An Algorithm For Determining Bayesian Attribute Single Sampling Acceptance Plans PDF Download

A dynamic approach to the Bayesian theory of sampling inspection by attributes for the single sampling case is presented. A model is developed which assumes a sequence of lots of equal known size and lots generated by a process operating in a random manner. The model also assumes constant associated costs for all lots and that the posterior distribution of the process quality of a given lot becomes the prior distribution of the process quality of the next lot. This allows the information from one lot to be used in the decision making for subsequent lots. The model is formulated by using a mixed binomial distribution with beta weights as the prior distribution of the lot quality. An improved algorithm for the solution of the single lot case, bounds for the optimal sample size, a lower bound for the expected cost of sampling for the single lot case and a lower bound for the expected cost for the sequence of lots are presented. Optimality conditions for the non-sampling alternatives, the 100% sampling case, and the convergence of the optimal acceptance plan when the number of lots in the sequence tends to infinity are investigated. The model is formulated as a dynamic programming problem with sampling, reject without sampling and accept without sampling as the possible actions; and the lots as the stages. Relationships between the optimal actions at different lots which are independent of the form of the expected cost of sampling function are presented. Exact and approximate solution algorithms are developed and tested. Experimental results indicate that the use of the bounds for the optimal sample size, the lower bound for the expected cost of sampling and the results on optimality of the non-sampling alternatives lead to the pruning of a large part of the decision tree. Approximate methods developed can be classified as forward-back ward procedures. The forward pass reduces the state space by fixing the sample size for all lots but the last one, according to a specified set of rules. The backward pass uses the dynamic programming formulation for finding the optimal policy for the reduced state space. The effectiveness of the approximate methods were evaluated in terms of the quality of the solutions and the computational effort to obtain the solutions. Results indicate that efficiency of two of the approximate methods is very high while computational requirements are drastically reduced.