© barringer & associates, inc. 2005 1 weibull probability paper for quick hand plots plus two...

© Barringer & Associates, Inc. 2005 1

Weibull Probability Paper For Quick Hand Plots

PlusTwo Worked Out Examples

Paul Barringer, P.EBarringer & Associates, Inc.P.O. Box 3985Humble, TX 77347-3985Phone: 1-281-852-6810FAX: 1-281-852-3749Email: [email protected]: http://www.barringer1.com


You’ve got 6 data points (N=6)representing age-to-failure whichis [(death date) – (birth date)]:140 37 37 63 69 --Step 1, Sort 69 X-data 73 73108 108 63 140

Calculate the Y-plot position using Benard’s median rank =(i-0.3)/(N+0.4) for N=6:i=1 10.9%i=2 26.6%i=3 --Step 2 42.2% Y-Datai=4 57.8%i=5 73.4%i=6=N 89.1%

Step 3 Plot the data on 1:1 Weibull paper (see attached Weibull paper)Step 4 Draw a trend line through the dataStep 5 Where the trend line crosses 63.2%, drop down and read eta which is the characteristic lifeStep 6 On the 1:1 paper literally measure the rise over run of the trend line to calculate beta which is the Weibull slope or shape factor

See the worked out example on the next page for the case of no censored(suspended) data. For plotting position details see plot position papers at http://www.barringer1.com/wa.htm

All Data Are Failures


134mm = rise

57mm = run

= rise/run = 134/57 = 2.35 = 92

= 92

W/1:1

Age-To-Failure weeks

Weibull Example-All Failures

3© Barringer & Associates, Inc. 2005


By Computer Calculations = 2.361= 92.67Goodness of fit criteria:R2= 0.95 (CCC2=0.8203 OK)PVE=70.8% (PVE>10% OK

Weibull Example-All Failures


Age-T-Failure weeks


Computer Regression

• The New Weibull Handbook, 5th edition by Dr. Robert B. Abernethy, ISBN 0-9653062-3-2, 2006 describes best practices for small datasets:– Regress Y-on-to-X using median rank regression – Use PVE% for goodness of fit

• For medium data sets (say 10 to 100 data)– If maximum likelihood estimation is required, use the reduced

bias adjustment to correct for small number of failures

• For large size data sets (say over 500 data)– Use maximum likelihood estimation

• For grouped or interval data use the inspection option– Regress data through top most data in a stack


You’ve got 7 data points (N=7)representing cycles-to-failure for thewire (W) failure mode (bond (B) failuremode is suspended) >Signifies suspension 28W >12B No plot >12B 18W >50B --Step 1, Sort >22B No plot 36W 28W X-data >22B 36W 42W 42W 18W >50B No plot

Calculate the Y-plot position using Benard’s median rank =(i-0.3)/(N+0.4) for N=7: InverseRank Rank Wire Modei=1 7 No ploti=2 6 11.4%i=3 5 --Step 2No plot i=4 4 29.9% Y-Datai=5 3 48.5%i=6 2 67.0%i=7=N 1 No plot

Step 3 Use Drew Auth’s correction for the failure data following the suspension by correcting the “i” value in Bernard’s median rank. (i-th adjustment) = {(Inverse Rank)*(Previous Adjusted Rank)+(N+1)}/{(Inverse Rank)+1} = {6*0+(7+1)}/{6+1} = 8/7 = 1.143 (1.143-0.3)/(7+0.4) = 0.843/7.4 = 11.4% {4*1.143+(7+1)}/{4+1} = 2.514 (2.514-0.3)/(7+0.4) = 29.9% {3*2.514+(7+1)}/{3+1} = 3.886 (3.886-0.3)/(7+0.4) = 48.5% {2*3.886+(7+1)}/{2+1} = 5.257 (5.257-0.3)/(7+0.4) = 67.0%Step 4 Follow steps 3-6 from uncensored data. Then see next page for plot

Failure Data Plus Censored Data (Suspensions)


128mm = rise

50mm = run

= 41

= 128/50 = 2.56 = 41

Weibull Example With Suspensions

Cycles-To-Failure cycles

W/1:1



By Computer Calculations = 2.579= 41.3Goodness of fit criteria:R2= 0.996 (CCC2=0.783 OK)PVE=96.07% (PVE>10% OK

Cycles-To-Failure Cycles

Weibull Example With Suspensions



Automate!

• Life is too short to make these plots by hand! Automate (the automation remembers all the rules for making Weibull plots)!

• Use SuperSMITH Weibull software. See http://www.barringer1.com/wins.htm for details and http://www.barringer1.com/supers.htm for costs.

• SuperSMITH Weibull follows all the requirements of The New Weibull Handbook. See http://www.barringer1.com/tnwhb.htm for details.

© barringer & associates, inc. 2005 1 weibull probability paper for quick hand plots plus two...

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