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Making use of reliability statistics

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Presenting "Making Use of Reliability Statistics" 6:30pm May 7th at the local IEEE Reliability Society meeting - join us if you can.

In general we need to master the use of statistics to make better decisions. Let the data talk, explore it to learn it's secrets, and conduct experiments with a purpose.

Published in: Data & Analytics
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Making use of reliability statistics

  1. 1. Making Use of Reliability Statistics Fred Schenkelberg
  2. 2. Everything Varies
  3. 3. Decisions to Make
  4. 4. Questions to Answer
  5. 5. Experiments to Analyze
  6. 6. Convincing Evidence
  7. 7. How do you do treat data?
  8. 8. EXPLORATORY DATA ANALYSIS Fun with Plotting
  9. 9. Given Some Data
  10. 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. 11. A B C D E F G H 25102050100 Box Plot
  12. 12. Histogram 1990 - 2010 California Temperatures (°C) Celisus Density -10 0 10 20 30 40 0.000.010.020.030.04
  13. 13. Q-Q Plot 0 5 10 15 051015 qchisq(ppoints(x),df=4)
  14. 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. 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. 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. 17. With the right tool this is easy
  18. 18. FIELD DATA Let’s explore some data
  19. 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. 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. 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. 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
  23. 23. Better Questions
  24. 24. Questions?
  25. 25. EXPERIMENTS Asking better questions
  26. 26. Setting Priorities R t( )= e − t η( ) β
  27. 27. 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
  28. 28. Regression Average Children Height in centimeters versus Age in Months
  29. 29. Regression height = 0.635 age + 64.928
  30. 30. Response Surface
  31. 31. Design of Experiments
  32. 32. Questions?
  33. 33. Sample Size? Just how many do we need?
  34. 34. Minimum Samples n = ln 1− C( ) mln R( )
  35. 35. Talk about the Risk
  36. 36. Options with Limited Samples
  37. 37. How do you extract value from limited samples?
  38. 38. Next Steps on Your Journey 1.  Gather failure data 2.  Plot the data 3.  Ask questions 4.  Embrace Statistics 5.  Enjoy!
  39. 39. DESIGNING EXPERIMENTS Consider objectives and possible outcomes
  40. 40. What is the Objective?
  41. 41. What are the possible outcomes?
  42. 42. What is the decision point?
  43. 43. Questions?
  44. 44. FINDING VALUE www.fmsreliability.com/accendo/join-accendo-reliability/
  45. 45. www.fmsreliability.com fms@fmsreliability.com (408) 710-8248

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