Optimum reliability acceptance sampling plans under progressive type-I interval censoring with random removal using a cost model

ABSTRACT

A reliability acceptance sampling plan (RASP) is a variable sampling plan, which is used for lot sentencing based on the lifetime of the product under consideration. If a good lot is rejected then there is a loss of sales, whereas if a bad lot is accepted then the post sale cost increases and the brand image of the product is affected. Since cost is an important decision-making factor, adopting an economically optimal RASP is indispensable. This work considers the determination of an asymptotically optimum RASP under progressive type-I interval censoring scheme with random removal (PICR-I). We formulate a decision model for lot sentencing and a cost function is proposed that quantifies the losses. The cost function includes the cost of conducting the life test and warranty cost when the lot is accepted, and the cost of batch disposition when it is rejected. The asymptotically optimal RASP is obtained by minimizing the Bayes risk in a set of decision rules based on the maximum likelihood estimator of the mean lifetime of the items in the lot. For numerical illustration, we consider that lifetimes follow exponential or Weibull distributions.

Keywords:

• Bayes risk
• Fisher information matrix
• maximum likelihood estimator
• variable sampling plan
• warranty cost

Acknowledgements

The authors are thankful to the Associate editor and reviewers for their invaluable comments and suggestions that led to considerable improvement in the presentation of the manuscript. They would also like to thank Professor Isha Dewan, Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi for her suggestions and cooperation.

Disclosure statement

No potential conflict of interest was reported by the authors.