Designing Bayesian sampling plans for simple step-stress of accelerated life test on censored data

ABSTRACT

This paper studies the problem about how to design a Bayesian sampling plan (BSP) for two exponential distributions linked by the cumulative exposure model through a simple step-stress accelerated life test (ALT). Such a Bayesian sampling plan through the ALT by a simple step-stress procedure is called BSPA. The BSPA with Type-II censoring in a general loss function is derived. Given joint gamma and uniform prior distributions, an explicit Bayes decision function under a certain loss function is derived. Illustrative examples are given to demonstrate how to find the Bayes decision function. A Monte Carlo simulation study is performed for searching the optimal BSPA. Comparison between the proposed BSPA and the conventional BSP is carried out to study the performance of BSPA. The numerical results indicate that the risk reduction of BSPA by applying the accelerated procedure is more significant if the experimental time cost is more expensive.

KEYWORDS:

• Accelerated life test
• Bayesian sampling plan
• exponential distributions
• simple step-stress test
• Type-II censoring

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F15
• 62C10
• 62N05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of first author was partially supported by the grant (MOST 106-2118-M-130-001) of Ministry of Science Technology in Taiwan.