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Bayesian process monitoring schemes for the two-parameter exponential distribution

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

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.

Suggested Citation

  • R. van Zyl & A. J. van der Merwe, 2019. "Bayesian process monitoring schemes for the two-parameter exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(7), pages 1766-1797, April.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:7:p:1766-1797
    DOI: 10.1080/03610926.2018.1440307
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    Cited by:

    1. Ignacio Cascos, 2021. "Simultaneous monitoring of origin and scale in left-bounded processes via depth," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 649-673, December.

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