Minitab calculates the mean and standard deviation for each sample and these serve as the point estimates of the population parameters if your data are normally distributed.

Tolerance intervals are a range of values for a specific quality characteristic of a product that likely covers a specified proportion of future product output. Because you cannot observe the entire population, the intervals are based on the sample data and are given with a specified level of confidence. If a tolerance interval has a 95% confidence level, you can be 95% confident that your specified proportion, or more, falls within the interval. Thus, if 100 such tolerance intervals were constructed, you would expect around 95 to contain at least the specified proportion.

Use the normal method interval if you can safely assume that your sample comes from a normally distributed population. Otherwise, use the nonparametric method interval if your sample data are continuous, but do not come from a normally distributed population. See Normal and nonparametric methods for tolerance intervals for more details.

Minitab uses an exact method to calculate the normal tolerance intervals.

For the nonparametric method, Minitab calculates the achieved confidence level. This is the exact confidence level obtained from your sample. It will generally be greater than or equal to your desired confidence level, unless your sample size is too small.

For the washer data, the statistics table displays the sample size and point estimates of the mean washer thickness (11.046 mm) and standard deviation (0.286) for the entire washer population. However, in this case, the manufacturer is more interested in the range that most washer thicknesses will fall in. The tolerance intervals contain this information.

The normal and nonparametric methods produce slightly different tolerance intervals. Because the data are normally distributed, the manufacturer is 95% confident that at least 95% of all washers produced will have thicknesses falling in the normal method interval [10.409 11.684].

The analyst compares this tolerance interval to a major client's washer specs [10 12]. Because the tolerance interval is contained within the client's requirements, the analyst concludes that current thickness variability is not excessive.