Bayesian reliability acceptance sampling plans under interval censoring

Abstract.

This work considers Bayesian reliability acceptance sampling plan (RASP) under interval censoring. It is considered that the consumer and manufacturer agree on a common lifetime distribution of the product. However, they differ in their assessment of the prior distributions and utility functions because of the adversarial nature of the consumer and manufacturer, but the manufacturer knows the consumer’s utility and prior. The consumer accepts or rejects a lot of products based on his/her own priors about the quality of the product and a utility function. If the consumer rejects the lot, the manufacturer gives additional information on lifetime based on a life test to update the consumer’s belief. The consumer decides on accepting or rejecting the lot based on updated information. The life test is conducted under an interval censoring scheme, where the decision on acceptance or rejection of the lot can be taken sequentially at pre-specified inspection times. The manufacturer’s task is to determine the optimal interval-censoring life testing plan which maximizes his/her utility. Last, we discuss a methodology where the manufacturer does not require knowledge of the consumer’s utility function and prior distribution for planning the life test.

Keywords:

• Bayesian decision theory
• Bayesian negotiation model
• interval censoring
• likelihood function
• utility function

Acknowledgment

We would like to thank the anonymous reviewers for their helpful comments and suggestions, which enhanced the quality and presentation of the article.

Disclosure statement

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