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SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006
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Page 1: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

SuperSMITH SoftwareWinSMITH Weibull Student Version

Step-by-Step Tutorial usingCase Studies

By Dr. Robert B. Abernethy

Copyrighted 2006

Page 2: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Problem#1:Plotting a Weibull with suspensions

Produce a Weibull plot based on the following data:Note the differences between the two plots.

1. Use Median Ranked Regression (MRR), 2. then Maximum Likelihood Estimates (MLE).

Failure Time (cycles) Status

1500 Failure1750 Suspension2250 Failure4000 Failure4300 Failure5000 Suspension7000 Failure

Page 3: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Step by Step

• Open WinSMITH Weibull Student Version (WSWS): double click the icon on the desktop or go to “Start--> Programs-->Supersmith Weibull

• Input the data, using a negative sign for suspensions. Or you can cut and paste from EXCEL.

Page 4: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Inputting data to SuperSMITH

Then click on the “paste”bottle graphic.

Page 5: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Notice that the suspensions that were put in as a negativenumbers show up as a >1750 and >5000

After a few seconds, SuperSMITH automatically produces your Weibull plot

Now, click on “Labels”to put your titles on the plot

Page 6: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Type in your title and click the green checkDo the same for the y-axis title, and put your initials in

Customize your plot with titles

Finally, click“Exit”

Click here to put a label on the plot

Page 7: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

In order to save this plot to a PowerPoint slide click on the “printer” graphic.

Getting your plot into PowerPoint

Page 8: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Now click on the “clipboard” graphic;Then go to a blank page in Powerpoint and “paste.”

Getting your plot into Powerpoint(continued)

Page 9: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Final Median Ranked Regression Weibull

Page 10: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To do an Maximum Likelihood (MLE) Weibull

Click on this symbol

Page 11: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To do an MLE Weibull(continued)

Click on this symbol

Page 12: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To do an MLE Weibull(continued)

This is an MLE Weibull, and note the poor fit

Page 13: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Problem #2

• The following data represents the life of precision grinder wheels measured in number of pieces produced.

• Fit a Weibull to this data.. Is a t0 needed?

Page 14: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Do a Ranked Regression as in Problem 1:Note the curvature in the Weibull plot

Page 15: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To do a t0 correction in WSWS

Click on t0 – 3 parameter Weibull button

Page 16: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To do a t0 correction in WSWS (continued)

Click on this button, then click On the green “check”

Page 17: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

.

Note the improvement in r2.. from 0.764 before to 0.98 now

To do a t0 correction in WSWS (continued)

Page 18: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Problem #3

• The following data represents the shear strength of brass and steel brake rivets.

• Do a Weibull of each… is there a significant difference between the two?

Page 19: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

First, the brass rivet Weibull

Cut and paste the data from EXCEL™, or punch in directly, then …Click here to put confidence bounds on the plot

Page 20: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Put confidence bounds on this Weibull

Click on this button for 2-sidedConfidence bounds……………...

Page 21: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Continuing to put Confidence bounds on a Weibull line

Accept 90% confidence…….

Page 22: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

You now have a Weibull Plot for Shear strength of Brass rivets , with 90% confidence bounds

Note that the confidence bound at 10% failure or 90% reliability is(8.7-104.7) This may be read from the plot or the “report.”

18 110

Page 23: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To see the “Report” Click on the right Tab

How to bring up the “Report”

Page 24: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

The Report Shows Exact Readings From The Plot

Here are the exact 90% Confidence B10 Bounds which are also 90% Reliability Bounds. Other B lives may be added using the report icon. Also shown are confidence bounds for eta and beta.

Page 25: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Now repeat this procedure for the steel rivets

90% confidence bounds at 10% reliability are (152.9-513.1)

Page 26: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Declare a Significant Difference

•Confidence bounds for Brass rivets at 90% reliability are (8.7-104.7).

•Confidence bounds for steel rivets at 90% reliability are (152.9-513.1).

Conclusion: Since these bounds do not overlap at the B10 level, there is a significant difference in the strength of the brass and steel rivets with 90% confidence.

Page 27: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Problem #4

• The following data represents the pull strength of spot welds from the lab:

• Fit a Weibull to this data.. Anything surprising … do you believe the value of the calculated

Pull Strength(Newtons)142146150154158162166

Page 28: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

seems high, try Lognormal andNormal.

Doing a Ranked Regression Weibull as before

Page 29: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Now try a Lognormal

Click on this button

Page 30: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Now try a Lognormal, continued

Click on this button (if you wait a second or twoThe name of the option will appear below it in a yellow box).

Page 31: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.
Page 32: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Now let’s try a Normal

Click on this button

Page 33: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Click on this button

Now let’s try a Normal (continued)

Page 34: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Click on this button, thenThen “NO” on “Lower bias?”

Now let’s try a Normal (continued)

Page 35: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.
Page 36: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

So far, where are we?

Hmmm, looks like log-normal or Normal..But wait , look at the original Weibull…It’s a little hard to tell, but it seems like There may be curvature .. Let’s try a T0 correction.

Distribution r^2Weibull 0.975Lognormal 0.992Normal 0.992

Page 37: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Doing a t0 correction

Click on this button

Page 38: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Doing a t0 correction (continued)

Click on this button, and the “No” will change to “Yes”,then click the Green check

Page 39: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Doing a t0:The fit is better,R2=.995,so, 3-parameter Weibullis your best choice????

Page 40: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To Find the Best Distributionr2 is a good measure of fit but (r2 – CCC2) is more accurate as explained in Chapter 3. Remember the “Report” we used in Problem 3? It contains (r2 – CCC2) and this allows us to do an accurate distribution analysis. If we click on the tab above the plot for each distribution, the results are:

Weibull 2-parameter (r2 – CCC2) = 0.1487Weibull 3-parameter = 0.0739Log Normal = 0.1511

Therefore from a statistical view the Log Normal best fits our data set. However, the physics of failure and prior experience may provide more information, at least equally important, as discussed in Chapter 3.

Page 41: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Remember the Pump Problem in Chapter 4?

-1000

-1000

2000

-2000

-2000

-2000

-2000

3000

-3000

-3000

-3000

-3000

-4000

-4000

-4000

-4000

-4000

Let’s see if we can do the Abernethy Risk failure forecast to predict the number of failures on the 18 remaining pumps in the next year. To make the Weibull plot, Figure 4.1, enter the data shown in Table 4-1 and repeated here.

Page 42: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Here is the plot. R squared is 1.0 because we only have two failures. The expected usage for 1 year is 1000 hours for each pump or 83.3 hours per month. Select the Abernethy Risk icon.

Page 43: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

To make a failure forecast click on the Abernethy Risk Icon which is here.

Page 44: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Enter Usage = 83.3 hours per month and click on the Green Check

Page 45: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

What does this tell us? Expect 2.3 failures in the next year. Expect the next failure in four months. The Now Risk is 2.5, close to the observed number 2, so a batch problem is not indicated. In five years expect 14 failures.

Page 46: SuperSMITH Software WinSMITH Weibull Student Version Step-by-Step Tutorial using Case Studies By Dr. Robert B. Abernethy Copyrighted 2006.

Summary

• We have illustrated how to input data, failures and suspensions, obtain MRR and MLE plots, add confidence bounds, do a distribution analysis and a failure forecast.

• We hope we have helped introduce you to Weibull Analysis and we would be pleased if you would send us your questions and/or comments.

• Bob Abernethy …[email protected]


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