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Normal Tolerance Interval
A normal tolerance interval is a statistical procedure for constructing an interval like: "With 95% confidence, 99% of the values fall between 1.32 and 1.43." Such an interval is called a 2-sided tolerance interval. One-sided intervals can also be constructed like: "With 95% confidence, 99% of the values fall below 1.45" (upper tolerance interval) or "With 95% confidence, 99% of the values fall above 1.30" (lower tolerance interval). Normal tolerance intervals for the data are displayed in Tabs 1 and 2 of the Test Distribution window.
To construct a normal tolerance interval you must specify: confidence level, percent in interval and whether to use a 2-sided, upper or lower tolerance interval. These options can be set using the Analysis Options and Tolerance Interval Options dialog boxes.
Normal tolerance intervals assume the underlying data fits the normal distribution. Before using one, you should pass a normality test. By default, the normal tolerance interval is only displayed if one of the normality tests passes. For data that fits some other distribution, the data is first transformed and the transformed values are used to construct a normal tolerance interval. This interval is then transformed back to the original units of measures.
It is commonly desired to make a confidence statement like: "With 95% confidence, 99% of the values are in spec." One way of accomplishing this goal is to construct a normal tolerance interval. If this interval falls inside the specs, then the same confidence statement can be made relative to the spec limits. This is a valid approach. A similar, but slightly more powerful approach, is to use a variables sampling plan.