Reliability Webull Analysis What happens behind all the
Reliability – Webull Analysis What happens behind all the Weibull Analyses we see in Accelerated Ageing Studies Nigel Hampton NEETRAC
Reliability – Webull Analysis This will be a practical, audience involvement presentation Go ahead and find something to write with and a straight’ish edge
Reliability – Webull Analysis History / Early Experience led concerns about ageing and increasing failures in service
Reliability – Webull Analysis To get a handle on performance with time, accelerated tests were developed AWTT Cores in water - tubes 1 yr Breakdown metric Multiple times Small samples ACLT Cores in water - tanks ? ? yr Time to Failure metric Continuum of times Moderate samples
Reliability – Webull Analysis CTL & NEETRAC AWTT Data – since 2000 5
Reliability – Webull Analysis European Maintenance Tests 6
Reliability – Webull Analysis Time to Failure Research Tests 7
Reliability – Webull Analysis We find Weibull Curves all the time They estimate the likelihood of Failure (Pf) for a known stress (S) and a given Scale Parameter a and Shape Parameter b The Weibull Distribution considers • Extreme Values – the longest, shortest, first etc • Addresses “one mechanism “at a time 8
Reliability – Webull Analysis With Natural Logs and Logs to Base 10 and Nifty Rearranging Becomes 9
Reliability – Webull Analysis Weibull Graph Paper gives Weibull Plots Y Axis = log (ln(1 -P)) - - we enter P X Axis is = log (S) - - we enter S
Reliability – Webull Analysis Y Axis = log (ln(1 -P)) - - we enter P X Axis = log (S) - - we enter S 11
Reliability – Webull Analysis Rank Order All we need is Pf & Tables give Pf Sample Size 1 2 3 4 5 6 7 8 9 10 1 50% 29% 21% 16% 13% 11% 9% 8% 7% 7% 2 71% 50% 39% 31% 27% 23% 20% 18% 16% 3 79% 61% 50% 42% 36% 32% 29% 26% 4 84% 69% 58% 50% 44% 39% 36% 5 87% 73% 64% 56% 50% 45% 6 89% 77% 68% 61% 55% 7 91% 80% 71% 64% 8 92% 82% 74% 9 93% 84% 10 93% 12
Reliability – Webull Analysis The problem We conduct an accelerated ageing test We get failures in terms of days rather than years We test six objects and get failures at the following days: 40 90 65 95 85 100 We have S, we need Pf 13
Reliability – Webull Analysis Look up Pf for the correct Rank Order for 6 tests S Times to Failure (days) 40 65 85 90 95 100 Pf Rank Order 1 2 3 4 5 6 11% 89%
Reliability – Webull Analysis Weibull Paper 15
Reliability – Webull Analysis Rank Order Tables give Pf Sample Size 1 2 3 4 5 6 7 8 9 10 1 50% 29% 21% 16% 13% 11% 9% 8% 7% 7% 2 71% 50% 39% 31% 27% 23% 20% 18% 16% 3 79% 61% 50% 42% 36% 32% 29% 26% 4 84% 69% 58% 50% 44% 39% 36% 5 87% 73% 64% 56% 50% 45% 6 89% 77% 68% 61% 55% 7 91% 80% 71% 64% 8 92% 82% 74% 9 93% 84% 10 93% 16
Reliability – Webull Analysis Weibull Paper 6 11% 27% 42% 58% 73% 89% 17
Reliability – Webull Analysis Weibull Paper 6 11% 27% 42% 58% 73% 89% 18
Reliability – Webull Analysis Weibull Paper 6 11% 27% 42% 58% 73% 89% 19
Reliability – Webull Analysis Weibull Paper 6 11% 27% 42% 58% 73% 89% The intersection of the fitted line with the 63 rd percentile gives the Scale Parameter 20
Reliability – Webull Analysis The gradient of the line gives the Shape Parameter Weibull Paper 6 11% 27% 42% 58% 73% 89% 21
Reliability – Webull Analysis Weibull Paper 6 90 days 3. 1 80 days 11% 27% 42% 58% 73% 89% 22
Reliability – Webull Analysis Weibull Paper 6 90 days 3. 1 +- 1. 5 80 +48, -32 days 11% 27% 42% 58% 73% 89% The size of the Confidence Intervals depend primarily on the Number of Samples and the Shape Parameter b 23
Reliability – Webull Analysis Weibull Paper 6 10 3. 1 +- 1. 5 80 +48, -32 days 3. 1 +- 1 80 +36, -24 days 11% 27% 42% 58% 73% 89% 24
Reliability – Webull Analysis In Conclusion • You should have a better grasp of where the curves come from • They are very efficient at conveying an immense amount of information • The importance of separate mechanisms • Why small sample sizes causes problems
Reliability – Webull Analysis More Information • The New Weibull Handbook – Bob Abernethy • IEEE Guide for the Statistical Analysis of Electrical Breakdown Data – Fothergill, Montanari, Hampton, Ross, Stone • Statistical Treatment of Fatigue Experiments – Leonard Johnson 26
- Slides: 26