Economic designs of life test sampling plans and scteening procedures

Abstract

This thesis is concerned with economic designs of life test sampling plans and screening procedures. Optimal sampling plans and screening procedures which minimize expected average cost are obtained. This thesis is organized as follows. (i) Two economic life test sampling plans for nonrepairable products which are sold under the general rebate warranty policy are considered ; one for exponential distribution based on curtailed Type II censoring and the other for Weibull distribution with unknown scale parameter based on Type II censoring. Cost models are constructed which involve test cost, accept cost, and reject cost. Optimal sampling plans which minimize the expected average cost are obtained and sensitivity analyses for the parameters of the prior distributions are performed. (ii) Economic designs of life test sampling plans for repairable products which are sold under the general rebate warranty policy are proposed. The power law process is considered as a model for describing the failure times of the products. It is assumed that the products in each lot have the same failure intensity function, but the parameters of the function vary from lot to lot according to a known prior distribution. Cost models are constructed and methods of finding optimal sampling plans which minimize the expected average cost are presented. Sensitivity analyses for the parameters of the prior distribution are also performed. (iii) An economic sequential screening procedure is considered for limited failure populations in which defective items fail soon after they are put in operation and nondefective ones never fail. A cost model is constructed which involves screening test cost and external failure cost. A sequential scheme which minimizes the expected average cost is derived in which at each stage we can either stop and accept the batch or continue to the next stage based on accumulated failure information up to that stage. The optimal decision at each stage is obtai...