A Bayesian control chart for a common coefficient of variation. Issue 12 (18th June 2017)

• Record Type: Journal Article
• Authors: van Zyl, R.; van der Merwe, A. J.
• Is Part Of: Communications in statistics. Volume 46:Issue 12(2017)
• Page Start: 5795
• Page End: 5811
• Publication Date: 2017-06-18
• Subjects: Coefficient of variation -- control charts -- probability-matching prior -- reference prior; 62F15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1112914
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: By using the medical data analyzed by Kang et al. (2007 ), a Bayesian procedure is applied to obtain control limits for the coefficient of variation. Reference and probability matching priors are derived for a common coefficient of variation across the range of sample values. By simulating the posterior predictive density function of a future coefficient of variation, it is shown that the control limits are effectively identical to those obtained by Kang et al. (2007 ) for the specific dataset they used. This article illustrates the flexibility and unique features of the Bayesian simulation method for obtaining posterior distributions, predictive intervals, and run-lengths in the case of the coefficient of variation. A simulation study shows that the 95% Bayesian confidence intervals for the coefficient of variation have the correct frequentist coverage.