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Level II

Sample sizing for future tolerance intervals

Is there a way to determine the appropriate sample size for a future tolerance interval, given some historical data?

In essence, I will gather data and construct a tolerance interval (one- or two-sided) from this new data and compare the tolerance bound(s) to a specification limit.  I need the tolerance bounds to be within the spec limit.  I would like to be able to use the information from a prior sample to inform the minimum sample size.

I've written a simulation that I believe gives me the appropriate power that a given sample size will have a tolerance interval within my limits, but is there a formal way to approach this problem?  Is there a formula somewhere that uses prior estimates/errors of the mean and standard deviation to inform a future tolerance interval sample size?  Equivalently, are there formulas for power sample size calculations for percentiles?

Thanks!

Charles

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Level II

Re: Sample sizing for future tolerance intervals

I recently co-authored a paper in Quality Engineering titled "Sample size determination strategies for normal tolerance intervals using historical data" that provides a solution to this problem by calculating values to be used in the Faulkenberry-Weeks approach.  It does not guarantee certain coverage levels but it did perform very well in numerical studies.  The norm.ss formula is available in the R package 'tolerance'.

http://www.tandfonline.com/doi/full/10.1080/08982112.2015.1124279

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Super User

Re: Sample sizing for future tolerance intervals

7.2.6.4. Tolerance intervals based on the largest and smallest observations

The NIST/SEMATECH e-Handbook of stats methods is a great (free) on-line resource for starting to answer such questions (NIST/SEMATECH e-Handbook of Statistical Methods).  I have provided the link the to one of the sections on tolerance intervals.  On that page is a link to the Hahn and Meeker book on statistical intervals in which you will find details on many types of statistical intervals, parametric and non-parametric solutions, including sample size calculations.

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Level II

Re: Sample sizing for future tolerance intervals

Thank you, Karen.  The links are very helpful and certainly relevant.  I do not believe, however, that they specifically inform the sample size of a future tolerance interval based on historical data for a power calculation.  Maybe my problem is unique.

Highlighted
Level II

Re: Sample sizing for future tolerance intervals

I recently co-authored a paper in Quality Engineering titled "Sample size determination strategies for normal tolerance intervals using historical data" that provides a solution to this problem by calculating values to be used in the Faulkenberry-Weeks approach.  It does not guarantee certain coverage levels but it did perform very well in numerical studies.  The norm.ss formula is available in the R package 'tolerance'.

http://www.tandfonline.com/doi/full/10.1080/08982112.2015.1124279

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