reliability prediction of electronic boards by analyzing field return data authors: vehbi cömert...
TRANSCRIPT
Reliability Prediction of Electronic Boards by
Analyzing Field Return DataAuthors: Vehbi Cömert (Presenter)
Mustafa Altun Hadi Yadavari Ertunç Ertürk
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•Performing a reliability analysis using a real field return data
•Motivation: Modeling hazard rate curve and making accurate reliability prediction
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Introduction• Field Return Data• Electronics Reliability
Filtering• Field return data may have obvious and hidden errors. • Surveying accuracy of the field return data to find errors• Based on beta parameter of Weibull distirubtion
Modeling of hazard rate curve• Reliability prediction with filtered field return data• Investigation of distributions that fits to data.• Change of hazard rate shape with respect to ‘Time to Failure’• Two phase hazard rate curve
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Field Return Data
• The field return data ,that we use, belongs to Arçelik (Beko), one of the biggest white apliance company in Europe • It is a warranty data and includes - 1 million sales - 3000 warranty claims - We have first 54 months of the data• Warranty involves 36 months.
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Electronics Reliability
• Good reliability• Expected long life• Usually catastrophic failures • Decreasing or constant hazard rate• Hard to see wear out signs
0 1000 2000 3000 4000 5000 60000
1
2
3x 10-5
Time /DayH
azar
d R
ate
A Sample Bathtub Curve for an Electronic Board
EarlyFailure
Wear out
Useful Life
exceeding 10 years
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FilteringEliminating errors in field return data
Step 1 : Eliminating Obvious Errors
Step 2 : Eliminating Hidden ErrorsStage 1: Forward analysis
Stage 2: Backward analysis
Stage 3: 6-month analysis
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Errors in field return data
• Obvious error : The errors that can be seen easily by checking claims
• Hidden error : The errors that cannot be seen at first glance What can be a hidden error?
Assembly date Return Date
11 November 2011 12 July 2016
Missing Claims
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Filtering Process
• To ensure the accuracy of the analysis, errors must be eliminated !!! Step 1 : Obvious errors must be filtered by checking hand
Records with;Unknown assembly dateUnknown return dateZero time to failureNegative time to failureUnreasonable time to failure
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Filtering Process• Step -2: Investigate the data using Weibull distribution to find hidden
errors.
• Weibull distribution parameters;- Beta(): shape parameter- Alfa (): scale parameter
<1 Decreasing Failure Rate
=1 Constant Failure Rate
>1 Increasing Failure Rate
10 0-6 0-12 0-18 0-24 0-30 0-36 0-42 0-48 0-54
00.5
11.5
22.5
33.5
44.5
55.5
65.284
1.8621.485
0.707 0.663 0.679 0.701 0.702 0.714
Filtering Process• Step -2 stage1 : Forward Analysis
1 6 12 18 24 30 36 42 48 54
problematic
Assembly date/Month
Weibull Fitting
𝛽
values for forward time intervals
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Filtering Process
• Step-2 stage-2: Backward analysis
1 6 12 18 24 30 36 42 48 54
47--54 43--54 37--54 31--54 25--54 19--54 13--54 7--540
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 1.517
1.140.995
0.923 0.865 0.8 0.771 0.744
values for backward time intervals
Lack of return data toward end of the time
Assembly date/Month
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Filtering Process• Step-2 stage-3: 6 - month periods analysis
0 6 12 18 24 30 36 42 48 54
0—6 7—12 13--18 19--24 25--30 31--36 37--42 43--48 49--540
0.51
1.52
2.53
3.54
4.55
5.56
5.284
2.157 1.943
0.6 0.747 0.842 0.954 11.517
values for 6-month periods
problematic
Assembly date/Month
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0-6 0-12 0-18 0-24 0-30 0-36 0-42 0-48 0-540
0.51
1.52
2.53
3.54
4.55
5.56
5.284
1.8621.485
0.707 0.663 0.679 0.701 0.702 0.714
Filtering Process
values for forward time intervals
problematic
47--54 43--54 37--54 31--54 25--54 19--54 13--54 7--540
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 1.517
1.140.995 0.923 0.865 0.8 0.771 0.744
values for backward time intervals
0—6
7—12 13--18 19--24 25--30 31--36 37--42 43--48 49--540
1
2
3
4
5
65.284
2.157 1.943
0.6 0.747 0.842 0.954 11.517
values for 6-month periods
problematic
First three intervals (1-18 months) should be filtered.
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Modeling of hazard rate curve To obtain an accurate hazard rate curve Searching points where the hazard rate tendency changes Forward and Backward analysis
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Modeling of Hazard Rate Curve
0 1000 2000 3000 4000 5000 60000
1
2
3x 10-5
Time /Day
Haz
ard
Rat
e
A Sample Bathtub Curve for an Electronic Board
EarlyFailure
Wear out
Useful Life
exceeding 10 years
Change Point (): From decreasing rate trend to constant rate trend
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Modeling of Hazard Rate Curve
• Method to find change point via Reliasoft Weibull++- Analyzing filtered field return data in terms of time to failure (TTF)
- Using ‘’best fit’’ option in Weibull++ and fitting with respect to different time intervals.
- Trying to find the point where the best fitting distribution changes by showing different hazard rate trend
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• Forward analysis
Modeling of Hazard Rate Curve
1 2 3 4 5 6 7 8 …………………………… Mf ……………………………………………..…………………………..36
Time to Failure/month
includes field returns that can have all TTF values between 1 and Mf
Results : At end of each interval analysis, decreasing hazard rate trend was observed for this filtered data. Weibull++ offered most commonly Weibull distribution in addition to Lognormal and Gamma distributionsWhat is the hazard
rate trend?
Most likelihood distribution
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Modeling of Hazard Rate Curve
• Backward analysis
Results : - Exponential distribution for , constant hazar rate
- Weibull, Lognormal and Gamma Distribution for decreasing hazard rate
1 2 3 4 5 6 7 8 …………………………… Mb …………………………………….……………33 34 35 36
includes field returns that can have all TTF values between Mb and 36 month
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Modeling of Hazard Rate Curve
(𝑂𝑣𝑒𝑟𝑎𝑙h𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛)h𝑜 (𝑡 )={ h1 ,𝑡<𝜏 (𝑊𝑒𝑖𝑏𝑢𝑙𝑙𝐷𝑖𝑠𝑡 .)h2 , 𝑡≥𝜏 (𝐸𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑖𝑎𝑙𝐷𝑖𝑠𝑡 .)
0 500 1000 1500 20002
4
6
810
t
Hazard rate vs. time plot of Weibull distribution
Haz
ard
Rat
e
x10-6
M < 14 Weibull Distribuiton
0 500 1.000 1.500 20000
2
4
6
8
10
t
Hazard rate vs. time plot of exp. distribution
Haz
ard
rate
x10-6
M > 14 Exponential Distribution
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Modeling of Hazard Rate Curve
• : overall hazar rate function : indicator function
0 500 1000 1500 20002
4
6
810
t
Hazard rate vs. time plot for ho(t), h1(t) and h2(t)
Hazard
rate Overall hazard rate function, ho(t)
Exponential hazard rate function, h2(t)
Weibull hazard rate function,h1(t)
x10-6
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Conclusion
• This study will be used by Arçelik • Usefull for high volume sales• This methods can be generalized for all field return datas
FILTERING• A systematic approach is offered for
elimination errors in field return data• To determine hidden errors. 1) Forward Analysis 2) Backward Analysis 3) 6-month Analysis• 18 months at begining of the data
seem as problematic
MODELING OF HAZARD RATE CURVE• We look for change of hazard rate
tendency 1) Forward Analysis 2) Backward Analysis• In the forward analysis we didn’t see a
change in the hazard rate shape• But in the backward analysis,
exponential distribution fits best between 14 and 36 months
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THANK YOU