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