Bayesian process monitoring schemes for the two-parameter exponential distribution. (English) Zbl 07530849
Summary: 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 [K. Krishnamoorthy and T. Mathew, Statistical tolerance regions. Theory, applications, and computation. Hoboken, NJ: John Wiley & Sons (2009; Zbl 1291.60001)] 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.
MSC:
| 62-XX | Statistics |
Keywords:
Bayesian procedure; control chart; Jeffrey’s prior; run-length; two-parameter exponential distributionCitations:
Zbl 1291.60001Software:
StIntReferences:
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