Basic Analysis • Distributions • Statistical Details for the Distribution Platform • Tolerance Intervals
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Tolerance Intervals
This section contains statistical details for one-sided and two-sided tolerance intervals.
Normal Distribution-Based Intervals
One-Sided Interval
The one-sided interval is computed as follows:
Upper Limit =
Lower Limit =
where:
=
t is the quantile from the non-central t-distribution.
is the standard normal quantile.
Two-Sided Interval
The two-sided interval is computed as follows:
where
s = standard deviation and is a constant.
To determine g, consider the fraction of the population captured by the tolerance interval. Tamhane and Dunlop (2000) give this fraction as follows:
where Φ denotes the standard normal c.d.f. (cumulative distribution function). Therefore, g solves the following equation:
where 1-γ is the fraction of all future observations contained in the tolerance interval.
More information is given in Tables J.1a, J.1b, J.6a, and J.6b of Meeker et al. (2017).
Nonparametric Intervals
For more information about the computation of the nonparametric tolerance intervals, see Meeker et al. (2017, sec. 5.3).

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Help created on 7/12/2018