using minitab for re

DEPARTMENT OF INDUSTRIAL &DEPARTMENT OF INDUSTRIAL &MANUFACTURING ENGINEERINGMANUFACTURING ENGINEERINGDEPARTMENT OF INDUSTRIAL &DEPARTMENT OF INDUSTRIAL &MANUFACTURING ENGINEERINGMANUFACTURING ENGINEERINGDEPARTMENT OF INDUSTRIAL &DEPARTMENT OF INDUSTRIAL &MANUFACTURING ENGINEERINGMANUFACTURING ENGINEERING

IE 7270: Reliability EstimationIE 7270: Reliability EstimationFall 2004Fall 2004

Reliability Estimation Using Minitab

IE 7270 Reliability Estimation Fall 2010

GS WASSERMAN



Using Minitab

MINITABHAS TWO MAIN WINDOWS –

A SESSION WINDOW and A WORKSHEET WINDOW



PART ONE:Generate Dataset

Weibull-Step 1


IE 7270: Reliability EstimationIE 7270: Reliability EstimationFall 2004Fall 2004 PART ONE:

Generate Dataset

Weibull-Step 2


IE 7270: Reliability EstimationIE 7270: Reliability EstimationFall 2004Fall 2004 PART ONE:

Generate Dataset

Lognormal-Step 2

ln tmed


IE 7270: Reliability EstimationIE 7270: Reliability EstimationFall 2004Fall 2004 PART TWO:

Data Analysis

Most widelyUsed procedure



Time or Failure

Gives:-MLE or LSXY-Confidence level

Distribution to fit:



STAT > REL. PARAMETRIC – RIGHT CENSORING

15001000500

99

95

90

80

70

60

50 40

30

20

10

5

1

Time to Failure

Per

cen

t

Probability Plot for TimeNormal Distribution - ML Estimates - 95.0% CI

Censoring Column in Censored = 0

LocationScale

MTTFStDev

MedianIQR

FailureCensor

AD*

946.19 124.11

946.19 124.11

946.19 167.43

5 1

1.9995

15001000500

99

95

90

80

70

60

50

40

30

20

10

5

1

Time to Failure

Per

cent

Probability Plot for TimeNormal Distribution - ML Estimates - 95.0% CI

Censoring Column in Censored = 0

LocationScale

MTTFStDev

MedianIQR

FailureCensor

AD*

946.19 124.11

946.19 124.11

946.19 167.43

5 1

1.9995

V13 output shown here



Column of Censor Flags

For multiply-censoredData, create a column of Indicator variables – 0 or 1-- to denote censored or not!



OPTIONS

• Graph

• Maximum Likelihood or Rank Regression

NOTE: In Minitab V15,the plotting position optionsare found in Tools ..> Optionson the main menu. Select probabilityplots, and explore the options within!



STAT > REL. PARAMETRIC – RIGHT CENSORING

Distribution Analysis: Time

Variable: Time

Censoring Information Count

Uncensored value 5

Right censored value 1

Censoring value: Censored = 0 = 0

Estimation Method: Maximum Likelihood

Distribution: WeibullParameter Estimates

Standard 95.0% Normal CI

Parameter Estimate Error Lower Upper

Shape 8.91335 3.07276 4.53525 17.5179

Scale 989.515 50.6525 895.056 1093.94

Log-Likelihood = -31.823

Goodness-of-Fit

Anderson-Darling (adjusted) = 3.089

Characteristics of Distribution


Estimate Error Lower Upper

Mean(MTTF) 936.625 52.8708 838.527 1046.20

Standard Deviation 125.579 37.9430 69.4595 227.040

Median 949.652 52.9506 851.341 1059.32

First Quartile(Q1) 860.433 66.2041 739.986 1000.49

Third Quartile(Q3) 1026.45 51.5637 930.202 1132.65

Interquartile Range(IQR) 166.016 53.3979 88.3823 311.841

Table of Percentiles


Percent Percentile Error Lower Upper

1 590.588 114.953 403.279 864.896

2 638.711 107.747 458.894 888.990

3 668.820 102.734 494.948 903.771

4 691.158 98.8003 522.274 914.651

5 709.092 95.5254 544.544 923.363

6 724.172 92.7022 563.479 930.690

7 737.242 90.2104 580.036 937.054

8 748.818 87.9742 594.803 942.711

9 759.237 85.9418 608.171 947.827

10 768.733 84.0766 620.411 952.515

20 836.256 70.7763 708.432 987.144

30 881.437 62.4473 767.161 1012.74

40 917.684 56.7372 812.955 1035.91

50 949.652 52.9506 851.341 1059.32

60 979.858 50.9185 884.973 1084.92

70 1010.34 50.7807 915.556 1114.93

80 1043.78 53.0748 944.772 1153.17

90 1086.58 59.5762 975.864 1209.85


IE 7270: Reliability EstimationIE 7270: Reliability EstimationFall 2004Fall 2004 STAT > REL. PARAMETRIC –

RIGHT CENSORINGWeibull – Rank Regression

Time

Perc

ent

1500

100090

080

070

060

050

040

030

0

99

90807060504030

20

10

5

3

2

1

Table of Statistics

Median 941.991IQR 193.816Failure 5Censor 1AD* 3.010

Shape

Correlation 0.971

7.56295Scale 988.765Mean 928.587StDev 145.190

Probability Plot for Time

Censoring Column in Censored = 0 - LSXY EstimatesWeibull - 95% CI

Distribution Analysis: Time

Variable: Time

Censoring Information Count

Uncensored value 5

Right censored value 1

Censoring value: Censored = 0 = 0

Estimation Method: Least Squares (failure time(X) on rank(Y))

Distribution: Weibull

Parameter Estimates


Parameter Estimate Error Lower Upper

Shape 7.56295 3.29313 3.22146 17.7554

Scale 988.765 59.5474 878.679 1112.64

Log-Likelihood = -31.929

Goodness-of-Fit

Anderson-Darling (adjusted) = 3.010

Correlation Coefficient = 0.971

Characteristics of Distribution


Estimate Error Lower Upper

Mean(MTTF) 928.587 61.4105 815.698 1057.10

Standard Deviation 145.190 55.5404 68.5997 307.293

Median 941.991 62.0240 827.943 1071.75

First Quartile(Q1) 838.588 82.4504 691.605 1016.81

Third Quartile(Q3) 1032.40 63.1884 915.697 1163.99

Interquartile Range(IQR) 193.816 79.2151 86.9949 431.804

Table of Percentiles


Percent Percentile Error Lower Upper

1 538.188 149.414 312.335 927.360

2 590.240 140.790 369.821 942.031



STAT > DISTRIBUTION ID



STAT > DISTRIBUTION ID OUTPUT

Time

Perc

ent

12501000750500

90

50

10

1

Time

Perc

ent

1200900600

99

90

50

10

1

Time

Perc

ent

10000100010010

90

50

10

1

Time

Perc

ent

15001000500

99

90

50

10

1

Correlation CoefficientWeibull0.971

Lognormal0.985

Exponential*

Loglogistic0.982

Probability Plot for TimeLSXY Estimates-Censoring Column in Censored = 0

Weibull Lognormal

Exponential Loglogistic



Distribution (adj) Coefficient• Weibull 3.010 0.971• Lognormal 2.966 0.985• Exponential 4.846 *• Loglogistic 2.972 0.982• 3-Parameter Weibull 3.006 0.983• 3-Parameter Lognormal 2.962 0.985• 2-Parameter Exponential 3.091 *• 3-Parameter Loglogistic 2.967 0.983• Smallest Extreme Value 3.041 0.965• Normal 2.958 0.985• Logistic 2.960 0.982

• Table of Percentiles• Standard 95% Normal CI• Distribution Percent Percentile Error Lower Upper• Weibull 1 538.188 149.414 312.335 927.360• Lognormal 1 629.833 118.034 436.220 909.379• Exponential 1 7.76524 2.90518 3.72991 16.1663• Loglogistic 1 589.331 126.776 386.588 898.398• 3-Parameter Weibull 1 749.089 5.91779 746.971 760.778• 3-Parameter Lognormal 1 611.877 137.129 343.109 880.644• 2-Parameter Exponential 1 771.599 0.847374 769.939 773.261• 3-Parameter Loglogistic 1 569.976 145.153 285.481 854.472• Smallest Extreme Value 1 437.715 239.707 -32.1025 907.532• Normal 1 579.636 172.859 240.840 918.433• Logistic 1 518.562 196.889 132.666 904.457

• Weibull 5 667.625 124.906 462.681 963.350• Lognormal 5 705.210 99.1708 535.325 929.008• Exponential 5 39.6310 14.8270 19.0361 82.5071• Loglogistic 5 693.414 102.899 518.416 927.485• 3-Parameter Weibull 5 757.883 19.9768 746.971 798.066• 3-Parameter Lognormal 5 697.362 110.129 481.513 913.212• 2-Parameter Exponential 5 779.260 4.32469 770.829 787.782• 3-Parameter Loglogistic 5 686.298 111.843 467.091 905.506• Smallest Extreme Value 5 634.819 162.917 315.507 954.131• Normal 5 683.597 129.462 429.856 937.339• Logistic 5 668.119 134.911 403.699 932.539



• Table of MTTF

• Standard 95% Normal CI• Distribution Mean Error Lower Upper• Weibull 928.587 61.411 815.698 1057.10• Lognormal 939.255 67.278 816.230 1080.82• Exponential 772.635 289.063 371.123 1608.54• Loglogistic 941.771 67.159 818.926 1083.04• 3-Parameter Weibull 963.863 116.291 760.882 1220.99• 3-Parameter Lognormal 937.329 65.727 808.508 1066.15• 2-Parameter Exponential 955.485 84.313 803.735 1135.89• 3-Parameter Loglogistic 939.558 65.914 810.370 1068.75• Smallest Extreme Value 924.193 65.442 795.929 1052.46• Normal 934.518 64.441 808.216 1060.82• Logistic 934.894 64.458 808.558 1061.23

STAT > DISTRIBUTION ID SESSION OUTPUT



DISTRIBUTION OVERVIEW• WEIBULL – RANK REGRESSION

Time

PD

F

12501000750500

0.003

0.002

0.001

0.000

Time

Perc

ent

12501000750500

90

50

10

1

Time

Perc

ent

12501000750500

100

50

0

Time

Rate

12501000750500

0.03

0.02

0.01

0.00

Table of Statistics

Median 941.991IQR 193.816Failure 5Censor 1AD* 3.010

Shape

Correlation 0.971

7.56295Scale 988.765Mean 928.587StDev 145.190

Probability Density Function

Survival Function Hazard Function

Distribution Overview Plot for TimeLSXY Estimates-Censoring Column in Censored = 0

Weibull

using minitab for re

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