Trickett-Welch 'Solution' to the Behrens-Fisher Problem Applied to One-Sided Tolerance Limits for Random Effects Model.

摘要

One-sided tolerance limits for random effects models is a topic of considerable importance in engineering statistics. The purpose of this paper has been to consider this tolerance limit problem from the point of view of the Welch interpretation of the Behrens-Fisher problem. This approach leads to a method which provides essentially the nominal coverage probability whatever the value of the nuisance parameter. We have demonstrated that in addition to excellent coverage properties, the distribution of the proposed tolerance limit compares favorably with an existing procedure and with an exact solution for known nuisance parameter. Keywords: Normally distributed random variables. (kr)