PNNL

Abstract

In many product quality situations, it is of interest to state with X% confidence that at least Y% of the product made during a given period has property values below a calculated value. Such a statistical statement can be made using an upper Y%-content tolerance interval with X% confidence, which is also referred to as an X%/Y% upper tolerance interval (X%/Y% UTI). In this article we present the methodology and formulas for calculating X%/Y% UTIs when there are multiple sources of nuisance uncertainty in addition to the source of variation of interest. The sources of nuisance uncertainty may include regression model uncertainty if a regression model is used to predict the product property of interest. The X%/Y% UTI methodology is developed and illustrated using an example in which there are sampling, analytical, and regression model nuisance uncertainties in addition to the source of variation for which a statistical tolerance statement is desired. The design and results of a simulation study conducted to assess the performance of the X%/Y% UTI method are described. The X%/Y% UTI method that adjusts for nuisance uncertainties is shown to generally achieve the nominal X% and Y% values, and yields significantly smaller UTIs than not adjusting for the nuisance uncertainties.