Data considerations for Tolerance Intervals (Nonnormal Distribution)

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The data must be continuous
Continuous data are measurements that may potentially be any numeric value within a range of values along a continuous scale, including fractional or decimal values. Common examples include measurements such as length, weight, and temperature.
The data must follow the chosen distribution to use the results from the parametric method
If your data follow the chosen distribution, then the parametric method is more precise and economical than the nonparametric method. The parametric methods allows you to achieve smaller margins of error, even when you have fewer observations, as long as the chosen distribution is appropriate for your data.
The parametric method is not robust to severe departures from the chosen distribution. Use the parametric method only if you know that your population follows the chosen distribution. If you are unsure whether the population follows the chosen distribution, or if you know that the population does not follow the chosen distribution, then use the nonparametric method.
Collect enough data for the nonparametric method
The nonparametric method usually requires larger sample sizes than the parametric method. For example, if the minimum percentage of the population in the interval is 95%, the sample size should be approximately 90 or more for the tolerance interval to be accurate. Larger percentages of the population in the interval require larger sample sizes. For example, if the minimum percentage of the population in the interval is 99%, the sample size should be approximately 500 or more to obtain an accurate two-sided 95% tolerance interval. To have an accurate tolerance interval, the achieved confidence level must be close to your target confidence level. If your sample size is not large enough, the nonparametric interval is a non-informative interval that ranges from negative infinity to infinity. In this case, Minitab displays a finite interval based on the range of your data. As a result, the achieved confidence level is much lower than the target confidence level.
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