How to calculate tolerance intervals for non-normal data?

[Jim Wynne]

Jim,

You were right, My English is not good today....

Your English is a lot better than my Spanish

 

[Dr. Electron]

Hello All,

I am a new guy here. First, I would like to thank the forum creators and participants. It is a cool place!

I have a question which made me find this place . I was asked to calculate the tolerance intervals for a given sample size for non-normal data ( say Weibull ) with certain confidence level and reliability ( population within the tolerance limits ). I was able to do this by using the homegrown software. However, I want to know the math ( simplified if possible ) beyond that. For normal data , it seems, I have found papers desribing the math. I would highly appreciate if anybody could help me find/understand the math for non-normal data.


Regards,
learner

Hi learner...you could also use the method Juran pointed out in his Quality Control Handbook. Section 22 pg 54 (22-54). Using table W and table X...how high does your confidence interval need to be? To use this at 95/95 you'll need a sample size of 93. With n=100 your "k" will be 0.954.

 

[nwillnow]

I didn't want to bother opening a new thread because my question seems to fall within this discussion.

If I'm trying to show confidence and reliability (95/95) that my tolerance interval is within a set specification limit, does my data have to be normal?

My quality system is written such that to validate any process output, I need a minimum of 30 data samples. At which point I perform an x +/- ks calc and compare to my spec limit. Where K is the one or two-sided statistical tolerance limit taken from Lieberman's 'Industrial Quality Control' or from Statgraphics.

The problem is just about every validation I do yields many sets of data that are not normal. I look at historical reports and see that most people just overlook this fact, perform the calculation, see that they pass, and file the findings. I've tried transforming the data, which often is possible using one of the many options available in MiniTAB, but once the data is transformed I can't reference my spec limit to check for confidence and reliability.

Any thoughts?

 

[Statistical Steven]

I didn't want to bother opening a new thread because my question seems to fall within this discussion.

If I'm trying to show confidence and reliability (95/95) that my tolerance interval is within a set specification limit, does my data have to be normal?

My quality system is written such that to validate any process output, I need a minimum of 30 data samples. At which point I perform an x +/- ks calc and compare to my spec limit. Where K is the one or two-sided statistical tolerance limit taken from Lieberman's 'Industrial Quality Control' or from Statgraphics.

The problem is just about every validation I do yields many sets of data that are not normal. I look at historical reports and see that most people just overlook this fact, perform the calculation, see that they pass, and file the findings. I've tried transforming the data, which often is possible using one of the many options available in MiniTAB, but once the data is transformed I can't reference my spec limit to check for confidence and reliability.

Any thoughts?

If a transformation on your data gives a normal distribution, you would use the same transformation on your specification or I prefer to just back transform the output of the tolerance interval. Remember, that back transforming your tolerance interval will usually give nonsymmetrical limits.