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A Margin-Based Approach to Determining Sample Sizes via Tolerance Intervals (302792)

Keywords: Tolerance Intervals, Sample Size, Quantification of Margin and Uncertainty, Component Performance

Many engineering applications rely on our ability to demonstrate that a component or system meets its performance requirements. This is often accomplished by calculating statistical tolerance intervals and comparing them to the requirements. If the tolerance interval is contained by the requirements, we conclude they are meeting the requirements. The width of the tolerance interval, however, is dependent on the sample size and, in some cases, we may conclude that we are not meeting requirements due to a small sample size, even if the underlying distribution does meet requirements. This paper proposes an approach to determining sample sizes based on an initial assumption of how much margin a components distribution has to its requirements. This approach provides a sample size large enough that an estimated tolerance interval will be contained by the performance requirement (assuming there is a true underlying positive margin). In addition, this paper explores the relationship between margin, the width of the tolerance interval, and sample size and provides recommendations for quantifying risk when sample sizes are limited.