Unbalanced Random-Effect Model with Unequal Group Variances: Estimation of Design Parameters Allowing for Screened Batches.

摘要

A random effects model is considered in which the within group variance is allowed to vary from group to group. The model is complicated by the presence of a testing program which will be used to screen out those groups which have estimated lower percentiles less than prescribed value. The aggregate distribution of the acceptable groups will then be skewed to the right. This type of screening thus tends to increase the value of any specific percentile. A method to estimate, prior to testing, the percentiles of the skewed distribution that would result from a given testing program is presented. Also, a method for constructing tolerance intervals for a particular group given only that it meets the acceptance criterion of the testing program is presented. The model is applied to a materials problem in which it is desired to increase the minimum strength of the material through the use of a screening program. (Author)