RPI DSES-6070 HV7 ProjectRPI DSES-6070 HV7 Project

Derk PhilipponaDerk Philippona

Fall 2008Fall 2008

Introduction: Description of the Introduction: Description of the ProblemProblem

Radar component failure data collected over Radar component failure data collected over a three year period on 241 Navy F/A-18 a three year period on 241 Navy F/A-18 aircraft, taken from Blischke reference, were aircraft, taken from Blischke reference, were analyzedanalyzedto provide a basis for making warranty to provide a basis for making warranty decisionsdecisions

Methodologies: Summary DescriptionMethodologies: Summary Description

• Data best fit failure distribution function identified with MINITAB

• Expressions and plots for failure functions obtained with MAPLE

• Constructed Monte Carlo model of data with EXCEL

• Verified no benefit for age replacement policy with EXCEL model

• Studied benefit of cold standby redundancy with MAPLE and EXCEL

Results: Analysis / DiscussionResults: Analysis / DiscussionExponential and Weibull distributions fit data Exponential and Weibull distributions fit data wellwell

1000100101

99.9

90

50

10

1

C1

Perc

ent

100010010

99.9

99

90

50

10

1

C1

Perc

ent

1000100101

99.9

90

50

10

1

C1

Perc

ent

10000100010010

99.9

99

90

50

10

1

C1

Perc

ent

Weibull0.992

Lognormal0.958

Exponential*

Loglogistic0.925

Correlation Coefficient

Probability Plot for C1LSXY Estimates-Arbitrary Censoring

Weibull Lognormal

Exponential Loglogistic

10005000

0.0045

0.0030

0.0015

0.0000

C1

PD

F

1000100101

99.9

90

50

10

1

C1

Perc

ent

10005000

100

50

0

C1

Perc

ent

10005000

0.45

0.30

0.15

0.00

C1

Rate

Mean 223.653StDev 223.653Median 155.025IQR 245.708AD* 0.912

Table of StatisticsProbability Density Function

Survival Function Hazard Function

Distribution Overview Plot for C1LSXY Estimates-Arbitrary Censoring

Exponential

12008004000

0.003

0.002

0.001

0.000

C1

PD

F

1000100101

99.9

90

50

10

1

C1

Perc

ent

12008004000

100

50

0

C1

Perc

ent

12008004000

0.0044

0.0042

0.0040

0.0038

C1R

ate

Shape 1.02844Scale 246.829Mean 244.020StDev 237.298Median 172.832IQR 265.603AD* 0.492Correlation 0.992

Table of StatisticsProbability Density Function

Survival Function Hazard Function

Distribution Overview Plot for C1LSXY Estimates-Arbitrary Censoring

Weibull

Results: Analysis / DiscussionResults: Analysis / DiscussionReliability functions definedReliability functions definedF := 1-exp(-t/(223.653)); 1 - exp(-0.004471212101 t)R := 1-F; exp(-0.004471212101 t)f := diff (F, t); 0.004471212101 exp(-0.004471212101 t)z := f/R; 0.004471212101MTTF := int (R, t = 0 .. infinity); 223.6530000

Results: Analysis / DiscussionResults: Analysis / DiscussionAge replacement policy does not reduce Age replacement policy does not reduce total costtotal cost(as expected with constant failure rate)(as expected with constant failure rate)

0

5

10

15

20

25

1 5 10 100 300 400 500 1000

t

Co

st R

atio

Results: Analysis / DiscussionResults: Analysis / DiscussionCold standby redundancy doubles MTTFCold standby redundancy doubles MTTF

Rs := exp(-0.004471212101 t) + 0.004247651496 exp(-0.004471212101 t) t evalf(subs(t = 223, Rs)); 0.7184390857 evalf(subs(t = 223, R)); 0.3689551089 MTTFs := int(Rs, t = 0 .. infinity); 436.1233500

Conclusions:Conclusions:

• Exponential distribution function fits failure data well

• Failure rate is approximately constant; 4.47 failures / 1000 flight hours

• MTTF is 223.65 flight hours

• An age replacement policy does not reduce total cost, as expected with a constant failure rate

• Modifying the radar system to add a cold standby exciter and switch could approximately double MTTF