Economic design of sampling plans and screening procedures with multi-decision alternatives

Abstract

This thesis is concerned with economic designs of sampling plans and screening procedures using a correlated variable to grade the quality of the products in situations where there are several markets with different profit/cost structures. Optimal sampling plans and screening procedures are obtained by maximizing the expected profit. This thesis is divided into the following four parts. (i) Two economic attributes sampling plans are considered;fixed size and inverse sampling plans. In a fixed size sampling plan, a random sample of sizen is drawn from the lot and the decesion for disposing the lot is mode based on the number of nonconforming items found in the sample. In an inverse sampling plan, items are sequentially drawn from the lot until the $c^{th}$ nonconforming item is obtained and the decision for disposing the lot is made based on the total number of items drawn. Profit models are constructed which involve four profit/cost components; profit from a conforming item, inspection cost, replacement cost, and cost from an accepted nonconforming item. For fixed size and inverse sampling plans, methods of finding optimal sampling plans are presented and examples with beta-binomial prior distribution are given. (ii) An economic variables sampling plan is considered. In a variables sampling plan, a random sample of size n is drawn from the lot and the decision for disposing the lot is made based on the sample mean. It is assumed that the quality characteristic is normally destributed with known variability and unknown mean having a normal prior distribution. Profit model is constructed which involve four profit/cost components;profit from a conforming item, inspection cost, replacement cost, and cost from an accepted nonconforming item. Methods of finding optimal plan are presented and a numerical example is given. (iii) Economic screening procedures with continuous performance and screening variables are considered. It is assumed that the performance variable ...