One-sided monte carlo tolerance limit factors in the case of the random effects one-way layout-an algorithm for application in statistical quality control

Abstract

Assuming the statistical model of the random effects one-way layout under the usual conditions (normality and independence) and considering a realization of this model, the present paper treats the problem of the computation of one-sided tolerance limits for the corresponding defining random variable on the basis of the Monte Carlo method. Since subpopulations occurring in this scope can be considered as batches and since the model under consideration is sometimes called ‘cluster sampling model’, it is obvious that the present problem has important applications in the field of statistical quality control.—The Monte Carlo approach together with its realization by a computer program for the determination of such tolerance limit factors proved elementary and effective. In particular, in the important cases of limited sampling information (costs), this approach led to more realistic values in comparison, with other approaches. An additional problem occurring in connection with simultaneous statistical inference was solved by means of the Bonferroni inequality. Finally, the paper contains a computer program (FORTRAN 77) the applicability and use of which is shown by numerical examples.