Curtailed Bayesian sampling plans for exponential distributions based on Type-II censored samples

ABSTRACT

This paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function.

KEYWORDS:

• Acceptance sampling
• Bayesian sampling plan
• curtailed decision function
• general loss function
• Type-II censoring

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N05
• 62N01
• 62C10

Acknowledgments

The authors would like to thank the Associate Editor and referee for their careful review and valuable suggestions which lead to the improvement of the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Lee-Shen Chen was partially supported by the grant (MOST 104-2118-M-130-003-) of Ministry of Science and Technology in Taiwan.