Bayesian process monitoring schemes for the two-parameter exponential distribution. Issue 7 (3rd April 2019)

• Record Type: Journal Article
• Authors: van Zyl, R.; van der Merwe, A. J.
• Is Part Of: Communications in statistics. Volume 48:Issue 7(2019)
• Page Start: 1766
• Page End: 1797
• Publication Date: 2019-04-03
• Subjects: Bayesian procedure -- Control chart -- Jeffrey's prior -- Run-length -- Two-parameter exponential distribution; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1440307
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper a Bayesian procedure is applied to obtain control limits for the location and scale parameters, as well as for a one-sided upper tolerance limit in the case of the two-parameter exponential distribution. An advantage of the upper tolerance limit is that it monitors the location and scale parameter at the same time. By using Jeffreys' non-informative prior, the predictive distributions of future maximum likelihood estimators of the location and scale parameters are derived analytically. The predictive distributions are used to determine the distribution of the "run-length" and expected "run-length". A dataset given in Krishnamoorthy and Mathew (2009 ) are used for illustrative purposes. The data are the mileages for some military personnel carriers that failed in service. The paper illustrates the flexibility and unique features of the Bayesian simulation method.