Reliability Analysis of Gas Turbine Power Plant Based on ... · similar onshore wind turbine...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:20 No:02 13

I J E N S 2020 IJENS AprilIJENS © -IJMME-9696-402200

Reliability Analysis of Gas Turbine Power Plant Based on

Failure Data *and Marwa M. Ibrahim *, M. A. Badr*Amal El Berry

*Mechanical Engineering Department, Engineering Research Division, National Research Centre (NRC) 12622, Egypt Abstract-- To predict the reliability of a product or a system, life data from a representative sample of the system

performance is fitted to the suitable statistical distribution.

Reliability analysis techniques have been accepted as standard

tools for the planning, design, operation, and maintenance of

thermal power plants. Therefore, the parameterized

distribution can be used to estimate important life

characteristics such as reliability, or probability of failure at a

given time, mean life, and failure rate.

In today’s competitive environment reliability analysis is the

most important requirement of almost all types of systems,

subsystems, and complex systems; whether they are

mechanical, electrical, or electronic devices. To alleviate

failures and improve the performance and increase the

operational life of these components and systems, key

performance indicators such as: Failure Rate, Reliability,

Availability, and Maintainabilityare

investigated.Weibull++/ALTA is used to fit the available data

set concerning three sets of gas turbines (GT) operating in a

power plant to estimate the probability density function (PDF),

plant reliability, and failure rate of each set and for the whole

plant. In this study data of a gas turbines (GT) power plant

(three groups of GTs) is used. Two methods for parameter

estimation are applied in the data fitting stage: Maximum

Likelihood (MLE) and Rank Regression Analysis X –axis

(RRX).

Using Mean Time Between Failure (MTBF) data, the results

show that the system overall reliability is 97% at 413 hr while

using Down Time (DT) data the system reaches the same

reliability at 289 hr. Also at 800 hr, the reliability of Group-1 is

74% while the reliability of Group-2 and Group-3 is 83% and

45% respectively. Downtime losses and cost of maintenance of

the power plant can be minimized by implementing a proper

mix of maintenance and repair approaches on system

reliability failure rate.

Index Term-- Reliability, Gas Turbine, MeanTime between Failures, Failure Rate, Mean Time to Repair,

WeibullDistribution

ABBREVIATIONS

Aggregate Criterion DESV Maximum Likelihood MLE

Availability A Mean Time Between Failure MTBF

Combined Cycle Power Plants CCPP Mean Time To Failure MTTF

Cumulative Distribution Function CDF Mean Time To Repair MTTR

Condition Monitoring CM Median Ranks MED

Correlation Coefficient Test CC Non-Homogeneous Poisson Process NHPP

Down Time DT Probability Density Function PDF

Fisher Matrix Confidence Bounds FM Pseudo Failure Characteristic PFC

Gas Turbine GT Rank Regression Analysis X –Axis RRX

Kolmogorov-Smirnov Test K-S Reliability R(t)

Likelihood Value Test LHV

1. INTRODUCTION Reliability life data analysis refers to the analysis and

modeling of observed data over the product life to estimate

important features such as system (or component)

reliability, failure rate, or mean time to failure (MTTF).

Several studies for reliability assessment were; and still are,

conducted. Mechanical equipment reliability evaluation is

highly important in condition-based maintenance to lower

costs and increase equipment efficiency;which is the reason, that it an important research field for reliability analysis of

mechanical equipment and life prediction.

1.1 Reliability Approaches and Indices

Failed machine must be removed from service for either

repair or replacement; this occurrence is known as a failure

and may have a negative impact on the system's ability to

provide the load required and impact on the system

reliability. A general approach to system reliability

assessment is to determine one or a number of its reliability

indices that measure some aspects of system reliability

performance such as Mean time between failure (MTBF), failure rate (ƛ) and Mean time to repair (MTTR)

[1].Numerous studies have found empirical models that are



focused on Weibull, exponential, uniform, and other

distributions.

Lack of reliability data leads to reduction of production,

excessive expenditure, equipment failure, and downtime. As

a result, reliability analysis techniques have increasingly

become adopted as standard tools for planning, constructing, running, and maintaining thermal power plants. The

efficiency of the generating system is subdivided into

adequacy and security [2], [3].

Reliability prediction approach depends upon the product

development stages and its related reliability metric [4].

Reliability prediction methods address application of

mathematical models and component data for the purpose of

estimating the field reliability of a system before failure data

are available for the system. Various reliability prediction

methods, their concepts of application, advantages, and

disadvantages were discussed by Thakur and Sakravdia[5].

The classical approach fits equipment failure rates to

statistical models[6]; while in the data-mining approach, it is

modeled using a data-mining algorithm; decision tree

instruction, establishing logical, mathematical, and

statistical relations between MTTF and its various factors of

impact (equipment conditions, failure history, etc.).

Component failure rates depend on time, and therefore can

be viewed as time series. Unplanned equipment failures and

their consequences have significant effect on the total

operating cost of the system.

Duane proposed the power law model on the failures of a

complex repairable system; where the accumulated MTBF

was linearly related to the operating time on log-log scale

[7]. On the other hand, Barabady and Kumar[8]used various

statistical distributions including Weibull, exponential,

normal, and log normal distribution to analyze the reliability

of a crushing plant, in order to identify the bottlenecks in the

system and to find the components or subsystems with low

reliability for a given designed performance.

To get a proper maintenance plan for individual components

in a complex system, Son et al [9] introduced Soft

Computing Methodology. They used a combination of neural network and evolutionary algorithm to discover the

relationship between individual parts of a complex system,

to improve their reliability.

Kuang[10]suggested a new model of reliability evaluation

based on quality loss and the development of quality

characteristics. Wang [11]showed that the limited intensity

procedure was appropriate for the reliability assessment of

degradation in machine tools with regular maintenance

behavior, while Li [12]examined the device reliability

assessment based on acoustic emissions signals. Another

research proposed a method of reliability assessment based

on the distribution of the degradation path related to the

signal characteristics [13]. The signal characteristics of the

machining process were used in this research to replace

traditional time data and fit equipment degradation model

with the characteristic of a pseudo failure.

The demand for reliable products and manufacturing processes with lower cost is persistently growing, especially

in the electronic industry. Factors, reliability, and cost

determine the warranty period allocation for electronic

equipment, Wu et al [14].

1.2 Reliability of Electric Components and Devices

A study reviewing the failure physics approach that is used

in developing highly reliable semiconductor devices was

presented [15]. The study summarized device failures in

fieldand discussed a failure rate prediction model. Pecht[16]

discussed the role of reliability prediction in design,

development, and deployment of electronic equipment;

overviews the history of reliability predictions for electronics.

The complete time series of end-of-life electronic products

for empirical failure rate can be used as an empirical

knowledge base of product reliability.Jónás et al developed

a novel approach focused on the application of both

analytical decomposition of the time series of empirical

failure rates and soft computational techniques to predict

bathub-shaped failure rate curves of consumer electronic

products [17]. Another method suggested by Perera[18]

provided an index of reliability for the estimation of mobile phone failure rates. However there was a significant

correlation between the reliability index and the failure rate.

1.3Reliability of Electric Power Generation System

Globally, the reliable availability of electricity is seen as an

effective and indispensable mechanism for the rapid

industrial and economic growth of any nation [19]. Types of

PV modules failure such as hot spot, diode failure and glass

breakage are highly dependent on the PV module design

technology and the installation site environmental

conditions [20]. Bravoet al. [21] used realistic operation and

maintenance data to estimate the failure rates, grouped by components and the relative effect of failures on the PV

plant's energy balance. Results showed that the impact of

failures in all evaluated PV plants energy losses are small,

reaching a maximum value of 0.96 percent of net energy

yield.

Reliability of generation system is mainly dependent on the generators reliability. Xu Zhang et al. [22]presented a

reliability analysis of floating wind turbines to overcome the

high cost of searching failure causes.Evaluation of floating

wind power system is based upon its structure and function,

which provide explicit internal relation of system and the



requirement of failure modes analysis using dynamic fault

tree analysis. Failure rate of an offshore wind turbine

gearbox was estimated based on the data available for

similar onshore wind turbine systems [23].

Techno-economical decisions ofpower plant equipment maintenance were based on the reliability modeling of the

combined cycle power plants and steam turbine power

plants, Sabouhi[24]. The author proposed reliability-

oriented sensitivity indices to identify the plant critical

components.

As gas turbine (GT) is considered acrucial component of

electric power and aerospace industries, it had prompted a

great number of researches in the fields of material,

mechanical, and electrical engineering to increase their

efficiency. Some gas turbine components work in an

extreme environment of high temperatures which impacts the maintenance cycle, and performance of the turbine.

Some available statistical techniques such as Pareto

analysis, Weibull probability density function, and

calculation of MTBF and Laplace test can be used to

develop failure and reliability analysisand provide an

accurate diagnosis [3].

System failure events and maintenance actionsof a GT were

derived from condition monitoring (CM) data and were

fitted to a non-homogeneous Poisson process (NHPP) using

maximum likelihood estimation (MLE)[25], [26]. The

modified CM data set was used to estimate the parameters of the system reliability models. These models represent the

failure levels of the gas turbine fordifferent life cycle

intervals.

GT power plant reliability is a function of failure rate,

maintenance which in turn depends on the equipment or

systems MTBF and MTTR. Other factors affecting GT

reliability are turbine or system design complexity, rank,

and age. Aneke et al [27] attempted to find the crucial

component in the GT power plant, determine the

relationship between the failure rate and the availability of

GT power plants, and consequently its reliability. Another

research examined the performance indices of selected Nigerian GT power stations [28].

In the same context, Chang evaluated the effect of high

thermo mechanical fatigue on the GT lifetimeduring a

steady-state operation [29]. The study results showed that

the generating units were underused because of inadequate

routine maintenance and fault development of the

equipment.

The above reviewed literature exhibits the importance of

estimating the failure rate and reliability of all types of

systems or components that require data availability over

reasonably long period of time. As for GT power plant

reliability estimation depends on availability of MTBF and

MTTR data. In the current work two data fitting techniques;

maximum likelihood estimation (MLE) method, and rank

regression analysis (RRX) are used.The performance

distributions are then evaluated using three forms goodness

of fit tests to compare the resulting distributions.To select the best-fitted distribution, the aggregate ranking criterion is

used.

2. METHODOLOGY As stated above data gathering, analysis, and fitting plays an

important role in reliability study. The parameters of the

fitted data distributionsare used to analyze the failure rate,

reliability, availability, and maintainability of gas turbine

power plants. The success of such research work depends on

the availability of statistical data from a target company; a

case study, beside the knowledge of reliability theories and

fitting statistical models.To evaluate system (or component)

different reliability functions such as failure rate, availability, etc are calculated; the following subsections

present different tools that are used to estimate the reliability

and maintainability of any mechanical or electric

component/or system.

2.1 Basic Concepts and Approaches for Reliability

Analysis

The techniques of reliability analysis were increasingly

accepted as standard tools for the planning, design,

operation and maintenance of various mechanical or

electrical systems[27] for;

Ability to fulfill basic needs

Efficiency to make effective use of the energy supplied

Reliability to start or continue operating

Maintainability of return to service quickly after one failure

2.1.1 Mean Time between failures (MTBF)

This is a measure of how long the equipment will; on

average, function as defined before an unplanned failure occurs. This can be determined by testing the system for

a total time period T during which N-faults occur. The

fault is repaired, and it puts the system back on test

when the repair time is removed from the total check T

period. The MTBF index is given by equation (1)[27],

[30]:

MTBF = 𝑇

𝑁 =

1

𝐹 (hours), F = expected failure rate. (1)

This error would allow for assumption from the gain. All

things are identical, the system with the biggest MTBF

is considered to be the most effective.



2.1.2 Frequency of Failure or Failure Rate (F)

This index is sensitive to sampling errors, as the method

is being tested for a single sample of its total life. This

error would allow for removal from the result the system

with the highest MTBF, therefore is considered the most efficient. This is a very major deficiency; because there

may be cases where it is more beneficial to have short

repair times than high MTBF. A better measure of

reliability is therefore needed which takes into account

the repair time.

2.1.3 Mean time to Repair (MTTR)

This is a measurement of how long it will take on average

to get the equipment back to normal service status if it

fails, as shown in the following equations [27], [30].

MTTR = 𝜑𝑡

𝜑𝑛 (2)

Where: φt= total outage hours per year.

φn= No. of failure per year

Also, MTTR = 1

𝜇 (3)

Where μ =expected repair rate.

2.1.4 Availability (A)

This is a measurement of the percentage of time that

equipment is able to produce the end product at a certain

acceptable level defined. For a turbine in a power plant, availability is a function of the fraction of time that the

nominal power output is being generated It is calculated

by dividing the whole time in a given period into two

categories that are:

a) 'Up Time', UT: 'when the machine is in operation'.

b) 'Down Time', DT: Where the machine is defective or

failed to fix. The total period is then UT + DT and

availability exhibited in equations 4&5[27]:

A=𝑈𝑇

𝑈𝑇+𝐷𝑇 (4)

A=𝑀𝑇𝐵𝐹

𝑀𝑇𝐵𝐹+𝑀𝑇𝑇𝑅 (5)

2.1.5 Reliability (R(t))

Reliability is considered and identified by Kuo et al.

[31], [32] as the capability of the equipment to perform

its required task satisfactorily under defined conditions

over a given time period. It can also be said that reliability is the possibility that the equipment will

work without fail over time t as shown in the equation

below [27], [32].

R(t)= 𝑒𝑡

𝑀𝑇𝐵𝐹 (6)

Using equation (1) in equation (6), we have

R(t)=𝑒−𝐹𝑡 (7)

Where; t = specified period of failure-free operation

2.2 Data fitting and Parameters’ Estimation

Also these data are commonly referred to as Weibull's reliability life data results. Life data from a representative

sample of units is fitted to the correct statistical distribution

to estimate the life of all items within the population. To fit

into a statistical model, it is important to estimate the

parameters of the statistical distribution which will make the

equation closely fit the data. The function with probability

density (pdf) is the mathematical function representing the

distribution. The pdf can be interpreted mathematically or on

a plot where the x-axis represents time. The pdf of the

statistical total distributions is shown in the following

subsections.

2.2.1 Weibull Distribution

The 3-parameter Weibull pdf is given by[33], [34]:

𝑓(𝑡) =𝛽

ƞ(

𝑡−𝛾

ƞ)𝛽−1𝑒

−(𝑡−𝛾

ƞ)𝛽

(8)

Where:f(t) ≥ 0, t ≥ 0 or 𝛾, β > 0, ƞ > 0, -∞ 0. An

exponential random variable with mean = 1/¸ represents the waiting time until the first event to occur, where

events are generated by a Poisson process with mean ¸



while the gamma random variable X represents the

waiting time until the athevent to occur. Therefore,

X = ∑ 𝑌𝑎𝑖 (10)

Where Y1, …. ; Yn are independent exponential random

variables with mean= 1/.

The probability density function of Gamma distribution is

given by[33]:

𝑓(𝑥; 𝛼, 𝛽) =1

Г(𝛼)𝛽𝛼 𝑒−𝑥 𝛽⁄ 𝑥𝛼−1,𝑥 > 0, 𝛼 > 0, 𝛽 > 0(11)

Where 𝛼 is the shape parameter, β is the scale parameter, and Γ is the gamma function which has the formula

2.2.3 G-Gamma Distribution

The generalized gamma X (α, β, y) is used to imply that

the generalized gamma distribution of the random

variable X has real positive parameters α, β, and y. In

equation 12 [33], a generalized gamma random variable

X with a scale parameter α and form parameters β has the

following probability density function.

𝑓(𝑥) = 𝛾𝑥𝛾𝛽−1𝑒−(𝑥 𝛼)⁄

𝛾

𝛼𝛾𝛽Г(𝛽), x>0 (12)

3. CASE STUDY

In this section a case study describing the reliability analysis

of gas turbine power plant as subsystems and overall is

presented. To investigate reliability and failure modes of

electricity generation system that is based on gas turbines,

data are obtained from a previous study of a power plant in

literature [27]. The plant power is generated from three

groups of gas turbines (GT). These data were collected over

a time period of 10years (from 2005 to 2015). The10-years

datafor group-1are exhibited in Table I, while the total set of

data are shown in appendix A.

Table I

Case study GT, Group-1 published data [27]

Year 2005 2007 2008 2009 2010 2011 2012 2013 2014 2015

No. of Failures 45 75 48 87 48 30 51 20 36 36

MTBF (h) 891.1 871.3 932.5 632.5 2540.5 1736.4 1608.0 370.2 632.7 1574.2

Downtime (h) 1415.3 1331.7 2754.9 1247.0 603.9 650.0 1621.1 1382 693.2 2934.4

MTTR (h) 283.74 221.19 1053.27 147.99 164.85 244.5 470.3 695.2 418.8 1090.1

3.1 Application of Weibull++ ALTA Package

The aim of life data analysis is to apply a statistical

distribution to fault time data in order to understand a

product's reliability performance over time or to make

predictions of future behavior. Several life features can be

derived from the study, such as probability of failure,

reliability, mean life, or failure rate. A quantitative

accelerated life testing data analysis is conducted where the

fault behavior of the product within normal conditions could

be extrapolated in a shorter time to obtain reliability

information about a product (e.g., mean life, probability of failure, etc.). Weibull++ ALTA package provides lifetime

distributions and analytical methods as follows:

"1, 2 and 3 parameter Weibull" "1 and 2 parameter Exponential" "Normal and Lognormal" "Gamma and Generalized Gamma" "Logistic and Log logistic" "Gumbel" "Bayesian-Weibull (with prior knowledge of the

Weibull shape parameter)"

"2, 3 and 4 subpopulation Mixed Weibull" (for situations when there are different trends in the data

and distinct failure mode for each data point can’t be identified)

All of the above distributions were applied in the mean time

between failures (MTBF) and down time data (DT) to get

the best fit, as shown in the section on goodness of fit

section.

3.2 Goodness of Fit Tests

Using goodness-of-fit test the fitted distributions are

determined. There are several ways to determine goodness-

of-fitness. Chi-square, among the most popular methods

used in statistics, "Kolmogorov-Smirnov test", "Anderson-Darling test", and the "Shapiro-Wilk

test"[33].Weibull++/ALTA package; used in this analysis,

provides three "fitness tests" in order to rate the fit

distributions to determine the best fit; these tests are:

"Kolmogorov-Smirnov (K-S)"; tests for the statistically significant correlation between the

expected results and those obtained from the

distribution fitted.

"Correlation coefficient (CC)"; analyses how well the plotted match a straight line.

https://www.itl.nist.gov/div898/handbook/eda/section3/eda363.htmhttps://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm



"Likelihood Value (LHV)"; estimates the log-likelihood value, given the distribution parameters.

3.3 Parameter Estimation

Determining the best fit distribution, reliability is then

estimated using the reliability function of the fitted distribution. There are several methods of parameter

estimation that can be used to estimate the distribution

parameters such as: the maximum likelihood estimation

(MLE) method, rank regression analysis, median ranks

(MED), and Fisher matrix confidence bounds (FM).

In order to obtain the distribution parameters, the regression

line is applied to the data points on the plot when the

parameters are determined using a rank regression analysis.

Therefore, the plot can be used to determine the extent to

which the distribution fits a given set of data. If the line of

regression closely follows the points on the plots the fit is stronger.

MLE method on the contrary, obtains the line solution using

probability function, not by plotting the data points.

Therefore the line is not supposed to follow the points of the

plot;hence the plot should not be used in this case to

determine the fit of a distribution.

4. RESULTS AND DISCUSSION After estimating the parameters, the best fitted distribution

is determined; as follows in sub-section 4.1. System reliability is then determined using the reliability function of

the fitted distribution.

4.1 Best Fit Distribution (Rank & Weight) Method

Using "Weibull++/ ALTA", MTBFGas Turbine data;shown

in table 1, are fitted using both MLEand RRX, then the

output distributions aretested using K-S goodness of fit test,

Correlation Coefficient (CC) test and Likelihood Value

(LHV) test.

To select the best-fitted distribution, the aggregate ranking

criterion is used. This method is based on calculating an

aggregate criterion (referred to as DESV) using the three

rankings values and weights assigned to the individual

criteria using equation (13)[33], [35]. The method assumes

that the lowest DESV value corresponds to the best-fitting theoretical distribution.

DESV= (K-S Rank × K-S Weight) + (CC Rank × CC

Weight) + (LHV Rank × LHV Weight) (13)

Performing goodness-of-fit statistics; for the three criteria,

ranks of different probability distributions are obtained. To

assign weights to the criteria, the default values of weights

selected by the software package are used in the current case

study. Finally, using the described DESV aggregate

criterion shown in Equation 13, the final ranking of the

eleven theoretical distributions was obtained. As previously stated, the distribution with the lowest DESV value was

identified as the best-fitting according to the aggregate

criterion, and was assigned number 1 in the ranking.

Theobtained lowest value of the DESV statistic was 3P-

Weibull distribution for both parameter estimation methods;

MLE and RRX as illustrated in tables II, III.

Implementing this method, the results of the ranking

procedure of gas turbine data (MTBF) for Group-1; (Table-

I), are summarized in Table-II for MLE method and Table-3

for RRX method while the results for Group 2& 3 are exhibited in appendix B.The first column exhibits the type

of the probability distribution, and the second shows the

probability of rejection of the working hypothesis for the

Kolmogorov–Smirnov (K-S) statistic. The third column

displays “Correlation coefficient”(CC) which gives the

mean absolute deviation of the theoretical Cumulative

Distribution Function (CDF) from the empirical CDF. The

fourth column exhibits theLikelihood Value (LHV) which

measures the goodness of fit determined using the log-

likelihood criterion. The value of calculated DESV is shown

in the fifth column.



Table II

DESV Results of Group-1fitted Data using MLEMethod

Distribution K-S CC LHV DESV

Rank Weight Rank Weight Rank Weight

1P- Exponential 11 62.329 10 9.434 10 -83.212 1040

2P- Exponential 5 6.722 8 7.579 1 -77.794 330

Normal 7 11.161 9 7.589 9 -82.535 820

Lognormal 3 4.863 2 5.435 4 -80.013 340

2P-Weibull 6 6.998 4 6.052 7 -80.982 630

3P-Weibull 1 0.337 1 5.270 3 -78.644 200

Gamma 9 12.626 5 6.429 6 -80.479 710

G- Gamma 8 12.028 7 7.138 2 -78.109 490

Logistic 4 5.379 6 6.690 8 -82.318 620

Log-logistic 2 4.142 3 5.865 5 -80.354 360

Gumble 10 25.294 11 10.078 11 -84.639 1060

Table III

DESV Results of Group-1fitted Data using RRX Method

From tablesII & III, the presented analysis of MTBF of

Group-1 of gas turbines plant shows that the best-fitted

distribution, according to the aggregate criterion, is 3P-

Weibull. It should also be noted that with successive failures, the aggregate method may indicate a different best-fit

distributionfornewly gathered data, if there is

significantdifference from that previously analyzed.

4.2 Effect of Each Group on System Reliability

Fig. 1 exhibits the probability density function of the three

groups of gas turbines, (Fig. 1-a) for MLE while (Fig. 1-b)

for RRX. Similarly, Fig.2&3 show the failure rate and

reliability distributions for the two fitting methods.

Distribution K-S CC LHV DESV

Rank Weight Rank Weight Rank Weight

1P- Exponential 11 68.598 10 10.186 10 -83.226 1050

2P- Exponential 5 0.0143 8 4.424 1 -79.882 200

Normal 7 11.394 9 7.597 9 -82.532 780

Lognormal 3 2.682 2 5.115 4 -80.096 420

2P-Weibull 6 15.326 4 6.961 7 -81.267 750

3P-Weibull 1 0.004 1 4.293 3 -78.832 100

Gamma 9 0.306 5 5.479 6 -80.689 500

G- Gamma 8 0.023 7 4.858 2 -80.116 330

Logistic 4 16.042 6 7.612 8 -82.505 870

Log-logistic 2 5.123 3 5.234 5 -80.409 550

Gumble 10 31.255 11 10.384 11 -88.457 1050



a) MLE fitting

MLE Group 1: 3P-Weibull



b) RRX Fitting

RRX Group 1: 3P-Weibull

RRX Group 2: Gamma

RRX Group3: 3P-Weibull

Fig.1. Probability Density Function of the Three Gas Turbine Groups for MLE & RRX Methods

a) MLE fitting




b) RRX Fitting


RRX Group 2: Gamma


Fig. 2. Failure Rate of the ThreeGas Turbine Groups for MLE & RRX Methods



a) MLE fitting




b) RRX Fitting


RRX Group 2: Gamma


Fig. 3. Reliability of the Three Gas Turbine Groups for MLE & RRX Methods

From fig. 1, 2, and 3, it is clear that all the3 groups best

fitting distributions are 3P-Weibull distribution except group 2 of RRX method; which is Gamma distribution.

Also, figures (1, 2, and 3) show that the parameters of each

group have the same values for both methods.

From fig. 1, PDF values for each group using MLE & RRX

are almost equal, and the same applies on fig. 2, 3.This leads

to the conclusionthat parameter estimation (MLE or RRX)

method doesn't affect the resulting values. From fig. 3 it

could be seen that at time = 871 hr, the reliability of Group-

1 reaches around 74% for both parameter estimation

methods; MLE & RRX, also for Group-3 at 760 hr, the reliability is 64.5% using both methods.

Form fig. 2 in case of MLE method, Groups 1& 3 failure

rate decreasedfrom 0.003 to 0.001 in about 4000hrs while

for RRX method the failure rate reached 0.00035at the same

time. For group-2, the failure rate highly increased to reach

0.0022 at 4000hrfor RRX method and >0.003 at the same

time(4000 hr)for MLE method. Hence, Groups (1&3)have

lower failure rates compared with Group-2.

The value of Weibull distribution shape parameter () has an effect on failure calculation [36].Xie et al. stated

thatWeibull distribution showed to fit the failure characteristics of equipment at different stages of its life, by

merely changing the value of the shape parameter

appropriately. Shape parameter < 1 represents decreasing

failure rate stage, = 1 represents constant failure rate and

> 1 represents increasing failure rate stage. This explains

the decreasing failure rate of Groups 1&3 (Fig. 2) as < 1

for both cases. As for Group-2, = 1.6312 (i.e. > 1) that is why the failure rate highly increased.

Form fig.3,it could be seen that for both MLH or RRX

methods, the reliability of Group-1 reached 93% after 632 hr while Groups 2&3 reached the same reliability value after

794 and 413 hr, respectively. This means that Group-3 has

the minimum reliability at a specific time compared to

groups 1&2, while group 2 has the maximum reliability at

the same time.

4.3 Reliability Performance of Overall System

Fig.4 illustrates gas turbines overall system failure rate

using MLE and RRX methodswhile fig. 5 exhibits

thesystem reliability.



Fig.4. Gas TurbineOverall System Failure Rate

From fig. 4, it is clear that system failure rate using MLE is higher than RRX method. In the beginning of system

operation, the two methods have the same trend of failure

rate till 0.0006 then the rate ofincrease of MLE curve is higher thanRRX. After 5000 hrMLE failure rate reaches

0.0015 whileRRX reaches0.0009.

Fig.5. Gas TurbineOverall System Reliability Using MTBF Data

As shown in figure5, it was found that value of system

overall reliability by MLE and RRX is almost the same. At

1800 hr, reliability is around 30% using MLH or RRX

methods. Similarly, at 3600 hr the reliability of MLE is 5%

while it is 7% of RRX method. Also, it could be seen that the

system reliability reaches 90% at around 400hrs.

All the above figures; MTBF data were used. Downtime

(DT) data werealso used to investigateGT system reliability

and it is compared with the results of MTBF data. Figure 6

illustrates reliability of GT overall system using DT data.

RRX

MLE

RRX

MLE Data Points



Fig.6. Gas Turbine Overall System Reliability Using DT Data

From fig. 6, it is clear that system overall reliability; using

DT data, reaches 97%at 289hrcompared to413 hr using

MTBF (fig. 5). The reason is that downtime is the total

timethe machine isnotworking whether it is due to failure, maintenance, or schedule,etc, while MTBF is the time due

to failure only.

5. CONCLUSIONS Gas Turbine power plant reliability is a function of the

failure rate, which in turn depends on the equipment or

systems' Mean Time between Failures (MTBF) and

Downtime (DT). Those also depend on the complexity of

the design, the environment, the age of the equipment or

system and the availability of spare parts to some extent.

The failure rate is a main measuring index for system

availability.Data fitting is the first step in reliability estimation, in this study two curve fitting methods are used

MLE and RRX. The obtained results show that:

Both pdf parameters have the same value using both investigated curve fitting methods.

Group-1 reliability reached 93% at 632 hr while groups 2&3 reached the same reliability level at 794

and 413 hr, respectively using MLH or RRX method.

Group-3 has the highest failure rate in the power plant, while Group-2 has the highest reliability.

System overall reliability was calculated using MTBF & DT data. The results showed that the system

reliability reaches 97% at around 413 hr in case of

MTBF and 289 hr in case of DT data.

6. CONFLICT OF INTEREST The authors declare that there is no conflict of interest.

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AppendixA

10 Year Reliability indices of Transcorp Power Plant, UgheliDelta State Nigeria[27]

II Group 1, III Group 2, IV Group 3



Appendix B

Group-1 Distributions Weight (MLE)

AVGOF: K-S AVPLOT: CC LKV: LHV

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