Bayesian control charts for tolerance limits in the case of normal populations

R. van Zyl; A. J. van der Merwe

doi:10.37920/sasj.2017.51.1.8

R. van Zyl Quintiles International
A. J. van der Merwe University of the Free State

DOI: https://doi.org/10.37920/sasj.2017.51.1.8

Keywords: Control charts, Probability-matching prior, Reference prior, Tolerance limits

Abstract

By using air-lead data analysed by Krishnamoorthy and Mathew (2009) a Bayesian procedure is applied to obtain control limits for the upper one-sided tolerance limit. Reference and probability matching priors are derived for the pth quantile of a normal distribution. By simulating the predictive density of a future upper one-sided tolerance limit, "run-lengths" and average "run-lengths" are derived. In the second part of this paper control limits are derived for one-sided tolerance limits for the distribution of the difference between two normal random variables. This article illustrates the flexibility and unique features of the Bayesian simulation method for obtaining the posterior predictive distribution of a future one-sided tolerance limit.

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