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.

1. Reliability
Distributions and
Their Use
Fred Schenkelberg

3. Reliability
Distributions?

4. What is
Life Data?
How do you define failure?

5. Lifetimes Vary

6. Human Mortality
From http://www.medicine.ox.ac.uk/bandolier/booth/Risk/dyingage.html

7. Types
of
data

8. What is wrong
with the data
you have
available?

9. What do we
need to know?
Common questions asked of the
data.

10. Good Enough?

11. Better Than?

12. Number Spares/Replacements

13. How can you
get the data
you need?

14. Data to
Histogram
Let’s take our first look at the data

15. A Big Pile of
Numbers

16. Weather Data
1990 - 2010 California Temperatures (°C)
Celisus
Density
-10 0 10 20 30 40
0.000.010.020.030.04

17. Warranty Returns Data

18. Warranty Histogram
Months
#Returns
0204060

19. What are your
favorite data
plots?

20. Data to
Weibull CDF
Cumulative Distribution Function.

21. Start Each at Time Zero

22. 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

23. Beta = 1.1
Eta = 51 months

24. First two months
Beta = 0.64
Eta = 110 months
After first two months
Beta = 1.4
Eta = 35 months

25. Do you
Weibull?

26. Exponential &
Weibull
Calculations

27. 30 Failures in First Year
Out of 500 Units

28. 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

29. 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

30. 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

31. Friends don’t
let friends use
MTBF

32. Binomial and
Sample Size
Success testing basic formula.

33. The magic
of 77
Samples

34. Success Testing
n =
ln 1- C( )
mb
´ ln R( )
77 =
ln 1- 0.95( )
1´ ln 0.96( )

35. My Favorite - 60% Confidence

36. Time to check
the qual
packages from
your vendors

37. Hypergeometri
c
A fun use of this distribution.

38. We had 15 out of 30 Fail

39. They Claim a 100 FIT Rate

40. 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

41. What are
other uses of
a life
distribution?

43. What are your
Questions?
Thanks for participating.