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Bayesian control charts for tolerance limits in the case of normal populations. (English) Zbl 1397.62605

Summary: By using air-lead data analysed by K. Krishnamoorthy and T. Mathew, “Bayesian Tolerance Intervals”, [(2009; doi:10.1002/9780470473900.ch11)]; in Statistical tolerance regions. Theory, applications, and computation. (2009; Zbl 1291.60001), 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 \(p\)th 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.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 1291.60001
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