Normal and nonparametric methods for tolerance intervals
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When you calculate tolerance intervals using Stat > Quality Tools > Tolerance Intervals, Minitab displays results for both the normal and nonparametric methods. Minitab also displays results for both methods when you plan for tolerance intervals using Stat > Power and Sample Size > Sample Size for Tolerance Intervals. To determine which method to use, consider the following:

·    If your data follow a normal distribution, then the normal method is more precise and economical than the nonparametric method. The normal method allows you to achieve smaller margins of error [link] with fewer observations. Use the normal method if you know from prior experience or analysis that your population is normally distributed. A normality test, such as the one that is included with Stat > Quality Tools > Tolerance Intervals, can also help you decide.

·    The normal method is not robust to severe departures from normality. If you are unsure of the parent distribution, or you know that the parent distribution is not normal, then use the nonparametric method. The nonparametric method requires only that the data are continuous.

·    The nonparametric method requires large sample sizes to cover a large percentage of the population. If your sample size is not large enough, the achieved confidence level for your tolerance interval can be much lower than the desired level.

Minitab uses an exact method to calculate normal tolerance intervals (see [6, 8, 9]). Minitab's sample size planning for normal tolerance intervals also uses an exact method (see [3, 4, 6, 8, 9, 10, 16]).