# Torque Confidence Testing (Non-normal Distribution)

R

#### Rob C

greetings all!

I have a torque process that we are qualifying. i have 30 samples that have been tested and the distribution is non-normal.
the test is to establish a 99% confidence that failure would not occur until >5 turns.
we experienced no failure <=5 turns. but the distribution is skewed toward the limit.

can anyone suggest a model or method to determine the confidence level?
thanks,

#### bobdoering

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If you can post the data (in an Excel spreadsheet is especially handy), it would greatly allow us to assist.

R

here's the data

thanks
Rob C

#### Attachments

• torque data.xls
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#### Tim Folkerts

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This sounds like a typical application of reliability engineering.

In reliability engineering, the Weibull Distribution is a commonly used instead of the normal distribution precisely because it can fit skewed, non-normal data.

There is lots of information on the web about Weibull analysis. A good website is https://www.weibull.com/basics/lifedata.htm They sell software, but they also have a lot of good information.

And I always recommend the NIST Engineering Statistics Handbook. They have quite a bit of info on reliability at https://www.itl.nist.gov/div898/handbook/apr/apr.htm, including discussion of Weibull analysis.

Tim F

P.S. if you post the data, there is a good chance someone will take a look at it.

#### bobdoering

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I have attached the 'best fit' distribution data from your data. I used my favorite program - Distribution Analyzer from Taylor Enterprises (www.variation.com)

#### Attachments

• data.doc
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#### Tim Folkerts

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One more question.... Are the numbers listed the next higher number from when it failed? For example, if the failure is listed at "7", I am guessing that means it survived 6 turns, but failed some time before the 7th turn? As opposed to "7" meaning sometime between 6.5 turns and 7.5 turns.

I ran the numbers thru Minitab and found that the 3-Parameter Weibull, the 3-Parameter Lognormal, and the 3-Parameter Loglogistic all fit quite well.

The results are listed below (in a format that is unfortunately a little hard to read). The bottom line is that 1% of the parts are predicted to fail after 5.07, 5.31, and 5.22 turns for he three different models. Unfortunately, the lower confidences limits for the 1% failure time is 4.95 turns. So you couldn't be 95% confident that 99% would survive 5 turn.

At least, that is how I interpret the results....

Goodness-of-Fit

Anderson-Darling Correlation
3-Parameter Weibull 0.665 0.954
3-Parameter Lognormal 0.757 0.979
3-Parameter Loglogistic 0.754 0.986

Table of Percentiles

Standard 95% Normal CI
Distribution Percent Percentile Error Lower Upper
3-Parameter Weibull 1 5.06815 0.313992 4.95 5.72249
3-Parameter Lognormal 1 5.30569 0.620517 4.95 6.67256
3-Parameter Loglogistic 1 5.22087 0.287229 4.95 5.81530

3-Parameter Weibull 5 5.35177 0.250414 4.95 5.86578
3-Parameter Lognormal 5 5.57592 0.424557 4.95 6.47333
3-Parameter Loglogistic 5 5.54601 0.227759 5.11710 6.01087

3-Parameter Weibull 10 5.63980 0.240373 5.18781 6.13116
3-Parameter Lognormal 10 5.79599 0.319429 5.20254 6.45712
3-Parameter Loglogistic 10 5.80170 0.222758 5.38113 6.25515

3-Parameter Weibull 50 7.78835 0.485794 6.89211 8.80114
3-Parameter Lognormal 50 7.39866 0.458349 6.55271 8.35382
3-Parameter Loglogistic 50 7.38317 0.370192 6.69212 8.14559