1. Making Use of
Reliability Statistics
Fred Schenkelberg

2. Everything Varies

3. Decisions to Make

4. Questions to
Answer

5. Experiments to
Analyze

6. Convincing Evidence

7. How do you do
treat data?

8. EXPLORATORY DATA
ANALYSIS
Fun with Plotting

9. Given Some Data

10. Rural Male
Rural Female
Urban Male
Urban Female
Rural Male
Rural Female
Urban Male
Urban Female
Rural Male
Rural Female
Urban Male
Urban Female
Rural Male
Rural Female
Urban Male
Urban Female
Rural Male
Rural Female
Urban Male
Urban Female
50-54
55-59
60-64
65-69
70-74
0 20 40 60 80 100
Death Rates in Virginia - 1940
Dot Plot

11. A B C D E F G H
25102050100
Box Plot

12. Histogram
1990 - 2010 California Temperatures (°C)
Celisus
Density
-10 0 10 20 30 40
0.000.010.020.030.04

13. Q-Q Plot
0 5 10 15
051015
qchisq(ppoints(x),df=4)

14. Basic
View of
Dataset 0 20 40 60 80 100 120
0200400600
x
020406080100
x
0 50 100 150
0.00.0100.020
Quantiles of Standard Normal
x
-2 0 2
020406080100

15. Scatter or
Run Plot
0 10 20 30 40 50
-2-1012
Simple Use of Color In a Plot
Just a Whisper of a Label

16. Scatter Plots
in Matrix
Sepal.Length
2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5
4.55.56.57.5
2.02.53.03.54.0
Sepal.Width
Petal.Length
1234567
4.5 5.5 6.5 7.5
0.51.01.52.02.5
1 2 3 4 5 6 7
Petal.Width
Edgar Anderson's Iris Data

17. With the right
tool this is easy

18. FIELD DATA
Let’s explore some data

19. 3 Months of Field Data
Concentrator Field Data 2p Weibull vs WeiBayes
Folio1Concentrator 1: m=1.5000, s=0.1000, Rb=2.1122, h=16.4576, Z=0.999817465905239
Folio1Concentrator: b=2.9361, h=9.0133, Z=0.999817465905239
Time, (t)
Unreliability,F(t)
0.100 10.0001.000
0.100
0.500
1.000
5.000
10.000
50.000
90.000
99.000
0.100
x 137
x 140
x 3
x 137
x 140
x 3
Probability-W eibull
Folio1Concentrator
W eibull-2P
MLE RRM MED FM
F=280/S=38062
Data Points
Probability Line
Folio1Concentrator 1
W eibull-Bayesian-2P
MLE MED MED BSN
F=280/S=38062
Data Points
Probability Line
Fred Schenkelberg
Consulting
8/21/2007
10:12:25 AM

20. 8 Months
by System
1.00 100.0010.00
0.01
0.05
0.10
0.50
1.00
5.00
10.00
50.00
90.00
99.00
0.01
ReliaSoft's Weibull++ 6.0 - www.Weibull.com
Probability - Weibull
Time, (t)
Unreliability,F(t)
9/30/2005 10:06
Fred Schenkelberg Consulting
Fred Schenkelberg
Weibull
Compressor
W2 RRX - RRM MED
F=849 / S=153493
β1=2.2557,η1=50.7130,ρ=0.9999
Plastics
W2 RRX - RRM MED
F=1314 / S=153028
β2=1.3281,η2=162.3354,ρ=0.9994
Sieve
W2 RRX - RRM MED
F=360 / S=143343
β3=2.0955,η3=89.5413,ρ=0.9998
Solenoid
W2 RRX - RRM MED
F=550 / S=153792
β4=2.4939,η4=48.1558,ρ=0.9999
System
W2 RRX - RRM MED
F=29930 / S=311217
CB[FM]@90.00%
2-Sided-B [T2]
β5=1.5656,η5=46.3456,ρ=0.9992

21. Time to Repair Data
ReliaSoft W eibull++ 7 - www.ReliaSoft.com
Probability - Lognormal
µ=−1.4625, σ=1.6508, ρ=0.9611
Time, (t)
Unreliability,F(t)
0.010 100.0000.100 1.000 10.000
0.010
0.050
0.100
0.500
1.000
5.000
10.000
50.000
99.990
0.010
Probability-Lognormal
Line 4 Depalletizer Single Serving MTTR
Lognormal-2P
RRX SRM MED FM
F=1245/S=0
Data Points
Probability Line
Fred Schenkelberg
Consulting
11/23/2007
2:19:26 PM

22. Count of
Failures
over Cut
Depth
DEPTH CUT
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2000 4000 6000 8000 10000 12000 14000 16000
FractionFailing
Thu May 11 17:05:37 PDT 2006
RSS DEPTH CUT data
Nonparametric CDF Estimate
with Nonparametric pointwise 95% Confidence Bands

24. Better
Questions

25. Questions?

26. EXPERIMENTS
Asking better questions

27. Setting Priorities
R t( )= e
− t
η( )
β

28. Comparison (hypothesis test)
1 2
-1012345
group
extra
Welch Two Sample t-test
data: extra by group
t = -1.8608, df = 17.776,
p-value = 0.07939
alternative hypothesis: true difference in
means is not equal to 0
95 percent confidence interval:
-3.3654832 0.2054832
sample estimates:
mean in group 1 mean in group 2
0.75 2.33

29. Regression
Average Children Height
in centimeters
versus Age
in Months

30. Regression
height = 0.635 age + 64.928

31. Response Surface

32. Design of
Experiments

33. Questions?

34. Sample Size?
Just how many do we need?

35. Minimum Samples
n =
ln 1− C( )
mln R( )

36. Talk about the Risk

37. Options with Limited
Samples

38. How do you
extract value from
limited samples?

39. Next Steps on Your Journey
1. Gather failure data
2. Plot the data
3. Ask questions
4. Embrace Statistics
5. Enjoy!

40. DESIGNING
EXPERIMENTS
Consider objectives and possible outcomes

41. What is the Objective?

42. What are the
possible
outcomes?

43. What is the
decision point?

44. Questions?

45. FINDING VALUE
www.fmsreliability.com/accendo/join-accendo-reliability/

46. www.fmsreliability.com
fms@fmsreliability.com
(408) 710-8248