The Effects of Autocorrelation and Outliers on Two-Sided Tolerance Limits

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Abstract
Tolerance limits are limits that include a specific proportion of the population at a given confidence level. They are used to make sure that the production will not be outside specifications. Tolerance limits are either designed based on the normality assumption, or established nonparametrically. In either case, no provision is made in the available design tables of tolerance limits for autocorrelated processes. In this article, we show how positive autocorrelation affects the confidence level of tolerance limits for a specified level of coverage of the population. We conclude that the effect of autocorrelation is negligible for standard tolerance limits (–0.4 ≤ p < 0.25). We give suggestions on how to use existing design tables for tolerance limits that assume normality and independence when in fact the process of interest is a first-order autoregressive process. We also address the effect of occasional outliers on the coverage of tolerance limits.