .......................................................................................... 62
Table 4.4: Estimated Parameters of Exponential Data for Propulsion System, where
sample size (n=20) ..................................................................................................... 63
Table 4.5: Estimated Parameters of Exponential Data for Fuel System, where sample
size (n=20) .................................................................................................................. 63
Table 4.6: Estimated Parameters of Exponential Data for Lighting System, where
sample size (n=20) ..................................................................................................... 64
Table 4.7: Estimated Parameters of Exponential Data for Communication System,
where sample size (n=20) .......................................................................................... 64
Table 4.8: Estimated Parameters of Exponential Data for Automatic Flight Control
System, where sample size (n=20) ............................................................................. 65
Table 4.9: Estimated Parameters of Exponential Data for Mission System, where
sample size (n=20) ..................................................................................................... 65
Table 4.10: Estimated Parameters of Weibull Data for Landing Gear System, where
sample size (n=20) ..................................................................................................... 66
Table 4.11: Estimated Parameters of Weibull Data for Electrical System, where
sample size (n=20) ..................................................................................................... 66
Table 4.12: Estimated Parameters of Weibull Data for Ice Protection System, where
sample size (n=20) ..................................................................................................... 67
Table 4.13: Estimated Parameters of Weibull Data for Propulsion System, where
sample size (n=20) ..................................................................................................... 67
Table 4.14: Estimated Parameters of Weibull Data for Fuel System, where sample
size (n=20) .................................................................................................................. 67
Table 4.15: Estimated Parameters of Weibull Data for Lighting System, where
sample size (n=20) ..................................................................................................... 68
xiv
Table 4.16: Estimated Parameters of Weibull Data for Communication System,
where sample size (n=20) ........................................................................................... 68
Table 4.17: Estimated Parameters of Weibull Data for Automatic Flight Control
System, where sample size (n=20) ............................................................................. 68
Table 4.18: Estimated Parameters of Weibull Data for Mission System, where
sample size (n=20) ..................................................................................................... 69
Table 4.19: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2) 72
Table 4.20: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2)
when n=20 for two-parameter Weibull Distribution .................................................. 72
Table 4.21: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2)
when n=100 for two-parameter Weibull Distribution ................................................ 72
Table 4.22: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2)
when n=20 for three-parameter Weibull Distribution ................................................ 73
Table 4.23: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2)
when n=100 for three-parameter Weibull Distribution .............................................. 73
Table 4.24: Reliabilities of systems after simulation study (exponential data) ......... 74
Table 4.25: Reliabilities of systems after simulation study (Weibull data) ............... 75
Table 4.26: Reliability of aircraft based on exponential data .................................... 76
Table 4.27: Reliability of aircraft based on Weibull data .......................................... 76
Table A. 1: Time to failure data for items under landing gear system ....................... 89
Table A. 3: Time to failure data for items under electrical system ............................ 91
Table A. 4: Time to failure data for items under ice protection system ..................... 93
Table A. 5: Time to failure data for items under propulsion system ......................... 94
Table A. 6: Time to failure data for items under fuel system .................................... 96
Table A. 7: Time to failure data for items under lighting system .............................. 97
Table A. 8: Time to failure data for items under communication system .................. 98
xv
Table A. 9: Time to failure data for items under AFCS system ................................ 99
Table A. 10: Time to failure data for items under mission systems ........................ 100
xvi
LIST OF FIGURES
FIGURES
Figure 1.1: Typology of UAVs by Performance .......................................................... 2
Figure 1.2: Bathtub Curve .......................................................................................... 10
Figure 2.1: PDF of Weibull distribution for different values of β ............................. 17
Figure 2.2: Reliability function of Weibull distribution for different values of β ..... 18
Figure 2.3: PDF of Weibull distribution for different values of η (eta) ..................... 19
Figure 2.4: Reliability function of Weibull distribution for different values of η (eta)
.................................................................................................................................... 19
Figure 2.5: Development of Reliability Block Diagrams within a System ................ 28
Figure 2.6: Series Configuration ................................................................................ 29
Figure 2.7: Parallel Active Redundancy Configuration ............................................. 30
Figure 2.8: Parallel Standby Redundancy Configuration ........................................... 31
Figure 3.1: METU Tactical UAV .............................................................................. 33
Figure 3.2: Mission Profile ......................................................................................... 35
Figure 3.3: Systems of Tactical UAV ........................................................................ 37
Figure 3.4: Main Landing Gears with Brake Disks and Callipers ............................. 38
Figure 3.5: Nose Landing Gear .................................................................................. 39
Figure 3.6: Lithium Polymer Battery with its embedded 5V and 12V DC-DC
Converters .................................................................................................................. 40
Figure 3.7: Junction Box ............................................................................................ 41
Figure 3.8: Cabling Diagram of METU Tactical UAV ............................................. 42
Figure 3.9: Limbach 275 E Engine ............................................................................ 43
Figure 3.10: Location of the Fuel Tank ...................................................................... 45
xvii
Figure 3.11: Avalon Digital Video Transmitter ......................................................... 47
Figure 3.12: Piccolo II Autopilot ............................................................................... 47
Figure 3.13: Servo Actuator mounted on Wing ......................................................... 48
Figure 3.14: Servo Actuator on Vertical Tail............................................................. 48
Figure 3.15: Environmental Conversion Factors ....................................................... 50
Figure 3.16: System Level RBD of METU tactical UAV ......................................... 53
Figure 3.17: RBD of Landing Gear System ............................................................... 54
Figure 3.18: RBD of Electrical System ..................................................................... 55
Figure 3.19: RBD of Ice Protection System .............................................................. 55
Figure 3.20: RBD of Propulsion System ................................................................... 56
Figure 3.21: RBD of Fuel System is .......................................................................... 56
Figure 3.22: RBD of Lighting System ....................................................................... 56
Figure 3.23: RBD Communication System ............................................................... 56
Figure 3.24: RBD of AFCS System ........................................................................... 57
Figure 3.25: RBD of Mission System ........................................................................ 57
Figure B. 1: Sensor (Engine Temperature) quantile plot for exponential distribution
by using exponential observed data ......................................................................... 101
Figure B. 2: Sensor (Engine Temperature) quantile plot for Weibull distribution
(shape parameter of 1.5) by using exponential observed data ................................. 102
Figure B. 3: Sensor (Engine Temperature) quantile plot for Weibull distribution
(shape parameter of 2.0) by using exponential observed data ................................. 102
Figure B. 4: Sensor (Engine Temperature) quantile plot for exponential distribution
by using Weibull observed data ............................................................................... 103
Figure B. 5: Sensor (Engine Temperature) quantile plot for Weibull distribution
(shape parameter of 1.5) by using Weibull observed data ....................................... 104
xviii
Figure B. 6: Sensor (Engine Temperature) quantile plot for Weibull distribution
(shape parameter of 2.0) by using Weibull observed data ....................................... 104
1
CHAPTER 1
INTRODUCTION
In this study, by using different reliability analysis methods the mission reliability of
METU Tactical Unmanned Aerial Vehicle (UAV) is investigated. In this chapter,
literature review of related reliability problems and Tactical Unmanned Aerial
Vehicle (UAV) investigations are given. The basic definitions of the reliability
discipline and general information about the UAVs are presented. Then, the scope of
this study is described.
1.1 Introduction to UAVs
An Unmanned Aerial Vehicle (UAV) is a ‘‘remotely piloted or self-piloted aircraft
that can carry cameras, sensors, communications equipment or other payloads’’ [1].
UAVs are widely used to perform many of functions related to both military and
civil applications. UAVs are classified according to functions they performed, these
classifications are; Target and Decoy, Reconnaissance, Combat, Logistics, Research
and Development, Civil and Commercial [2]. UAVs are also categorized with respect
to their capabilities, size, weight, endurance, maximum altitude, etc. Categorization
of UAVs also includes the performance parameter Figure 1.1 below indicates the
performance classification of the UAVs [3].
Today’s World, UAVs became the one of the most important figure for military
operations. However, history of Unmanned Aerial Vehicles started with the idea of
flying machine, which was first thought about 2500 years ago. First documented
2
UAV in the history was a flying pigeon, which was a mechanical bird flying with its
moving wing getting energy from the mechanism in its stomach and was created by
Archytas in B.C. 425. It is reported that it flew about 200 meters before hitting the
ground. Over the years, different ideas about UAVs were generated such as “flying
bird” during the Renaissances, Air Screw design of Leonardo Da Vinci, etc.[4].
Figure 1.1: Typology of UAVs by Performance
First designed and built UAVs which were called as flying bombs V-I and V-II for
military purposes was used by the Germans during the World War II. It has been
showed that UAVs can result in a destructive effect on targets. Then, Snark was
designed as unmanned intercontinental range aircraft by USA during the 1950s [5].
With V-I, V-II and Snark, UAVs started to play important role in the history of
military operations.
UAVs have been being currently used in different military operations such as
targeting and decoying operations, reconnaissance purposes and combat. In targeting
and decoying operations, UAVs provide ground and aerial gunnery a target that
simulates an enemy aircraft or missile. Reconnaissance operations of UAV give
opportunity to get battlefield intelligence over the enemy. One of the most important
3
functions of UAVs is that attack for high risk missions have been performed by
combat UAVs. In shortly, by performing tasks such as surveillance; signals
intelligence; precision target designation; mine detection; and chemical, biological,
radiological, nuclear (CBRN) reconnaissance, unmanned systems have made key
contributions to the Global War on Terror [6].
UAVs have critical advantages over manned aircraft in terms of missions of UAVs
being categorized by three Ds: Dull, Dirty and Dangerous [7]. Dull has a meaning of
long endurance missions which continuous for many hours or even days. Because
UAVs are not limited with the physiological limitations of human pilots, they can be
designed for maximized on-station times. Missions which include threat of biological
or chemical contaminations are called dirty missions and these missions comprise
risks for manned aircrafts. Many pilots have been killed while attempting to
accomplish their missions. Most combat missions are dangerous; number of pilot
died during the dangerous missions could not be undervalued. Briefly, the
development of uninhabited or unmanned aerial vehicles (UAVs) raises the
possibility of more efficient, secure, and cost effective military operations [8].
In addition to military purposes, UAVs offer some potential both civil and
commercial applications such as traffic monitoring, meteorological monitoring,
forestry inspections, hurricane monitoring, oil, gas and mineral exploration and
maritime surveillance, etc.
1.2 Reliability
The probability that an item will perform its intended function for a specified interval
under stated conditions or the duration or probability of failure-free performance
under stated conditions is defined as reliability [9]. Practically, there are many
definition of reliability used in daily life. In general, reliability is defined such that it
is considered as an expression of user’s trust to a material used [10]. Another
4
description of reliability is the performance of the product in time [11]. A
comprehensive definition of reliability is that “it is the conditional probability, at a
given confidence level, that the equipment will perform its intended functions
satisfactorily or without failure and within specified performance limit, at a given
age, for a specified length of time (mission time) when used under specified
application and operational environments with their associated stress levels” [12].
History of reliability starts with the application of the probability concept for the
problem of electrical power generation during 1930s. However, application of basic
reliability concept to design of V-I and V-II missiles performed by German during
the World War II is considered as an actual starting point of the reliability
application. Then, many studies about failures of electronic equipment, equipment
repair and maintenance cost had been performed by United States Air Force, Navy
and Army during years between 1945 and 1950 [13]. 1950s is the milestone for the
development of the mathematical theory of the reliability [14]. Firstly, Statistical
distribution representing the breaking strength of materials had been published by
Professor W. Weibull in 1950 [15]. In 1952, failure data and result of goodness of fit
tests for failure probability distributions had been represented by D.J.Davis.
Assumptions made for the exponential failure distribution which is widely used
today for representing the items’ failure behavior was supported by these failure data
and result of goodness of fit tests [16]. Today, there are many specialized areas in
reliability field for instance; software reliability, mechanical reliability and human
reliability etc.
Reliability is one of the most important parameter showing performance of the
product and reliability activities are continuing activities throughout the design and
development of a project, from initial conception to production. According to the
definition of the reliability, there are there critical parameters being; intended
function which will be performed by item, operating conditions that item will face
5
and duration (time) in which item will operate. These three parameters shape the
item reliability.
Item’s tasks are specified by intended function. Intended functions are considered as
a starting point of reliability analysis since it describes which failures of the item are
critical in terms of the reliability sense [12]. It has vital importance to specify the
definition of intended functions clearly before starting the reliability analysis in order
to state the first point of the failures required to be assessed. In regards to intended
functions, what is success by one user may seem to be failure by another user.
Therefore, intended functions with respect to the user expectations should be defined
in detail.
Operating condition that item will face during its life cycle or a specific mission
should be well defined since it has a significant effect on reliability of an item. Item’s
failure rate is influenced by the operating conditions of temperature, stress,
environment, etc. For example, semiconductor component operating in environment
of 20 °C has higher failure rate than semiconductor component operating in
environment of 10 °C.
Reliability of the item indicates decreasing characteristics with time on which failure
causes are dependent. Duration is also called risk time that item is at risk under the
specified operating conditions. Intended functions or operating conditions may also
depend on the time, For instance, in each phases of specific mission profile, user may
expect from item to perform different function.
Reliability modeling, allocation and prediction are main methodologies of the
reliability analysis. “The purpose of the reliability modeling is to express the
specified requirements, functions and operating and maintenance conditions for a
system in such a way that the reliabilities of the items comprising the system can be
assessed and combined to predict the system reliability, indicate shortcomings and
6
assess logistic implications” [17]. Reliability allocation is the process of assigning
reliability target and requirements to subsystems or individual components so as to
attain a specified overall reliability for the whole system. Reliability requirements for
basic reliability parameters and mission reliability are allocated to the level specified
and used to establish baseline requirements to designers. Reliability allocations are
required to be consistent with the reliability mathematical models. Reliability
prediction is performed in order to estimate the logistic (basic) reliability and mission
reliability of the system/subsystem and to determine if the requirements are
achievable for that level. Reliability predictions are a basis for the system/subsystem
mission reliability analysis, maintainability analysis, logistics support analysis and
life cycle cost.
Reliability modeling and prediction are used to indicate that item whether or not has
ability to meet the reliability requirement. Reliability requirements are derived from
the user for reliability in logistics point of view and/or in mission standpoint where
mission reliability estimates the probability that system will not fail to complete the
mission and logistic reliability is the estimation of logistic and maintenance support
resulting from the unreliability of the item [18].
In mission reliability analysis, complex series-parallel arrangements of items under
the system are evaluated. Modeling of the items’ relationships in accordance with
reliability point of view and mission success definition may become a significant
problem for complex systems including redundancies and alternative modes of
operation. Therefore, in order to estimate the mission reliability of the system, some
definitions about mission need to be clearly defined. First one is the definition of the
item performance indicating which operation of the item should be considered as
success, which one is thought to be failure. Definition of the mission condition is the
second one which defines the environmental condition affecting the item throughout
the mission. It also includes the periods of operation or duty cycle. Items may be
expected to perform different functions at different stages of the mission, thus
7
definition of mission time is also critical information during the mission reliability
analysis. Last critical definition is the definition of item’s reliability variable which is
considered as a number (time, cycles, events, etc.) used to describe the duration
required by each item element to perform its intended functions [18].
Logistic (basic) reliability measures the probability a system is able to operate
without logistics support, regardless of the effect on the mission. It is a measure of
the amount of logistics resources necessary to support the system: the higher the
logistics reliability, the lower the amount of resources and logistics needs required.
Logistics (basic) reliability is of tremendous concern to the logistician since every
component failure places a burden on the logistics system (supply, maintenance,
transportation, etc). As would be expected, logistics reliability is degraded by the
redundancy of a system's design while redundancy leads to an improvement in the
mission reliability.
Reliability is considered as a part of system design and branch of engineering
application. The technical discipline of estimating, controlling and managing the
probability of failure in devices, equipment and systems is defined as reliability
engineering. The main purpose of the reliability engineering studies is to eliminate
possible failures. If the failure cannot be eliminated, the severity of the effect of the
failure should be decreased. However, after any design change performed to increase
reliability, system reliability must be reevaluated. The traditional way of reliability
determination is real time testing and number of test samples. Therefore, sample size
required in the tests increases rapidly with the increasing reliability. When the
reliability test of an expensive and safety critical system is considered e.g. engines of
Tactical UAVs, it is seen that such tests are difficult because of cost and safety
requirements during testing. Also, it is difficult to perform failure analysis for
individual components as they are all destructed during the test. Demonstrating
reliability by testing has many difficulties. Therefore, during the early stages of the
8
design, other approaches to assess the reliability of the components/system should be
used.
There are many ways to improve reliability of the system. Any one of the methods
may be applied by taking time and cost into account. Methods to be used;
- Reduce Number of Parts: reducing number of part in design will increase
reliability. Since more parts in design means more failures the user will face.
Innovative design ideas are required to reduce the number of parts without
performance degradation of the system. Reduction in number parts also
provides the weight that is one of the most critical design parameter for
aircrafts and space advantages to the designer
- Part Selection: High quality and high reliability parts are selected to improve
reliability of the system. However, high quality may result in a higher cost for
the user. Cost parameter may limit the quality parts selection.
- Derating: Part failure rates generally decrease as applied stress levels
decrease. Therefore, derating the part at levels below its ratings (for current,
voltage, power dissipation, temperature, etc.) increase reliability. While
selecting part, part with ratings well above given applied stress selection will
also help to increase reliability.
- Burn-In: Burn-in is a process to accelerate the rate of infant mortality failures
at elevated temperature. Burn-in allows designer to eliminate the infant
mortality failures of part before it is used in the field. Burn-in process can be
applied at the part, item, or system level.
- Redundancy: system reliability may also be enhanced by using redundancy
design techniques. However, it should be noted that redundancy only
increases mission reliability. Every redundant part or equipment will require
logistic support.
9
The utility of UAVs for both military and civilian applications have been emphasized
by recent world events nevertheless UAVs have been showing undesired reliability
characteristics in practice. Approximately half of the current-generation unmanned
aircrafts have been lost with respect to a recent report. When it is compared with loss
rate of combat manned aircrafts, Loss rate of unmanned aircrafts is almost 10 times
worse [38].
This is the reason why reliability is considered as one of the critical design parameter
for UAV design. Reliability of UAVs, in a sense, is the indication of their
affordability, their mission availability and their acceptance into civil airspace.
UAVs’ reliability is considered to be highly related to their affordability since UAVs
are expected to be less expensive compared to manned counterparts during their life
cycle. This expectation for UAVs arises from the smaller size of them since smaller
means savings of some $1,500 per pound. Enhanced reliability increases chance of
UAVs to be more prone to perform their missions, in other words UAVs spend less
time for maintenance purposes thus it result in a better mission availability
performance. Enhancing reliability is also a key to get the confidence of the general
public, the acceptance of other aviation constituencies such as airlines, general
aviation, etc. and aviation authorities like FAA [39].
1.2.1 Bathtub Curve
The life time of a population of products can be represented by curve. This curve is
called as “bathtub” curve. “Bathtub” curve is a model which is generally accepted
model for variation of failure rate with time for both non-repairable items and items
which when repaired are restored [17]. In Figure 1.2 the bathtub curve is shown. This
curve consists of three distinct periods: First period is an infant mortality period with
a decreasing failure rate. Second is a normal life period (also known as "useful life")
with a low, relatively constant failure rate and last period is a wear-out period which
exhibits an increasing failure rate [20].
10
In the first period of the bathtub curve, failure rate is relatively high due to design
and manufacturing weaknesses. Manufacturing weaknesses includes poor joints and
connections, damaged components, chemical impurities, dirt and contaminations,
assembly errors and inadequate skills used in manufacturing, etc. [9]. Failure rate of
item is decreasing with time as defects in design and manufacturing are detected and
eliminated. In order to avoid infant mortalities, appropriate specifications, adequate
design tolerance and sufficient component derating can be considered as a method to
eliminate the defects. In addition to methods mentioned, decrease rate of the curve
during the infant mortality period depends on the maturity of the design and
manufacturing process. From a customer satisfaction point of view, infant mortalities
are unacceptable since significant number of failures occurs in a short time and they
result in "dead-on-arrival" products, causing early customer dissatisfaction and
warranty expense [21].
Figure 1.2: Bathtub Curve
The second period of bathtub curve is called normal life (useful life) period and by
assumption it is characterized by a relatively constant failure rate. Even though some
failures still appears due to manufacturing weaknesses and wear out, Majority of the
failures are caused by operating stresses such as temperature, vibration, electrical
stresses, shock, etc. to which the item is subjected in its particular application and
11
theoretically occur randomly which means failures does not depend on time pattern.
Because of the assumptions below, normal life (useful life) period is the most
focused interval in respect to reliability prediction [17].
- Most of the early life (infant) failures have been eliminated before an item
enters service
- It will be ensured by in-service maintenance policy that items are replaced
before its wear-out
Random failures can be eliminated via controlling the operating stresses, in other
words, external environment and/or increasing the robustness of the design [22].
Wear out period is the last part of the bathtub curve and is mainly result of ageing
phenomena. During the wear-out period, exposure of operating and environmental
stresses affects items such that they start to deteriorate. It is assumed that wear out
failures increase with time as the wear out mechanism accelerates, owing to
corrosion, oxidation, fatigue, friction wear, shrinkage etc. Failure rate of the item
increases due to this deterioration in a way that items reach the end of their useful
life. Wear-out failures can be avoided by replacing the item or on-condition
monitoring for item [17].
1.3 Scope of the Research
In this study, by using different reliability analysis methods the mission reliability of
METU Tactical Unmanned Aerial Vehicle (UAV) is investigated. Mission reliability
of Tactical UAV is examined according to the some specified mission profiles which
are determined based on the operational scenarios of the UAV.
12
In Chapter 2, reliability mathematics and reliability analysis methods are given.
Types of probability distribution, graphical methods used in analysis, methods
conducted for parameters estimation and reliability modelling are explained in detail.
METU Tactical UAV and its operational concepts are defined in In Chapter 3.
Reliability characteristics are also predicted for system under UAV with assumption
of data being exponentially distributed.
Chapter 4 is the section in which simulation study is performed and comparisons of
predicted reliability characteristics of system among two different approaches are
evaluated.
In Chapter 5, conclusions obtained in this study are summarized and what can be
performed for future studies is emphasized.
13
CHAPTER 2
RELIABILITY MATHEMATICS
Reliability engineering is a kind of discipline that strongly depends on statistics and
mathematical probabilities to measure and analyze data and draw inferences about
performance of items and systems [19]. Mathematical model of the items and
systems failures is an essential parameter to obtain any idea about the performance
during the operation of items and systems.
2.1 Distributions
Probability distribution models such as Exponential, Weibull, Binomial, Normal etc.
are chosen to model the different life distribution characteristics in the “bathtub”
curve. Both exponential distribution and Weibull distribution are taken into
assessment within the scope of this thesis.
2.1.1 Exponential Distribution
The randomly occurring failures are modelled via exponential distribution model
during the useful life period of the “bathtub” curve in which only constant failure
rate characteristic of items are obtained. Main advantage of the exponential
distribution over other statistical distributions is that it is described by the single
parameter λ and therefore it has wide applicability compared to other statistical
distributions. Reliability is defined in terms of probability and probabilistic
14
parameters such as density functions, random variables, and distribution functions
[9]. Mathematical formulation for exponential distribution is given as follows:
The cumulative distribution function F(t) is defined as the probability in a random
trial that the random variable is not greater than t. F(t) is also called unreliability
function and it gives the percentage of the population has failed for a specific time.
t
dttftF )()( (2.1)
Where f (t) is called probability density function and it describes the “where” failure
occurs over time. Reliability function can be described in terms of the unreliability
function since it represents the percentage that item has survived for a specific time.
By definition, reliability function formula is;
t
dttftFtR )()(1)( (2.2)
By differentiating the reliability function equation;
dt
tdRtf
)()( (2.3)
Failure rate is the ratio of probability that failure occurs in the interval and it is given
by;
)(
)()()(
tRt
ttRtRt
(2.4)
As interval length ∆t approaches zero, limits of the failure rate is called instantaneous
failure rate or specifically called “hazard rate”.
dt
tRd
tRtRt
ttRtRth
t
)(
)(
1
)(
)()(lim)(
0 (2.5)
15
By substituting the differentiated reliability function equation (2.3) into hazard rate
equation; hazard rate equation becomes;
)(
)()(
tR
tfth (2.6)
Hazard rate or instantaneous failure rate has a significant and fundamental
relationship because relationship does not depend on the statistical distribution.
Taking the derivatives of both side of the hazard rate equation (2.6);
dtthtR
tdR)(
)(
)( (2.7)
then,
t
dtthtR
0
)(exp)( (2.8)
For exponential distribution, hazard rate is assumed to be constant and denoted by λ,
then
tetR )( (2.9)
where R is the reliability, t is time that the item is at risk under specified operating
conditions, and λ is the failure rate of the item.
Exponential distribution has different characteristics compared to other statistical
distributions such that [19];
- Failure rates of the item are same at each point in time; this means that failure
rate is constant. This describes the useful life period of the bathtub curve
where failures occur randomly
- For complex systems in which there many different electronic and
electromechanical components, exponential distribution are convenient
16
distribution even though, each component in the complex systems may not
have an exponential characteristic.
- Exponential distribution is relatively east to fit to data. Therefore,
misapplication of exponential distribution to data sets, which requires more
complex distributions, may occur.
2.1.2 Weibull Distribution
Weibull distribution was introduced first by a physicist, Waloddi Weibull (1939).
Three parameter Weibull distributions are characterized by three parameter; shape
parameter β (i.e. dimensionless), scale parameter (also called as characteristic life) η
(time) and threshold parameter (also called as location parameter) γ (time).
Probability density function of three-parameter Weibull distribution is given by [50];
xxxf exp),,;( (2.10)
Where 0,, x
Thus, related cumulative distribution function is as follows;
x
exF 1)( (2.11)
Most practical reliability applications, it is assumed that failure starts occurring at
time is equal zero (γ=0). Then, cumulative distribution function, which is defined for
two-parameter Weibull distribution, becomes;
x
exF 1)( (2.12)
Then, Reliability function is given as;
17
x
exR )( (2.13)
Weibull distribution is widely preferred in reliability engineering because of its
versatility. When shape parameter (β) is taken as one then, Weibull distribution turns
out to be identical to exponential distribution and when it has the value of 3.5,
Weibull approximates the normal distribution.
The effect of shape parameter (β) on probability density function (PDF) of Weibull
distribution is given in Figure 2.1 based on the assumption that scale parameter is
constant.
Figure 2.1: PDF of Weibull distribution for different values of β
Weibull distribution is particularly useful distribution since it can be used to model
the different life distribution characteristics with the help of changing distribution
parameters. When shape parameter β<1 has the meaning that the failure rate of item
decreases with time and thus infant mortality period of bathtub curve can be
18
modelled. Useful life period, in which failure rate is assumed to be almost constant,
can be modelled with Weibull distribution having shape parameter equal to or close
to one. When shape parameter β>1, failure rate of item increases that is also known
as Wear out period in bathtub curve. Briefly, shape parameter is considered to be
basic indication for tendency of item’s failure rate characteristics. Effects of shape
parameter on the reliability function of Weibull distribution is shown in Figure 2.2
below.
Figure 2.2: Reliability function of Weibull distribution for different values of β
Scale parameter (also called as characteristic life) η (time) is indication of life units
at which 63.2% of population have failed or 36.8% of population have survived. The
functional effect of scale parameter (η) on probability density function (PDF) of
Weibull distribution is given in Figure 2.3 with respect to constant shape parameter
of three.
19
Figure 2.3: PDF of Weibull distribution for different values of η (eta)
Figure 2.4 also provides the how reliability function of Weibull distribution changes
with respect to time for different values of scale parameter (η).
Figure 2.4: Reliability function of Weibull distribution for different values of η (eta)
20
Threshold parameter γ (time) states that for that period, reliability of item is 100%
since no failure is expected to occur. Threshold parameter depends on the physics of
failure modes in the items. Damage results from stress variables before threshold
time could not be significant when it is compared to strength of the item. Thus,
failure modes of items cannot be triggered before threshold time.
2.2 Graphical Methods
Graphical methods are widely used methods to determine whether time to failure
data follows a specific distribution profile or not. Graphical methods shortly provide
visual ways for analyzing distribution of variables. To determine how well a
theoretical distribution models the empirical data, Quantile-Quantile (Q-Q) plot and
Probability-Probability (P-P) plot are generally used graphical methods. One of the
most important advantages of graphical methods is that data can be assessed quickly
without necessity of detailed knowledge of statistical mathematics. [9] In the
following sections, both P-P plot and Q-Q plot are explained in detail.
2.2.1 Probability-Probability Plotting
The probability-probability plot (also known as p-p plot or percent plot) compares
the empirical cumulative distribution function (cdf) of a variable with a specific
theoretical cumulative distribution function (cdf). In the P-P plot, if data points are
close to reference line, it can be easily concluded that related data follows a specified
distribution. This method has some advantages such that estimation of the intercept
and slope of fitted line are estimates of scale and location parameter for given
distribution.
Theoretical cumulative distribution function (F(x)) of the given model is used to
draw the probability-probability (P-P) plot. The values in the sample of data, in
order from smallest to largest, are denoted )()...2(,)1( nxxx . For ni ...2,1 , )()( ixF is
21
plotted against 4.03.0 ni that is widely preferred in engineering approach. In
the literature, 1ni and 2/1i are also taken into account in P-P plotting.
2.2.2 Quantile-Quantile Plotting
Quantile-Quantile Plot (also known as Q-Q plot) is defined as a plot of the
percentiles of any specific distribution against the corresponding percentiles of the
observed data. The Q-Q plot was first introduced by Wilk and Gnanadesikan (1968).
Q-Q plot simply indicates that if observed data and percentiles of any distribution are
identically distributed, after that the plot of data will be a straight line with slope 1.
Quantile-Quantile Plotting have the basic property such that if time to failure data
has linear relation with percentiles of any distribution then the corresponding Q-Q
plot will still be linear with possible change in location and slope [40]. Construction
of quantile-quantile plot bases on cumulative distribution function of specified
probability distributions. Assuming theoretical cumulative distribution function, F(x)
then, for Q-Q plotting;
For ni ...2,1 , )(ix is plotted against )( )(iZE ,
)(
)(
i
i
xZ , where μ and σ are,
respectively, location and scale parameters. This is the expected value of the ith
standardized order statistics for a location scale family. Location scale parameter is a
family of unvariate probability distributions, which are parameterized by location
parameter and scale parameter having non-negative value.
For practical purposes, one can take )4.03.0()( 1
)( niFZE i . For some
literature, a simpler form )1(1 niF is also considered for )( )(iZE
Quantile function and cumulative distribution function are inverse of each other on
condition that they are continuous functions [41].
22
Quantile-quantile plotting provides the information related to behavior of observed
data according to compared probability distribution. Skewness and nonlinear
tendencies of the observed data can also be figured out when it is compared to
selected probability model and other possible distribution models can be preferred.
Linear tendency in plot shows that observed data follows a theoretical distribution
profile. However, any deviation from linear tendency like right skewed profile or left
skewed profiles compared to theoretical distributions shall be reassessed to
determine the best distribution model.
Detailed explanations for quantile functions of Weibull distributions that were
specifically used during the analysis are given in following sections.
2.2.2.1 Quantile Function of Weibull Distribution
Cumulative distribution function of two parameter Weibull distribution is given by
equation (2.12). Quantile function, which is the inverse of cumulative distribution
function, is determined as follows;
1
1 )1ln()(
p
pF (2.14)
Figure B. 6 indicates the Q-Q plotting performed for engine temperature sensor in
Propulsion System and it can be concluded from the figure that linear tendency in
simulated data exists according to quantile function of Weibull distribution. Quantile
function of Weibull distribution is used to determine behavior of observed data set
follows a theoretical Weibull distribution whether or not. Any significant separations
from the line or nonlinear tendencies are indications that Weibull distribution
assumptions are not considered to be feasible.
23
2.3 Parameter Estimation
After the time to failure data for items is obtained, properties of data distribution
including mean, standard deviation, etc., can be found with the application of some
methods. In the first instance, graphical methods namely; Probability-Probability
plotting and Quantile-Quantile plotting are used to visualize that how time to failure
data fits to some statistical distribution. These methods are useful ways of choosing
among the types of distribution. After determination of which one of probability
distribution is a good representation of time to failure data, task of estimation of the
parameters for the probability distribution follows. There exist analytical techniques
being taken into consideration to decide parameters of probability distributions i.e
Weibull distribution specifically while performing this analysis. Scale (η) and shape
(β) parameters of Weibull distributions are estimated based on widely used analytical
techniques; maximum likelihood and least square method. In addition to two
parameter Weibull distribution, third parameter, which is threshold parameter, is also
estimated. When variable is time in reliability calculations, assumption for two
parameter Weibull which is based on time of failure starting after time zero, may not
be considered to be realistic evermore. Threshold parameter gives some information
about the variables’ minimum value [50].
2.3.1 Maximum Likelihood Method (MLE)
The mathematical expression known as likelihood function for the sample data is the
beginning of the maximum likelihood estimation. The likelihood of a set of data is
the probability of obtaining that particular set of data given the chosen probability
model. This expression contains the unknown parameters of chosen probability
model. Those values of parameter maximizing the sample likelihood are known as
the maximum likelihood estimates.
All the limitations of probability plots are addressed by Maximum likelihood
estimation and MLE provides more precise parametric fits than graphical
estimations.
24
),(
1
i
n
i
i xxfL
(2.15a)
0log
d
Ld (2.15b)
Likelihood function for two-parameter Weibull distribution; and its β derivative and
η derivative that maximizes the function, are given as follows [42];
n
i
x
in
i
ex
xxL
1
1
1 ),;,...,(
(2.16a)
0ln1
lnln
11
n
i
ii
n
i
i xxxnL
(2.16b)
01ln
12
n
i
ixnL
(2.16c)
Firstly, scale and shape parameter are estimated with respect to equations above. To
find the estimator for the threshold parameter in the 3-parameter Weibull
distribution, taking the derivative with respect to γ, it is given by [51];
1
1
1
1
1ln
n
i
in
i
i xxL (2.16d)
2.3.2 Least Square Estimation (LSE)
Least square method is generally applied in engineering and widely used while
determining the unknown parameters of Weibull distribution. It assumed within the
contents of LSE that there exists linear relation between the two variables i.e scale
and shape parameter of Weibull distribution exist [43].
Three-parameter Weibull distribution density function is [50];
25
0,0,0,)()( 1
tet
xf
t
(2.17)
Then, Cumulative Weibull distributions function;
t
exF 1)( (2.18)
Where β (shape parameter), η (scale parameter) and γ (location or threshold
parameter). Two parameter Weibull distributions where location parameter is taken
as 0, for which derived equations are given below;
t
exF )(1 (2.19a)
t
exF )(1
1 (2.19b)
t
xF )(1
1ln (2.19c)
tnxF
lnln)(1
1lnln
(2.19d)
Since equation (2.19d) indicates that there exists linear relationship for both sides,
and then equation can be written as;
n
i
n
int
1
4.0
3.01
1lnln
1 (2.20a)
n
i
itn
y
1
ln1
(2.20b)
26
2
11
2
1 1
2
11
2
1
)ln()(ln
ln
4.0
3.01
1lnln
)ln()(ln
)
4.0
3.01
1ln)(ln(ln
n
i i
n
i i
n
i
n
i i
n
i i
n
i i
n
i i
ttn
t
n
i
ttn
n
itn
(2.20c)
ˆ
ty
e (2.20d)
From the equations above, scale and shape parameters can be calculated where n is
the sample size and median rank is calculated 4.03.0 ni with i is the data rank.
With the help of LSE, threshold parameter of three-parameter Weibull distribution is
found with minimizing the equation below [51],
2
0 4.0
3.0)(exp1
n
itn
i
(2.21)
2.4 Reliability Modeling
Main object of the reliability modeling is to provide a mathematical picture, which is
a representation of relationships between items, equipment comprising the system.
While performing the reliability modeling; system, system elements and
environmental conditions in which systems are expected to operate, should be
defined in detail.
27
System is defined as a combination of items that are interfaced and interconnected
with each other to perform a specific operational function or functions [17].
Definition of a system is important to be focused on since it includes operational
requirements and constraints, configuration of a system and relationships of items to
perform intended functions, operating (environmental) conditions and failure criteria.
Both operational requirements and intended functions give reliability engineer
information about when items of system are operational mode, when not, in any
phase of the mission profile. In reliability model, failures of items and subsystems
and intended function identified by user determine how modeling needs to be
performed. System continues its operation until time where the items and subsystems
under the system fail. Therefore, complexity of system meaning the number of items
in the system, interrelationships of items and reliability of individual items,
determines the reliability of the system. In briefly, key information during the
reliability modeling is; Detail system definitions including operational requirements
i.e. intended functions, configuration of system and any identified constraints.
Systems are modeled via using a tool called Reliability Block Diagram (RBD). “A
Reliability Block Diagram is a method of representing, in a single and visual way,
the reliability relationships between the system and items in the system” [17]. RBD
is also considered as a method that shows how components and sub-system failures
combine to cause system failure [23]. RBDs are not only used to predict reliability of
the system, but also identify the critical items in the system from reliability point of
view. For one system, there may be more than one RBD generated owing to different
functions performed by system or different operating states that system experiences.
One element of each function in the item is represented by block in RBD and series,
active parallel, standby parallel or a combination of all these configurations
constitutes the RBD.
28
Constructions of RBD are initiated at system level and continue down to component
level where failure rates or reliabilities of components can be obtained. Figure 2.5
below indicates the process [24].
Figure 2.5: Development of Reliability Block Diagrams within a System
Some assumptions are made to calculate the reliability of the RBDs. These
assumptions are [9], [18]:
- Connection lines in RBD do not have any effect on reliability calculations.
They only represent the linkage between the blocks.
- Each block represents single element or function of the item with its own
related reliability data.
29
- All inputs for the item are given within specification limits.
- Each block is considered as independent from all other blocks, meaning that
reliability of one block has no effect on the reliability of other blocks.
- Each block is considered as independent from all other blocks, meaning that
reliability of one block has no effect on the reliability of other blocks.
- Failure of any block in the reliability block diagram will also result failure of
the entire item, if the system is configured in series configuration
As it was described above, different configurations such as series, active parallel,
standby parallel or a combination of these configurations are used to construct RBDs.
2.4.1 Series Configuration
Series configuration is the most commonly used and simplest configuration in RBDs.
Series configuration means that any one of failure in the block results in a system
failure. In other words, successful operation of a system depends on success of all
items under system. The reliability of a system with items of system in series cannot
be greater than the reliability of the least reliable component/item [27]. Reliability
model for series configuration is given in Figure 2.6 below.
Figure 2.6: Series Configuration
If it is assumed that items under system are mutually independent. When calculating
reliability for mutually independent events, probabilities of events are multiplied.
The reliability of the system is given as follows,
Nsystem RRRRR .....321 (2.22)
30
2.4.2 Parallel (Active Redundancy) Configuration
In parallel and active redundant modeling, all items under the system are in
operational mode individually and independently. The only way to failure of the
system is that failure of all items in model. Parallel redundancy design technique
improve the system reliability since as it was described in Section 1.1, it results in a
reduction in a logistic (basic) reliability. To determine the reliability of a system, the
individual unreliability (1-R) of the items in the system in parallel are multiplied
together and the unreliability is taken again (1-(1-R)), resulting in the predicted
reliability for the system [28]. Reliability model for parallel (active redundancy)
configuration is given in Figure 2.7below.
C1
C2
.
.
.
Cn
Figure 2.7: Parallel Active Redundancy Configuration
Reliability equation for parallel configuration is given as;
)1(....)1()1(1 21 Nsystem RRRR (2.23)
where, (1-R) is considered as a failure probability or unreliability of item.
31
2.4.3 Parallel (Standby or Passive Redundancy) Configuration
Active parallel systems are thought to be inefficient in way that all parallel elements
are operational and they are subjected to failure. In parallel (standby or passive
redundancy) configuration, system consists of one operational item performing
system function and other standby or passive items. When operation item fails,
decision switch controls the system health status and activates standby or passive
item immediately. Decision switch is a switching mechanism; it is assumed that it is
100% reliable i.e. failure rate of switching mechanism is considered to be zero [25].
System which has parallel standby configuration fails when both operational item
and standby items in the system fail. Passive item and standby item has different
characteristics in way that passive item is switched off totally where standby item is
a partially activated.
Reliability model for parallel (active redundancy) configuration is shown in the
Figure 2.8 below.
C1
C2
.
.
.
Cn
Figure 2.8: Parallel Standby Redundancy Configuration
Reliability equation for parallel standby redundancy configuration is given as [26];
32
in
i
tsystem
i
teR
1
0!
(2.24)
where, λ is the items’ failure rate and equation gives the reliability of the system at
time is equal to t.
2.4.4 k out of n Redundancy Configuration
A k-out-n redundant configuration of item functions well when at least k items are
functional. In other words, n number of operational items is connected in parallel and
at least k number of items must continue to operate for system to perform the
intended functions. One of the well-known examples for this type of configuration
might be an aircraft with four engines. It is known that out of which three engines
should continue functioning for aircraft to fly successfully [13].
Reliability equation for “k out of n redundancy configuration” with the assumption,
that items are identical and failure of items are mutually independent, is given as
[13];
inin
ki
system RRi
nR
)1( (2.25)
33
CHAPTER 3
OVERVIEW OF METU TACTICAL UAV AND ITS SYSTEM RELIABILITY
In this chapter, concept of METU Tactical UAV, its mission profile and systems are
presented. In addition, component and system reliability of UAV is calculated based
on assumption that failure rate is constant over time.
3.1 METU Tactical UAV
In Figure 3.1, Middle East Technical University (METU) Tactical UAV is shown.
This UAV has been designed to perform reconnaissance and observation operations.
METU Tactical UAV is developed as non-lethal. It has been designed to perform
reconnaissance operations for a certain period in a certain range of diameter to get
information. It consists Gimbaled Day/Night IR Camera System and Hyperspectral
Camera System. It has been designed and first prototype was constructed by
Aerospace Engineering Department of METU with the financial support of State
Planning Organization in 2005.
Figure 3.1: METU Tactical UAV
34
Main technical specification of METU Tactical UAV is given in Table 3.1 [29].
Table 3.1: Main Technical Specification of the UAV
Maximum take-off weight 105 kg
Maximum payload weight 20 kg
Wing span 4.3 m
Aspect ratio of the wing 8.4
Taper ratio of the wing 0.45
Aspect ratio of the horizontal tail 4
Aspect ratio of the vertical tail 1.2
Overall length 3 m
Cruise altitude 3000 m
Maximum velocity at sea level 80 m/s
Engine 21 HP two cylinder gasoline engine
Maximum endurance 3- 4 hours
METU Tactical UAV is a pusher type aircraft with Twin wing-tail boom
configuration. As it is seen in Table 3.1 Main Technical Specification of the UAV,
Tactical has capability of flying with the maximum endurance of 3-4 hours and its
maximum take-off weight is 105 kg and maximum payload is 20 kg.
Typical Mission Profile of METU Tactical UAV is given and explained in Section
3.2 and systems constituting the Tactical UAV are described in Section 3.3 in detail.
3.2 Mission Profile of METU Tactical UAV
Figure 3.2 below indicates the mission profile that has been set for METU Tactical
UAV to fly.
35
Figure 3.2: Mission Profile
Table 3.2 below gives information about the flight phases of the Tactical UAV and
approximated duration related to each flight phase. Definitions of flight phases have
also been added in the Table. As it was described in the Section 3.1, Tactical UAV
flies with maximum endurance up to 4 hours; thus it will spend almost 3.4 hours of
total flight time for reconnaissance missions. At worst case, Tactical UAV is
expected to perform reconnaissance and observation missions at altitude of 3000 m,
which is the highest cruise altitude of it.
36
Table 3.2: Flight Phases of METU Tactical UAV Flight and Their Durations
Flight Phases Definitions Duration (hr)
Start/Warm-up UAV on the ground with engine running
(Engine starting to Idle condition). 0.0500
Taxi
UAV is moving under the power of its
engine on runways, with guidance
provided by the ground personal.
0.1000
Take-off Starts after taxi is complete. Generally,
Engine of UAV runs at full power. 0.0500
Climb Starts after takeoff and ends when
intended cruising altitude is reached. 0.1000
Cruise + Loiter
Starts when UAV levels at intended
cruising altitude and ends when UAV
begins descent with intention to land.
Loiter is assumed to be performed in mid-
flight.
3.4000
Descend Starts when UAV begins descent with
intention to land. 0.1000
Approach Starts at the end of the descent phase and
ends when landing begins. 0.0500
Landing
Starts at the end of descent, and continues
while the UAV contacts the ground, and
until the UAV has been brought to a low
speed under control.
0.0500
Taxi and OFF
UAV is moving under the power of its
engine on runways, with guidance
provided by the ground personal. Finally,
UAV becomes stationary and engine is
shutdown.
0.1000
Total Flight Time 4.000
3.3 Systems of METU Tactical UAV
During the design phase, design team has decided system, which is used in this
UAV. They design some of items in systems some of them are selected from items,
which have been already used by similar products. While systems in UAV being
determined, design requirements, which have been derived according to the
operational requirements and current technology level, have been taken into
consideration.
37
There have been mainly two types of systems in accordance with their functionalities
i.e. one type of system, which may be called “UAV system”, is required for UAV to
fly safely and another type system which may be called “Mission System” is
essential for UAV to perform its intended mission successfully. Systems of Tactical
UAV are shown in the Figure 3.3.
Figure 3.3: Systems of Tactical UAV
3.3.1 Landing Gears
Landing Gears are composed of two main landing gears and one nose landing gear.
The main landing gears are selected in way that they have capable of stopping the
Tactical UAV and standing the loads generated during braking action on the ground.
To obtain effective and efficient UAV braking, main landing gears have been
38
supported with the hydraulic brake system. Each main landing gear has individual
brake discs powered by a central hydraulic pump. Braking of UAV on the ground is
initiated by a servo actuator by means of controlling the hydraulic pump. Figure 3.4
indicates the main landing gear with brake callipers and brake disks [30].
Figure 3.4: Main Landing Gears with Brake Disks and Callipers
Nose landing gear has different functionality when it is compared to the main landing
gear. Main objective of the nose landing gear is to steer the UAV on the ground and
in addition to steering function, it is also expected to level the UAV. Wheels of both
main landing gears and nose landing gear are selected to be identical in order to
reduce variety with respect to logistic needs although nose landing gear wheel are
subjected to lower loads comparing to main landing gear wheels. On the contrary the
main landing gear, nose landing gear does not consist of a brake system i.e. no
caliper and no brake disc in it. Figure 3.5below indicates the nose landing gear [30]
39
Figure 3.5: Nose Landing Gear
Briefly, Landing gears are used to steer, level and stop the Tactical UAV on ground
and absorb the ground loads created during the landing. Items and components
comprising the landing gears are given in Table 3.3 below.
Table 3.3: Item and Components of Landing Gears
Items/Components in Landing Gear System Quantity
Main Wheel 2
Servo Actuator 2
Hydraulic Pump 1
Calliper 2
Brake Disk 2
Nose Landing Gear 1
3.3.2 Electrical System
Main power supply for the Tactical UAV is a Lithium Polymer battery, which
comprises certain combination of cells connected in parallel and series [29].
Required total power of aircraft is 300W for which this type of battery has been
chosen to be used. 200W of the total power is required for avionics system whereas
40
payloads, which are cameras, require 100W electrical power. Battery is capable of
providing both 5V and 12V voltage output with its embedded DC-DC converters.
Since some equipment requires 5V voltage output while 12 V for others. Lithium
Polymer battery with its embedded 5V and 12V DC-DC converters are shown in
Figure 3.6.
Figure 3.6: Lithium Polymer Battery with its embedded 5V and 12V DC-DC Converters
Electrical power generated by the battery is distributed to equipment and item by
means of junction box. All cables coming from wings, tail, forward fuselage and rear
fuselage are connected to junction box by the military type connectors. Military type
connectors provide a chance for user to disassemble the UAV easily during
transportation since connections are not permanent. Junction box also consists of
receiver port for external Futaba RC Receiver, which enables ground personal to
control UAV manually, and remotely Figure 3.7 below indicates junction box with
receiver port and military type connectors [29].
41
Figure 3.7: Junction Box
Items and components comprising electrical system are given in Table 3.4 below.
Table 3.4: Items and Components of Electrical System
Items/Components in Electrical System Quantity
Lithium Polymer Battery 2
5V DC-DC Converter 1
12V DC-DC Converter 1
Junction Box 1
Connector 6
Cables N/A
It is well known that electrical systems somehow are associated to electrical cables.
However, with respect to reliability point view, cables can be neglected due to its
very high reliability characteristics comparing the other electrical equipment. This is
why electrical cables are not considered as a part of the table. The cables used have
fireproof Teflon covering and they are put in braid tubes for EMI/RFI protection. In
Figure 3.8, METU Tactical UAV’s wiring/cabling diagrams are given.
42
Figure 3.8: Cabling Diagram of METU Tactical UAV
Three colors of cable have been used in cable layout of Tactical UAV; red for power,
black for ground and white for signal
3.3.3 Ice Protection System
Ice protection systems are designed to keep atmospheric ice from accumulating on
aircraft flight surfaces while aircraft in flight. Shortly, they protect aircraft from ice
accretion. “The effects of ice accretion on an aircraft can cause the shape of airfoils
and flight control surfaces to change, which can ultimately lead to a complete loss of
control and/or insufficient lift to keep the aircraft airborne” [31]. Briefly, when ice
accumulates the over the wing and control surfaces, airflow over wings is changed
and thus icing affects the controllability of the UAV adversely. Flight control
surfaces and shape of airfoils may change in a case of extreme icing conditions.
Therefore, change in airfoil shape results in a significant reduction in controllability
of UAV and even in loss.
43
There are two resistance type heaters have been located to both right and left wing.
Table 3.5 below indicates the components in the ice protection system.
Table 3.5: Components of Ice Protection System
Components in Ice Protection System Quantity
Heater 2
3.3.4 Propulsion System
Tactical UAV has a pusher configuration that is widely used and popular for UAVs.
Pusher configuration has also been used for similar UAVs such as Seeker II designed
by DENEL, Shadow 200T of AAI Corporation in USA and Aerosky of Aeronautics
Defense Systems in Israel. Since UAV will perform reconnaissance operations, nose
section of the UAV has been left empty to be used for camera systems. Camera
system has been located nose section of the UAV to obtain better angle of sight.
L275 model Limbach engine had been selected to meet the power requirement with a
safety factor of 10 % [30]. Limbach L275 model shown in Figure 3.9 has a
horizontally opposed air-cooled, two cylinder, two-cycle engine, with solid-state
magneto ignition, mixture lubrication [33]. It provides between 20-25 HP at 7000
rpm at sea level and has approximately 8 kg dry weight with magneto ignition.
Figure 3.9: Limbach 275 E Engine
44
Items and components of propulsion system is seen in Table 3.6 below.
Table 3.6: Items and Components of Propulsion System
Items/Components in Propulsion System Quantity
Limbach L275 piston-prop engine 1
Sensor (Engine RPM, Engine Temperature) 2
Servo actuator (Engine Throttle) 1
To control and observe the healthy status of the engine, engine RPM sensor and
engine temperature sensor have been integrated to the propulsion system. One servo-
actuator has also been added to configuration and located at the back of the fuselage
for controlling the throttle of the engine.
3.3.5 Fuel System
The Tactical UAV has been designed to have high aspect ratio wings within a
significant number of rib and beam structure. Thickness of the wings has also been
taken into consideration that it is almost small to put the fuel tanks inside.
Consequently, fuel tanks have been mounted in fuselage of the UAV [30].
Figure 3.10 below indicates where fuel tank is placed in fuselage of the UAV.
Location of fuel tank has been designed to be very close UAV’s center of gravity,
thus fuel consumption will not result in a significant change in the center of gravity
[30].
45
Figure 3.10: Location of the Fuel Tank
Fuel system mainly consists of fuel tank and fuel line up to engine which are given in
Table 3.7 below.
Table 3.7: Items and Components of Fuel System
Items\Components in Fuel System Quantity
Fuel Tank 1
Fuel line 1
3.3.6 Lighting System
Aircraft must have appropriate navigation and fixed lights according to the Federal
Aviation Administration (FAA). “Section 91.209- Aircraft lights” [34] of FAA
describes which lighting system requirements must be introduced to aircraft
configuration for airworthiness point of view.
The navigation lights provides the indication of the aircraft’s position, heading and
status for other aircraft or ground personnel. In accordance with the regulations, three
flashers, which are located in left wing tip, right wing tip and tail rudder, have been
46
mounted on UAV. In addition to navigation lights, UAV also consists of headlight
for purposes of anti-collision system.
Briefly, components of the lighting system is seen in Table 3.8 below.
Table 3.8: Items and Components of Lighting System
Components in Lighting System Quantity
Left Wing Tip Flasher 1
Right Wing Tip Flasher 1
Headlight 1
Tail Rudder Flasher 1
3.3.7 Communication System
Communication system has been adopted in this Tactical UAV in order to have two
functional purposes i.e.; first one is to monitor the flight of UAV and second one is
to provide manual controllability of UAV. Items and Components of the
Communication System are given in Table 3.9.
Table 3.9: Items and Components of Communication System
Items/Components in Communication System Quantity
Video Transmitting System 1
Receiver of remote controller 1
Avalon digital video transmitter system, which has a capable of real time image
transmitting in 2.4 GHz, has been chosen to be used for flight monitoring. The
transmitter can accept two video inputs that are beneficial for selecting between
standard & IR cameras [35]. Figure 3.11 indicates the Avalon digital video
transmitter.
47
Figure 3.11: Avalon Digital Video Transmitter
Another link between the UAV and ground personal is receiver of remote controller
that is embedded to junction box. Receiver of remote controller is used for
controlling the UAV manually by means of proving the ground personal’s control
input to servo actuators.
3.3.8 Automatic Flight Control System
METU Tactical UAV is either controlled autonomously by automatic flight control
system of the UAV, or under the remote control of a ground personal on the ground.
Piccolo II of Cloud Cap Technology shown in Figure 3.12 below is used as an
autopilot system and it has been referred due to having an onboard inertial, datalink
radio, air data and GPS sensors and EMI shielded enclosure [32]. It serves and
generates control inputs to seven servo actuators.
Figure 3.12: Piccolo II Autopilot
48
Main purpose of servo actuators is to provide actuation of control surfaces of the
Tactical UAV. Five Pegasus PA-R-250-8 type electro mechanical servo-actuators in
Figure 3.12, which operate on 12V electrical power, provide controls of ailerons and
flaps and elevator. Five Pegasus PA-R-250-8 type electro mechanical servo-actuators
have ability to provide powerful torque and high speed positioning [36]. Four of
them have been mounted on each wing of the UAV for ailerons and flaps as it is
shown in Figure 3.13 below on the other hand one of them has been located on
horizontal tail for elevator.
Figure 3.13: Servo Actuator mounted on Wing
There are also two small servo actuators for control of rudders in vertical tail section.
They are Savöx SC-1256TG type servo actuators [37] operating at 5V electrical
power and each one has been mounted on each vertical tail of the UAV. Figure 3.14
indicates the position of rudder’s servo actuators.
Figure 3.14: Servo Actuator on Vertical Tail
49
Items and components, which comprise the automatic flight control system of the
Tactical UAV, are given in Table 3.10.
Table 3.10: Items and Components of Automatic Flight Control System
Item/Components in Automatic Flight Control System Quantity
Automatic Flight Control 1
Servo actuators
(Pegasus PA-R-250-8 type and operating at 12V) 5
Servo actuators
(Savox SC1256TG type and operating at 5V) 2
3.3.9 Mission System
Similar UAVs whose objectives are reconnaissance operations have been equipped
with developed camera systems for both daylight and night operations. Because of
the reason, METU Tactical UAV has been designed to perform reconnaissance
missions; Gimbaled Day/Night IR Camera System has been adopted. Gimbaled
Day/Night Infrared Camera System is considered as a main payload of the Tactical
UAV and it has been located under forward fuselage. Configuration of mission
systems is seen in Table 3.11 below.
Table 3.11: Items in Mission System
Items in Mission System Quantity
Gimbaled Day/Night IR Camera System 1
Camera at Horizontal tail 1
One camera system has also been placed on the horizontal tail for monitoring the
attitude of the airplane during flight [29].
50
3.4 Component and System Reliability of UAV
Component and system reliability of UAV is calculated based on assumption that
failure rate is constant over time. That is the common approach used in reliability
engineering in industries. In this section, total reliability characteristics of METU
tactical UAV will be calculated according to similar approach in industry. MTBF
values of components are obtained from Non-Electronic Reliability Part Data
(NPRD-95), its own specification in which MTBF values are predicted for a specific
environment or similar UAV’s data. If any one of component has different
environmental usage, environmental conversion factors needs to be implemented.
According to MIL-HDBK-338B, Figure 3.15 below defines the environmental
conversion factor. METU Tactical UAV is considered to be in the category of
Airborne Uninhabited Cargo (AUC).
To Environment
From
Environment
GB GF GM NS NU AIC AIF AUC AUF ARW SF
GB X 0.5 0.2 0.3 0.1 0.3 0.2 0.1 0.1 0.1 1.2
GF 1.9 X 0.4 0.6 0.3 0.6 0.4 0.2 0.1 0.2 2.2
GM 4.6 2.5 X 1.4 0.7 1.4 0.9 0.6 0.3 0.5 5.4
NS 3.3 1.8 0.7 X 0.5 1.0 0.7 0.4 0.2 0.3 3.8
NU 7.2 3.9 1.6 2.2 X 2.2 1.4 0.9 0.5 0.7 8.3
AIC 3.3 1.8 0.7 1.0 0.5 X 0.7 0.4 0.2 0.3 3.9
AIF 5.0 2.7 1.1 1.5 0.7 1.5 X 0.6 0.4 0.5 5.8
AUC 8.2 4.4 1.8 2.5 1.2 2.5 1.6 X 0.6 0.8 9.5
AUF 14.1 7.6 3.1 4.4 2.0 4.2 2.8 1.7 X 1.4 16.4
ARW 10.2 5.5 2.2 3.2 1.4 3.1 2.1 1.3 0.7 X 11.9
SF 0.9 0.5 0.2 0.3 0.1 0.3 0.2 0.1 0.1 0.1 X
GB – Ground Benign; GF – Ground Fixed; GM – Ground Mobile; NS – Naval Sheltered; NU
– Naval Unsheltered; AIC – Airborne Inhabited Cargo; AIF – Airborne Inhabited Fighter;
AUC – Airborne Uninhabited Cargo; AUF – Airborne Uninhabited Fighter; ARW – Airborne
Rotary Winged; SF – Space Flight Figure 3.15: Environmental Conversion Factors
51
Table 3.12 - Table 3.20 present the METU tactical UAV’s systems MTBF and
reliability parameters with information in which source of MTBF values exist.
Table 3.12: Landing Gear System Reliability Data
Equipment Quantity MTBF (hours) MTBF (AUC)
(hours)
Main Wheel 2 309000 (NPRD-95-GM) 185400
Servo Actuator 2 7660 (NPRD-95-AUC) 7660
Hydraulic Pump 1 16818 (NPRD-95-AUC) 16818
Calliper 2 496170 (NPRD-95-GM) 297702
Brake Disk 2 196000 (NPRD-95-AUC) 196000
Nose Landing Gear 1 309000 (NPRD-95-GM) 185400
Table 3.13: Electrical System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Lithium Polymer Battery 2 2860 (NPRD-95-AUC) 2860
5V DC-DC Converter 1 5200 (NPRD-95-AUC) 5200
12V DC-DC Converter 1 5200 (NPRD-95-AUC) 5200
Junction Box 1 1572 (NPRD-95-AUC) 1572
Connector 6 253000 (NPRD-95-AUC) 253000
Table 3.14: Ice Protection System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Heater 2 52000 (NPRD-95-AUC) 52000
52
Table 3.15: Propulsion System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Limbach L275 piston-
prop engine 1 4250 (NPRD-95-AUC) 4250
Sensor (Engine RPM) 1 212760 (NPRD-95-GM) 127656
Sensor
(Engine Temperature) 1 99930 (NPRD-95-AUF) 169881
Servo actuator
(Engine Throttle) 1 7660 (NPRD-95-AUC) 7660
Table 3.16: Fuel System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Fuel Tank 1 145000 (NPRD-95-AUC) 145000
Fuel Line 1 330000 (NPRD-95-GM) 198000
Table 3.17: Lighting System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Left Wing Tip Flasher 1 28100 (NPRD-95-AUC) 28100
Right Wing Tip Flasher 1 28100 (NPRD-95-AUC) 28100
Headlight 1 13770 (NPRD-95-AUC) 13770
Tail Rudder Flasher 1 28100 (NPRD-95-AUC) 28100
Table 3.18: Communication System Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Video Transmitting System 1 2310 (NPRD-95-NS) 924
Receiver of remote controller
(including the receiver port) 1 4000 (NPRD-95-GB) 400
53
Table 3.19: AFCS Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Automatic Flight Control 1 8000 (NPRD-95-AUC) 8000
Servo actuators
(Pegasus PA-R-250-8 type) 5 24820 (NPRD-95-AUC) 24820
Servo actuators
(Savox SC1256TG type) 2 127730 (NPRD-95-AUC) 127730
Table 3.20: Mission Systems Reliability Data
Equipment Quantity MTBF MTBF (AUC)
(hours)
Gimbaled Day/Night IR
Camera System 1 950 (NPRD-95-AUC) 950
Camera System 1 1985 (NPRD-95-AUC) 1985
Reliability assessment for METU tactical UAV and its subsystems is performed by
using series reliability block diagrams. Series block diagram indicates that any
failure in the system will result in a mission cancellation. In other words, mission
success depends on the success of each system individually. Figure 3.16 below is
indication of system level reliability block diagram.
Figure 3.16: System Level RBD of METU tactical UAV
Equation (3.1) is the representation of exponential distribution, which is used to
estimate the reliability for items being assumed to have constant failure rate.
54
Reliability calculation was performed for a 4-hour mission for which detail mission
phases and related durations are given in Table 3.2. As it is stated in Section 1.2.1, λ
is the failure rate of the item and is equal to inverse of MTBF (1/MTBF). In order to
determine the each system reliability following equation is used.
n
i
iSYSTEM RR
1
(3.1)
Reliability block diagrams and associated reliabilities for each of system are
presented below:
3.4.1 Reliability of Landing Gear System
Figure 3.17: RBD of Landing Gear System
By using equations (2.22) and (2.25), reliability of landing gear system is calculated as
follows:
NoseLGMainWheelBrakeDiscCallipertorServoActuaumpHydraulicPSystemGearLanding RRRRRRR (3.2)
99998,099998,099998,099999,099948,099976,0 2222 SystemGearLandingR (3.3)
0.99858636SystemGearLandingR (3.4)
55
3.4.2 Reliability of Electrical System
Figure 3.18: RBD of Electrical System
By using equations (2.22) and (2.25), reliability of electrical system is calculated as follows:
40.99304921SystemElectricalR (3.5)
3.4.3 Reliability of Ice Protection System
Figure 3.19: RBD of Ice Protection System
By using equation (2.22), reliability of ice protection system is calculated as follows:
60.99984616Pr SystemotectionIceR (3.6)
56
3.4.4 Reliability of Propulsion System
Figure 3.20: RBD of Propulsion System
By using equation (2.22), reliability of propulsion system is calculated as follows:
0.99848290SystemPopulsionR (3.7)
3.4.5 Reliability of Fuel System
Figure 3.21: RBD of Fuel System is
By using equation (2.22), reliability of fuel system is calculated as follows:
30.99995221SystemFuelR (3.8)
3.4.6 Reliability of Lighting System
Figure 3.22: RBD of Lighting System
By using equation (2.22), reliability of lighting system is calculated as follows:
50.99928272SystemLightingR (3.9)
3.4.7 Reliability of Communication System
Figure 3.23: RBD Communication System
57
By using equation (2.22), reliability of communication system is calculated as follows:
70.98577316SystemionCommunicatR (3.10)
3.4.8 Reliability of AFCS System
Figure 3.24: RBD of AFCS System
By using equations (2.22) and (2.25), reliability of AFCS is calculated as follows:
20.99863250SystemAFCSR (3.11)
3.4.9 Reliability of Mission System
Figure 3.25: RBD of Mission System
58
By using equation (2.22), reliability of mission system is calculated as follows:
0.99379369SystemMissionR (3.12)
System reliability calculations are based on the probability that METU tactical UAV
will successfully complete reconnaissance and observation operations in a four-hour
flight. Summary of the probabilities of systems as follows;
Table 3.21: Reliabilities of systems
System Reliability
Landing Gear System 0.99858636
Electrical System 0.99304921
Ice Protection System 0.99984616
Propulsion System 0.99848290
Fuel System 0.99995221
Lighting System 0.99928272
Communication System 0.98577316
Automatic Flight Control
System 0.99863250
Mission Systems 0.99379369
Aircraft level reliability characteristic is estimated by using equation (2.22) with
assumption that all system under platform need to be operational during entire flight,
as follows:
0.9678alUAVMETUTacticR
Result indicates that when 10000 UAVs start operations, of 9678 will have
probability to successfully complete the mission. In other words, 322 UAVs will fail
to perform related mission. Unreliability of aircraft is 0.0322 according to
exponential distribution assumption.
59
CHAPTER 4
SIMULATION STUDY AND RELIABILITY COMPARISONS
In this chapter, simulation study has been performed in accordance with time to
failure data created for both Weibull distribution and exponential distribution and
two different approaches have been compared for predicted reliability characteristics
of METU tactical UAV.
4.1 Reliability Estimation
In order to determine reliability characteristics of METU Tactical UAV, time to
failure data for each component or items composing the platform needs to be
collected. For the reliability analysis, the best way would be to use time to failure
data obtained and collected from operational UAVs, especially whose operational
usage similar to METU tactical UAV. Using a real time data would provide a good
benchmark for us to show our systems’ reliability. However, it is important to note
that time to failure data is only logged and reviewed by UAV’s owners and not
presented for public usage. Consequently, simulation study is performed taking mean
time between failure (MTBF) data, which is commonly provided by the
manufacturers, into consideration.
For aim of simulation study, time to failure data for each item of system is created
for both Weibull distribution and exponential distribution. After that, well
representing failure distribution model is determined based on a three-step process
60
including in order of identification of possible distribution models, estimation of
parameters for identified distribution and application of goodness-of-fit tests.
In order to identify candidate distribution, graphical methods, which are explained in
Section 2.2 in detail, is basically used. In APPENDIX B, Q-Q plots are constructed
as a sample for data set of Sensor (Engine Temperature) in Propulsion System to
show that exponential assumption fails when original data comes from Weibull
Distribution and additionally Weibull assumption fails when original data comes
from exponential distribution. Assessments associated to Q-Q plots are mentioned in
detail in APPENDIX B.
The three-parameter Weibull distribution is selected based on common usage in
engineering. The most crucial advantage of this distribution is to model bathtub
curve i.e. decreasing, constant, and increasing failure rates.
4.2 Estimation of Three-parameter Weibull Distribution Parameters
Both maximum likelihood estimation (MLE) and least square estimation (LSE) are
used mathematically to fit a line to time to failure data in order to estimate the
parameters of three-parameter Weibull distribution whose probability density
function (PDF) is denoted by the formula as follows:
xxxf exp),,;( (4.1)
And formula of cumulative distribution function (CDF)
x
exF 1)( (4.2)
61
Estimated parameters of three parameter Weibull distributions are; shape , scale
(time) and threshold .
A summary of estimated parameters of exponential data for each system is given in
Table 4.1 through Table 4.9 below. Tables include both MLE and LSE based
estimated parameters.
Table 4.1: Estimated Parameters of Exponential Data for Landing Gear System, where
sample size (n=20)
LANDING GEAR
SYSTEM
Maximum Likelihood Least Square
Main wheel 1.3994 203774 10785 1.2972 205031 11215
Servo actuator 1.7232 8496 437.3 1.5927 8552 445.61
Hydraulic pump 1.0342 17077 1285.2 1.0776 16896 1323.7
Calliper 1.3459 324396 12756 1.2024 328753 14611
Brake disk 1.2405 210347 16271 1.1557 211582 15016
Nose landing gear 1.3994 203774 10785 1.2972 205031 11215
62
Table 4.2: Estimated Parameters of Exponential Data for Electrical System, where sample
size (n=20)
ELECTRICAL
SYSTEM
Maximum Likelihood Least Square
Lithium polymer
battery 1.476 3165 163.4 1.3512 3195 165
5V DC-DC
Converter 1.5151 5790.4 373 1.4441 5801.7 380
12V DC-DC
Converter 1.5151 5790.4 373 1.4441 5801.7 380
Junction Box 1.5311 1752.3 96.37 1.4862 1745.6 95.45
Connector 0.9728 249711 32785 0.9718 251305 32212
Table 4.3: Estimated Parameters of Exponential Data for Ice Protection System, where
sample size (n=20)
ICE
PROTECTION
SYSTEM
Maximum Likelihood Least Square
Heater 1.4460 56984 2678 1.1567 59043 2771
63
Table 4.4: Estimated Parameters of Exponential Data for Propulsion System, where sample
size (n=20)
PROPULSION
SYSTEM
Maximum Likelihood Least Square
Limbach L275
piston-prop engine 1.1339 4450 337 1.0670 4468 341
Sensor
(Engine RPM) 0.8605 118117 4763 0.8262 117973 5036
Sensor
(Engine
Temperature)
1.5080 189720 10257 1.5493 188683 12720
Servo actuator
(Engine Throttle) 0.9798 7595 0 0.8601 7796 0
Table 4.5: Estimated Parameters of Exponential Data for Fuel System, where sample size
(n=20)
FUEL SYSTEM
Maximum Likelihood Least Square
Fuel line 0.8358 179601 97589 0.8090 180093 10418
Fuel tank 0.9633 142715 5437 0.8435 146941 5652
64
Table 4.6: Estimated Parameters of Exponential Data for Lighting System, where sample
size (n=20)
LIGHTING
SYSTEM
Maximum Likelihood Least Square
Left Wing Tip
Flasher 1.2631 30147 2036 1.0757 30821 2147
Right Wing Tip
Flasher 1.2631 30147 2036 1.0757 30821 2147
Headlight 1.0958 14266 983.9 1.0512 14263 981.7
Tail Rudder Flasher 1.2631 30147 2036 1.0757 30821 2147
Table 4.7: Estimated Parameters of Exponential Data for Communication System, where
sample size (n=20)
COMMUNICATION
SYSTEM
Maximum Likelihood Least Square
Video transmitting
system 1.2304 1058 71.27 1.1960 1060.6 70.71
Receiver of remote
controller 1.0006 399.6 0 0.9752 399.25 0
65
Table 4.8: Estimated Parameters of Exponential Data for Automatic Flight Control System,
where sample size (n=20)
AFCS
Maximum Likelihood Least Square
Automatic flight
control 1.3585 8676.7 582 1.3538 8675.7 583
Servo actuators
(operating at 12V) 1.0331 25171 1362 1.0216 25110 1376
Servo actuators
(operating at 5V) 0.9747 126312 3654 0.8938 128371 3662
Table 4.9: Estimated Parameters of Exponential Data for Mission System, where sample
size (n=20)
MISSION
SYSTEM
Maximum Likelihood Least Square
Camera 1.4233 2189 158.4 1.3411 2196 162
IR Camera 1.4177 1053 83.2 1.4949 1045 86.5
A summary of estimated parameters of Weibull data for each system is given in
Table 4.10 through Table 4.18 below. Tables include both MLE and LSE based
estimated parameters for Weibull data sets.
66
Table 4.10: Estimated Parameters of Weibull Data for Landing Gear System, where sample
size (n=20)
LANDING GEAR
SYSTEM
Maximum Likelihood Least Square
Main wheel 1.6291 207284 8413 1.4614 210170 6930
Servo actuator 1.8023 8623 672.8 1.5918 8724 497.61
Hydraulic pump 1.2868 14699 765.6 1.5583 19313 768
Calliper 1.825 335361 9677 1.6194 339370 8262
Brake disk 1.6936 219941 13584 1.5276 222190 10128
Nose landing gear 1.6291 207284 8413 1.4695 211630 6585
Table 4.11: Estimated Parameters of Weibull Data for Electrical System, where sample size
(n=20)
ELECTRICAL
SYSTEM
Maximum Likelihood Least Square
Lithium polymer
battery 1.5588 3195 157.4 1.5098 3208.7 158
5V DC-DC
Converter 1.4215 5738.2 362.8 1.3756 5754 347
12V DC-DC
Converter 1.4215 5738.2 362.8 1.3756 5754 347
Junction Box 1.7294 1773.4 61.87 1.7512 1793 63.85
Connector 1.434 280843 21683 1.4851 279350 19521
67
Table 4.12: Estimated Parameters of Weibull Data for Ice Protection System, where sample
size (n=20)
ICE
PROTECTION
SYSTEM
Maximum Likelihood Least Square
Heater 1.1173 43384 1652 1.2028 60757 1912
Table 4.13: Estimated Parameters of Weibull Data for Propulsion System, where sample
size (n=20)
PROPULSION
SYSTEM
Maximum Likelihood Least Square
Limbach L275
piston-prop engine 1.2565 4587.5 216.8 1.242 4598 217.7
Sensor
(Engine RPM) 2.0259 144693 12637 2.0656 144220 3517
Sensor
(Engine
Temperature)
1.8018 190607 9627 1.503 195060 6544
Servo actuator
(Engine Throttle) 1.3903 8473.7 654.3 1.5 8423 567.7
Table 4.14: Estimated Parameters of Weibull Data for Fuel System, where sample size
(n=20)
FUEL SYSTEM
Maximum Likelihood Least Square
Fuel line 1.0539 202038 3795 0.9206 208060 4882
Fuel tank 0.9978 144822 1873 0.8648 150160 2896
68
Table 4.15: Estimated Parameters of Weibull Data for Lighting System, where sample size
(n=20)
LIGHTING
SYSTEM
Maximum Likelihood Least Square
Left Wing Tip
Flasher 1.8267 31728 2308 1.69 31872 1726
Right Wing Tip
Flasher 1.8267 31728 2308 1.69 31872 1726
Headlight 1.293 14976 1365 1.31 14885 1182
Tail Rudder Flasher 1.8267 31728 2308 1.69 31872 1726
Table 4.16: Estimated Parameters of Weibull Data for Communication System, where
sample size (n=20)
COMMUNICATION
SYSTEM
Maximum Likelihood Least Square
Video transmitting
system 1.2425 795.5 69.53 1.8584 1036 58.4
Receiver of remote
controller 1.6298 448.77 23.15 1.5813 449 24.78
Table 4.17: Estimated Parameters of Weibull Data for Automatic Flight Control System,
where sample size (n=20)
AFCS
Maximum Likelihood Least Square
Automatic flight
control 1.4749 8856.5 431 1.3643 8936.3 443
Servo actuators
(operating at 12V) 1.6022 27769 875 1.4828 28369 910
Servo actuators
(operating at 5V) 1.1271 133354 2493 0.9763 138920 2641
69
Table 4.18: Estimated Parameters of Weibull Data for Mission System, where sample size
(n=20)
MISSION
SYSTEM
Maximum Likelihood Least Square
Camera 1.7901 2237.7 145.8 1.6537 2247 118.4
IR Camera 1.4204 1051.7 55.7 1.4467 1050 59.6
Parameters estimated based on maximum likelihood estimation and least square
estimation are taken to be used for following analysis.
Third step is the application of goodness of fit tests. Goodness-of-fit tests are means
of examining how well a sample of data agree with assumed distribution as its
population. There is a wide literature and study especially on exponential and normal
distributions. However, Goodness-of-fit tests for Weibull distribution have been less
studied when it is compared to other distributions. Some GOF approaches have been
suggested by Mann, Scheuer and Fertig (1973) [45] and Tiku and Singh (1981) [46].
According to the assumption that the sample comes from two-parameter Weibull
distribution, Smith and Bain (1976) statistic is on the basis of correlation between
expected value of the order statistics and order statistics of the sample [47]. Smith
and Bain have provided critical values for the samples containing 8, 20, 40, 60, or 80
observations. Tables for the asymptotic critical values of the Anderson-Darling A2
statistic [52] and the Cramer-von Mises W2 statistics for various significance levels
has been produced Stephens (1977) [48].
In order to perform GOF tests for two-parameter Weibull distribution for which
location parameters are assumed to be zero, the Cramer-von Mises (W2) test and
Anderson-Darling (A2) test are used at five different significance levels.
These two tests are based on the empirical distribution function (EDF) which is a
step function and calculated from the sample. EDF is measure of the difference
70
between the EDF and given distribution function and used for testing the fit of the
sample to the distribution.
Size of exponentially created data for each item is 20, i.e. T1, T2,…, T20 and let T(1) <
T(2) < …. < T(20) be the order statistics; and also supposing that F(T) is the
cumulative distribution function of T.
4.2.1 Modified Cramer-von Mises (W2):
Equation of Cramer-von Mises (W2) ;
tdFtFtFnW n
22
(4.3)
where,
n
i
in tftF1
(4.4)
)(tFZ , where iZz (4.5)
Substituting equation (4.5) into equation (4.4), following equation is obtained as
1,...,2,1,1
1
ni
zZ
ZzZn
inZ
n
i
n (4.6)
00 z and 11 nz (4.7)
then,
nn
iz
nz
nzn
dzzn
indzznznW
n
i
i
n
i
ii
n
i
z
zn
i
i
12
1
2
12113
2
11
233
1
2
1
1
0
22 1
(4.8)
71
4.2.2 Modified Anderson Darling (A2):
Equation of Anderson Darling (A2);
tdFtFtF
tFtFnA n
))(1)((
122
(4.9)
* xy , (4.10)
where y* is approximately distributed as two-parameter Weibull distribution for
practical purposes.
n
iini
n
zzin
n
dzzz
znznA
11
1
0
22
1lnln)12(1
)1(
1
(4.11)
Main assumption for analysis to be valid is that distribution is continuous.
We assume here that distributions of the goodness-of-fit test statistics are not
affected that much when the threshold parameter is estimated and plugged in the
formula (4.11). However, one should also study the distributional properties when it
is done so. Results of goodness-of-fit test considering the third parameter are given
in Table 4.22 and Table 4.23.
Table 4.19 gives critical values for five different significance levels for both Cramer-
von Mises (W2) [49] and Anderson-Darling (A2) [52].
72
Table 4.19: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2)
Sample
Size
Test
Statistics
Significance Levels
0.01 0.05 0.10 0.15 0.20
20 A2 0.9529 0.7539 0.6439 0.2423 0.2025
W2 0.2369 0.2116 0.1999 0.1815 0.1659
100 A2 0.9556 0.7642 0.6514 0.2486 0.2078
W2 0.2429 0.2173 0.2048 0.1881 0.1702
In order to perform simulation study, 10000 random samples of size 20 and 100 for
each item are generated and for which the goodness-of-fit test for Weibull
distribution with the help of the tests W2 and A2 have been carried out. Number of
acceptance of hypothesis for each significance level value of both W2 and A2 test
statistics are given in Table 4.20 and Table 4.21 respectively.
Table 4.20: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2) when
n=20 for two-parameter Weibull Distribution
Significance Level Cramer Von Mises Test
W2
Anderson Darling Test
A2
0.01 0.30 0.95
0.05 0.24 0.90
0.10 0.22 0.85
0.15 0.18 0.75
0.20 0.14 0.69
Table 4.21: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2) when
n=100 for two-parameter Weibull Distribution
Significance Level Cramer Von Mises Test
W2
Anderson Darling Test
A2
0.01 0.10 0.91
0.05 0.08 0.85
0.10 0.07 0.78
0.15 0.05 0.72
0.20 0.03 0.66
73
As a result of analysis, for n=20, both Cramer-von Mises test statistic and Anderson
Darling test statistics are considered to agree with two parameter-Weibull
distribution for all significance levels. Thus, for exponentially created time to failure
data, two-parameter Weibull distribution is thought to be well-fitted distribution
when percent of passed data sets for each significance level are considered. Similar
to Cramer-von Mises, Anderson Darling A2 test statistic indicates that it can be
assumed that sample data comes from two parameter Weibull distributions.
When size of sample data is 100, there exists a difference in the test results of
Anderson Darling test statistics when it is compared to n=20. However, both test
results show that two-parameter Weibull distribution is still valid for different size of
sample.
Table 4.22: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2) when
n=20 for three-parameter Weibull Distribution
Significance Level Cramer Von Mises Test
W2
Anderson Darling Test
A2
0.01 0.33 0.96
0.05 0.27 0.90
0.10 0.24 0.85
0.15 0.19 0.76
0.20 0.15 0.70
Table 4.23: Critical values for Cramer-von Mises (W2) and Anderson-Darling (A2) when
n=100 for three-parameter Weibull Distribution
Significance Level Cramer Von Mises Test
W2
Anderson Darling Test
A2
0.01 0.14 0.91
0.05 0.11 0.84
0.10 0.09 0.76
0.15 0.08 0.68
0.20 0.05 0.60
The tables above indicates that Cramer-von Mises test statistic and Anderson Darling
test statistics are considered to have almost similar test results for two-parameter
74
Weibull distribution and three-parameter Weibull distribution having smaller
location parameters.
4.3 Systems Reliability Based on Weibull Distribution
Items reliability are recalculated by using equation (2.22) and their estimated
parameters i.e. shape (β), characteristic life (η) and Threshold parameter (γ) given
through tables 4.1 to Table 4.9.
On the contrary to exponential distribution, when Weibull distribution is employed,
infant mortality and wear out characteristics of item are taken into account for
reliability estimations. Summary of the predicted probabilities of systems;
Table 4.24: Reliabilities of systems after simulation study (exponential data)
System Reliability
Landing Gear System 0.99985446
Electrical System 0.99945656
Ice Protection System 0.99996989
Propulsion System 0.99775964
Fuel System 0.99968706
Lighting System 0.99961783
Communication System 0.98758403
Automatic Flight
Control System 0.99912295
Mission Systems 0.99954465
Items reliability for time to failure data generated for Weibull distribution are
recalculated with respect to 4-hour mission profile by using equation (2.22) and their
75
estimated parameters i.e. shape (β), characteristic life (η) and Threshold parameter
(γ) given through tables 4.10 to Table 4.18.
Table 4.25: Reliabilities of systems after simulation study (Weibull data)
System Reliability
Landing Gear System 0,99998798
Electrical System 0,99980388
Ice Protection System 0,99998131
Propulsion System 0,99983150
Fuel System 0,99984382
Lighting System 0,99997822
Communication System 0,99939459
Automatic Flight
Control System 0,99988950
Mission Systems 0,99965526
4.4 Reliability Comparisons
Based on three-parameter Weibull distribution, aircraft level reliability characteristic
is to be estimated by using equation (2.22) with assumption that all system under
platform need to be operational during entire flight, as follows:
0.9827_ lExponentiaalUAVMETUTacticR
Firstly, reliability of aircraft has been calculated based on time to failure data for
exponential distribution. It is predicted as 0.9678 according to assumption of sample
data to be well fitted to exponential distribution, namely constant failure rate. By
using same data set, Weibull distribution assumption is taken into account and
reliability of METU Tactical UAV is calculated accordingly. Reliability of aircraft is
0.9827 when is the assumption is Weibull distribution. Both results Weibull may be
considered to be so close when success point of view is into account. However,
76
difference in two approaches is indeed more meaningful with respect to unreliability
considerations. It can be concluded from the result that 173 of 10000 UAVs will fail
to carry out mission for exponential assumption and on the other hand, 322 of 10000
UAVs with assumption of Weibull distribution will fail.
Table 4.26: Reliability of aircraft based on exponential data
Exponential Distribution Weibull Distribution
0.9678 0.9827
Secondly, reliability of aircraft is also predicted and calculated when time to failure
data having characteristics of Weibull distribution by using equation (2.22).
0.9983_ W eibullalUAVMETUTacticR
It is observed that when the time to failure data has the characteristics of Weibull
distribution, significant differences exist between both approaches. Unreliability of
aircraft is 0.0017 when the original data comes from Weibull distribution. It is 0.322
when exponential assumption is made and failure rate is assumed to be constant.
Table 4.27: Reliability of aircraft based on Weibull data
Exponential Distribution Weibull Distribution
0.9678 0.9983
Two different approaches are assessed and differences in reliability of aircraft are
investigated. Results are given in Table 4.26 and Table 4.27 for both data sets
coming from exponential distribution and Weibull Distribution respectively.
Additionally, in order to identify METU tactical UAV to be competitive in the
market, reliability comparison needs to be taken into account with other similar
platforms’ reliability. However, due to lack of information about reliability or
unreliability of current UAVs such as Aerosky of Aeronautics Defense Systems,
Seeker II by DENEL and Shadow 200 T of AAI Corporation, etc. Thus, competitor
study cannot be conducted.
77
CHAPTER 5
CONCLUSIONS AND FUTURE WORK
5.1 Conclusions
In this simulation study, a method has been developed to emphasize difference
between common reliability approaches preferred in the industry and advantages of
usage of time to failure data collected during the actual operational environment of
UAV. Even though it is difficult to obtain “time to failure data” during actual
operational conditions of use, simulation study has been performed. Reliability
analysis model based on Weibull distribution and Exponential distribution approach
will give alternatives to the designer to select the convenient approach for different
situations.
“SAE ARP 4761 Aerospace Recommended Practice” which is commonly used by
industry for civil aircraft certifications and states that probability calculations are
based on average probabilities. The failure rates are assumed to be constant over time
for which this distribution of failures is known as the exponential distribution is
appropriate. In chapter 3, under this assumption, reliability of METU tactical UAV is
predicted. However, in a case where wear-out or infant mortality is a consideration,
other distributions must be taken into account for the prediction of reliability, which
is best characterized.
In Chapter 4, simulation study is carried out to analyze time to failure data such that
any other probability distributions are necessary and thus employed for reliability
78
prediction. For created time to failure data with respect to both exponential
distribution and Weibull Distribution, three-step process is employed to determine of
proper failure distribution that best represents. Then reliability of aircraft is predicted
and criticality of assumed distribution is emphasized. Instead of making assumption
about the distributions, best fitting distribution for given data set needs to be
analyzed. Some assumptions may result in significant differences in the analysis.
When the original data comes from Weibull distribution but exponential assumption
is performed, approximately 18 times difference may exist between the unreliability
of two analyses.
Proper failure distribution is identified based on the Q-Q plotting, parameters for
identified distribution are estimated and goodness-of-fit tests are applied
respectively. In Appendix B, Q-Q plots are drawn for two different data which are
time to failure derived from exponential distribution and another one derived from
Weibull distribution respectively. Q-Q plots are the indication that Weibull
distribution assumption fails when original data comes from the exponential
distribution (See Figure B.1, Figure B.2 and Figure B.3). Additionally, exponential
distribution assumption fails when original data comes from the Weibull distribution
(See Figure B.4, Figure B.5 and Figure B.6). The linearity of Q-Q plots are distorted
when different distribution is assumed. Q-Q plots are also drawn for elements of
other systems in APPENDIX B, nearly same results are obtained.
Goodness of fit tests is employed to see how well the data fit two-parameter Weibull
distribution. As described in section 2.1.2. The main advantage of Weibull
distribution is that both increasing and decreasing failure rate can be modelled.
In this thesis, two different approaches are applied to predict reliability
characteristics of METU tactical UAV and to show effects of the assumption on the
time to failure data sets. This analysis is a simulation study and depends on
availability of time to failure data.
79
5.2 Future Work
In future work, firstly this study may be superseded with availability of real time data
obtained under actual aircraft-operating environment during life cycle of METU
tactical UAV. As far as reliability of METU tactical UAV is concerned, time to
failure data for items, which will be used by similar aircrafts possibly, tracked and
obtained to update the analysis.
In addition to approach applied in the thesis, different probability distribution models
(i.e. Gamma, Normal, Lognormal, etc.) may also be chosen to be investigated to
model reliability characteristics for each item in the UAV. Generalized distribution
models (especially, generalized gamma distribution) could be preferred to model
time to failure data. Generalized gamma distribution is a kind of non-parametric
model and it is very flexible distribution containing Weibull, exponential, lognormal
and gamma distributions for special cases.
Secondly, in order to quantify the statistical uncertainty in the estimation, analysis
needs to be extended in a way that confidence interval for time to failure data
analyzed and investigated.
Possible changes in design of systems give chance to designer and reliability
engineer to consider reliability improvement techniques. Part selection, derating
factor application, redundancy and similar improvements techniques can be carried
out the increase reliability of whole aircraft.
80
81
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88
89
APPENDIX A
TIME TO FAILURE DATA
Time to failure data is generated for both exponential distribution and Weibull
distribution for each item under the systems are given as;
Table A. 1: Time to failure data for items under landing gear system
Main Wheel Servo Actuator Hydraulic Pump
Exponential
Data Weibull
Data Exponential
Data Weibull
Data Exponential
Data Weibull Data
18499 19039 1233 1574 1408 2066
32462 40209 1837 1696 2615 4386
57864 67969 2346 1996 3300 4699
62972 79383 2961 2986 3884 6245
74164 91719 3650 3488 4056 8635
81024 94145 3772 4381 4314 10769
85973 101459 4058 4596 5036 12488
91579 117061 5495 5070 7356 12729
97946 135218 5989 5485 7528 13250
106374 135350 6716 7623 8076 15708
159352 175779 7871 8007 12344 17186
210295 177443 8272 8639 14001 18685
212812 231022 9373 8678 16234 18984
241147 235765 9511 10020 16591 21431
280033 235908 10058 10851 17677 23616
314081 297939 11105 12074 22482 23911
337982 298058 11173 12306 28382 24033
384458 370294 12160 12561 45754 25970
404794 372135 14399 14588 51273 34095
454196 432114 19218 16575 64144 37474
90
Table A. 1: Continued
Calliper Brake Disk Nose Landing Gear
Exponential
Data Weibull
Data Exponential
Data Weibull
Data Exponential
Data Weibull Data
21261 57280 18435 33428 18499 19039
62412 58577 30332 47215 32462 40209
74831 103206 35734 61626 57864 67969
75424 109903 43105 62544 62972 79363
98546 145168 43131 64269 74164 91719
102626 185358 78236 101282 81024 94145
122685 186255 80757 143121 85973 101459
139608 232611 97839 143604 91579 115061
184492 234115 134385 160667 97946 124568
226257 253704 147864 165005 106374 165350
298910 261807 164373 166748 159352 195779
311635 310616 193181 212410 210295 215443
360532 356987 234064 216061 212812 241022
392621 381306 266493 258273 241147 245715
486762 386785 269139 291044 280033 245908
506203 432586 275633 303338 314081 248569
522015 546160 357065 325985 337982 298058
560145 548509 399982 328095 384458 310294
655575 553177 468158 362080 404794 372215
752096 609938 583484 473214 454196 436114
91
Table A. 2: Time to failure data for items under electrical system
Lithium Polymer Battery 5V DC-DC Converter
Exponential Data Weibull Data Exponential Data Weibull Data
285 342 770 609
497 854 1177 1003
817 1114 1229 1335
959 1190 1621 1497
1171 1277 2455 2420
1207 1371 2539 2482
1756 1392 3018 2774
1852 1605 3525 2976
1991 1998 3577 3957
2102 2611 3678 4653
2436 2631 4467 4717
3103 2944 4687 5282
3179 2935 5943 5308
3733 3297 6679 5693
4092 3298 6931 5942
4404 3787 8316 7823
4454 4559 8850 8535
5251 5896 9418 8933
6363 6960 11539 12411
7554 7134 13670 15644
92
Table A. 2: Continued
12V DC-DC Converter Junction Box Connector
Exponential
Data Weibull
Data Exponential
Data Weibull
Data Exponential
Data Weibull
Data
770 609 196 217 31951 54024
1177 1003 486 755 35680 84421
1229 1335 504 760 48538 85271
1621 1497 514 771 49767 88309
2455 2420 642 846 51520 92295
2539 2482 833 1019 57619 106236
3018 2774 853 1077 59518 114860
3525 2976 964 1173 77537 128145
3577 3957 1115 1227 85158 168795
3678 4653 1277 1286 91250 170727
4467 4717 1293 1399 100371 207018
4687 5282 1495 1431 150709 210560
5943 5308 1548 1451 270886 229198
6679 5693 1806 1711 282454 280665
6931 5942 2173 1791 358128 317908
8316 7823 2338 2028 442389 411351
8850 8535 2566 2115 595399 440900
9418 8933 3281 2363 684150 554837
11539 12411 3377 3436 737368 591792
13670 15644 4170 4593 850064 722678
93
Table A. 3: Time to failure data for items under ice protection system
Heater
Exponential Data Weibull Data
3517 2873
6843 6940
8077 11204
14698 19056
15444 26125
28470 26216
30297 33473
32722 34588
37940 48200
42722 48914
51389 52490
64922 55282
69135 69696
71146 74288
76568 74959
83975 78854
95853 87899
97117 87702
99327 95390
109835 105844
94
Table A. 4: Time to failure data for items under propulsion system
Limbach L275 piston-prop engine Sensor
(Engine RPM)
Exponential Data Weibull Data Exponential Data Weibull Data
361 308 4574 33850
581 717 6795 46526
642 1105 10189 59259
728 1393 15556 64880
874 1703 20437 73033
1284 2190 24333 80698
1736 2222 29084 84993
1893 2386 38085 95148
2412 2636 39426 96456
2927 2854 49576 105634
3144 3412 84874 119308
3692 3512 91429 140651
4876 3581 114106 151030
5468 3870 156109 153753
6809 4627 184384 158769
7155 6415 225513 163888
8267 7389 296514 177237
8697 9691 326715 195376
9873 11759 403603 245751
13581 13225 431810 306878
95
Table A. 4: Continued
Sensor
(Engine Temperature) Servo actuator (Engine Throttle)
Exponential Data Weibull Data Exponential Data Weibull Data
43103 20776 168 1102
45673 34996 329 2395
53781 46525 950 2480
59469 63881 1508 3741
67102 79089 1889 3944
79769 107515 2085 4203
93236 119666 2518 4275
94123 131606 2827 4435
110067 132593 3573 4560
130732 151364 4957 4893
141825 179804 5503 5041
152602 187520 6498 7005
163242 204807 7940 7231
179280 215540 8116 7898
213078 236458 12073 8342
259875 230581 13786 8450
297372 280762 17237 10425
374368 306675 18132 18787
380911 302979 20365 19206
458009 364492 22741 24789
96
Table A. 5: Time to failure data for items under fuel system
Fuel Tank Fuel line
Exponential Data Weibull Data Exponential Data Weibull Data
5332 2431 9973 4518
6832 8624 12232 15959
7782 16324 17016 22274
16049 29859 18267 47262
29982 31333 21391 51474
48113 55055 24912 74856
60829 58227 57531 89494
63008 81743 64153 96386
74971 83182 76410 116522
98859 97136 78621 126010
111581 98096 86428 131025
125288 106034 97979 138391
178377 114854 160042 175907
180373 129981 274414 208313
193606 239159 307900 322086
202658 253495 353565 353366
218718 270729 474303 465585
386253 352599 476733 460484
394343 432051 593490 516303
497046 439087 754640 543777
97
Table A. 6: Time to failure data for items under lighting system
Flasher Headlight
Exponential Data Weibull Data Exponential Data Weibull Data
2316 6589 1027 1700
3197 7391 1514 3024
4365 9644 2369 4295
4723 11343 2526 4748
7156 12045 3418 4780
8950 13419 3959 5545
11741 17175 4750 5591
14109 20866 5634 6058
19030 22162 6945 7941
24704 22673 8559 8352
29158 27829 9482 10100
31368 30954 15043 11091
34536 32568 15591 12752
41274 32762 17644 18091
45066 34635 18755 18690
47469 48387 20489 20214
49879 50764 26158 25039
58731 51099 27866 33126
61657 52790 41330 35197
62600 56907 42331 39068
98
Table A. 7: Time to failure data for items under communication system
Video Transmitting System Receiver of remote controller
Exponential Data Weibull Data Exponential Data Weibull Data
91 284 64 64
134 300 93 93
159 327 157 157
301 485 167 167
342 486 170 170
417 514 245 245
458 580 259 259
553 641 264 264
599 686 270 270
803 761 280 280
829 792 298 298
937 807 378 378
1079 875 419 419
1080 984 545 545
1124 1109 556 556
1144 1336 596 596
1729 1410 636 636
2280 1515 695 695
2321 1889 903 903
3342 2690 1005 1005
99
Table A. 8: Time to failure data for items under AFCS system
Automatic Flight
Control Computer
Servo actuators
(operating at 12V)
Servo actuators
(operating at 5V) Exponential
Data Weibull
Data Exponential
Data Weibull
Data Exponential
Data Weibull
Data
970 776 1406 2141 3328 2547
1423 1654 1966 7511 7805 19854
1868 2071 4910 11955 12924 28589
3169 2536 5337 12074 18649 32698
3351 3011 6160 13114 39469 36315
3657 4277 8638 14552 42716 42887
3662 5112 9435 14895 53637 58137
3717 5149 9708 15266 57794 62460
6254 6316 12247 18983 64780 77387
6885 6420 13054 19568 65622 84039
7037 6643 16374 19985 82067 95929
7164 7438 21760 22387 87632 118472
7883 7732 22965 23789 117340 121877
8797 9235 27209 26235 148303 148930
10258 11808 30027 29190 158967 163594
10572 12541 30497 31780 193539 175339
10765 13021 51242 41533 267163 240589
16123 15126 61533 50451 319187 298302
18777 17368 69614 55061 397650 352573
25845 21769 92351 65921 415932 394078
100
Table A. 9: Time to failure data for items under mission systems
Gimbaled Day/Night IR Camera
System Camera System
Exponential Data Weibull Data Exponential Data Weibull Data
201 111 273 376
233 247 352 491
265 305 480 661
302 425 583 896
376 457 671 955
446 507 879 1052
511 524 901 1068
629 584 1129 1446
699 628 1471 1461
705 652 1698 1591
790 705 1717 1922
878 714 2051 1969
930 746 2239 2232
966 938 2599 2509
1031 1273 2744 2787
1254 1554 2956 3340
1529 1572 3499 3509
2031 1901 3761 3561
2135 2313 4078 3575
3087 2848 5627 4300
101
APPENDIX B
QUANTILE-QUANTILE PLOTS
Quantile-Quantile Plots related to data set of Engine Temperature Sensor under
Propulsion System are shown in the following figures. Figure B. 1, Figure B. 2 and
Figure B. 3 provides the QQ plots for simulated exponential data with respect to
exponential distribution and Weibull distribution having shape parameter of 1.5 and
2.0 respectively. It is indicated and proved that exponential data set lie along the line
when exponential distribution is assumed theoretically. If QQ plots are performed
based on the theoretical Weibull distribution assumption, some skewness exists and
thus Weibull distribution with shape parameter 1.5 and 2.0 are not considered to
suitable distribution for such data sets.
Propulsion System:
Figure B. 1: Sensor (Engine Temperature) quantile plot for exponential distribution by using
exponential observed data
102
Figure B. 2: Sensor (Engine Temperature) quantile plot for Weibull distribution (shape
parameter of 1.5) by using exponential observed data
Figure B. 3: Sensor (Engine Temperature) quantile plot for Weibull distribution (shape
parameter of 2.0) by using exponential observed data
103
Figure B. 4, Figure B. 5 and Figure B. 6 provides the QQ plots for simulated Weibull
data with respect to exponential distribution and Weibull distribution having shape
parameter of 1.5 and 2.0 respectively. For Weibull data set, exponential distribution
assumption are not considered to be feasible since as it can be concluded from Figure
B. 4 that both some skewness and big separations exist with respect to line. Weibull
distribution having shape parameter of 2.0 can be selected as the most appropriate
distribution to model for this data set which lie along the line.
Figure B. 4: Sensor (Engine Temperature) quantile plot for exponential distribution by using
Weibull observed data
104
Figure B. 5: Sensor (Engine Temperature) quantile plot for Weibull distribution (shape
parameter of 1.5) by using Weibull observed data
Figure B. 6: Sensor (Engine Temperature) quantile plot for Weibull distribution (shape
parameter of 2.0) by using Weibull observed data
105
APPENDIX C
CURRICULUM VITAE
PERSONAL INFORMATION
Surname, Name: Koç, Yılmaz
Nationality: Turkish (TC)
Date and Place of Birth: 23 May 1984, Malatya
Marital Status: Single
Phone: +90 312 811 18 00
Email: [email protected]
EDUCATION
Degree Institution Year of Graduation
BS METU Aerospace Engineering 2007
High
School
Ankara 50.Yıl High School, Ankara 2002
WORK EXPERIENCE
Year Place Enrollment
2008-Present Turkish Aerospace Industries (TAI) Safety/Reliability
Engineering
FOREIGN LANGUAGES
English
