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Reliability Distributions

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How do you use the Weibull Distribution? It’s just one of many useful statistical distribution we have to master as reliability engineers. Let’s explore an array of distribution and the problems they can help solve in our day to day work.

Detailed Information: When confronted with a set of time to failure data, what is your goto analysis approach. For me it’s a Weibull plot. It’s quick, often provides some insight to ask better questions, and easy to explain to others. A histogram is another great starting point. If we know a little about the source of the data, we may favor the normal or lognormal distributions. If discreet data, then binomial is the first choice, yet Poisson or hypergeometric have uses, too. A basic understanding of statistical distributions provides you a way to summarize data providing insights to identify or solve problems. In this webinar we’ll explore a few distributions useful for reliability engineering work and talk about how to select a distribution, basics on interpreting distributions and just touch on judging if you have selected the right distribution.

This Accendo Reliability webinar originally broadcast on 14 April 2015.

Publicado en: Tecnología
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Reliability Distributions

  1. 1. Reliability Distributions and Their Use Fred Schenkelberg
  2. 2. Reliability Distributions?
  3. 3. What is Life Data? How do you define failure?
  4. 4. Lifetimes Vary
  5. 5. Human Mortality From http://www.medicine.ox.ac.uk/bandolier/booth/Risk/dyingage.html
  6. 6. Types of data
  7. 7. What is wrong with the data you have available?
  8. 8. What do we need to know? Common questions asked of the data.
  9. 9. Good Enough?
  10. 10. Better Than?
  11. 11. Number Spares/Replacements
  12. 12. How can you get the data you need?
  13. 13. Data to Histogram Let’s take our first look at the data
  14. 14. A Big Pile of Numbers
  15. 15. Weather Data 1990 - 2010 California Temperatures (°C) Celisus Density -10 0 10 20 30 40 0.000.010.020.030.04
  16. 16. Warranty Returns Data
  17. 17. Warranty Histogram Months #Returns 0204060
  18. 18. What are your favorite data plots?
  19. 19. Data to Weibull CDF Cumulative Distribution Function.
  20. 20. Start Each at Time Zero
  21. 21. Track Time to Failure & Number Not Failed Yet Ship Date Ship # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Jan 568 2 34 22 16 7 9 2 5 8 12 6 Feb 479 3 15 12 4 8 3 7 9 12 15 Mar 378 1 9 3 2 4 5 8 11 12 Apr 550 1 4 3 2 6 2 9 12 May 472 0 2 3 5 8 7 9 Jun 280 0 1 1 4 8 4 Jul 197 1 5 15 5 7 Aug 732 0 3 8 4 Sep 840 0 4 7 Oct 937 0 2 Nov 358 1
  22. 22. Beta = 1.1 Eta = 51 months
  23. 23. First two months Beta = 0.64 Eta = 110 months After first two months Beta = 1.4 Eta = 35 months
  24. 24. Do you Weibull?
  25. 25. Exponential & Weibull Calculations
  26. 26. 30 Failures in First Year Out of 500 Units
  27. 27. Exponential Calculation for # Failures in Second Year 1year = 8760 hours 500 ´ 8760 = 4,380,000 q = 4,380,000 / 30 = 146,000 F(t) = 1- e - t q( ) F(8760) = 1- e - 8760 146,000( ) = 29.11
  28. 28. Weibull Calculation for # Failures in Second Year Fit a Weibull Distribution b = 0.5 h = 2,290,000 F(t) = 1- e - t h( ) b 500 ´ F(2 ´ 8760) = 500 ´ 1- e - 2´8760 2,290,000( )é ëê ù ûú = 42 42 - 30 = 12
  29. 29. Weibull Calculation for # Failures in Second Year Fit a Weibull Distribution b = 2 h = 35,200 F(t) = 1- e - t h( ) b 500 ´ F(2 ´ 8760) = 500 ´ 1- e - 2´8760 35,200( )é ëê ù ûú = 110 110 - 30 = 80
  30. 30. Friends don’t let friends use MTBF
  31. 31. Binomial and Sample Size Success testing basic formula.
  32. 32. The magic of 77 Samples
  33. 33. Success Testing n = ln 1- C( ) mb ´ ln R( ) 77 = ln 1- 0.95( ) 1´ ln 0.96( )
  34. 34. My Favorite - 60% Confidence
  35. 35. Time to check the qual packages from your vendors
  36. 36. Hypergeometri c A fun use of this distribution.
  37. 37. We had 15 out of 30 Fail
  38. 38. They Claim a 100 FIT Rate
  39. 39. It could be random chance… P(X = k) = K k æ èç ö ø÷ N - K n - k æ èç ö ø÷ N n æ èç ö ø÷ P(X = 15) = 100 15 æ èç ö ø÷ 109 -100 30 -15 æ èç ö ø÷ 109 30 æ èç ö ø÷ = 8.48 ´10-98
  40. 40. What are other uses of a life distribution?
  41. 41. What are your Questions? Thanks for participating.

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