Design of economically and statistically optimal sampling plans

Abstract

This paper attempts to develop four types of acceptance sampling plans under the objectives of minimizing the total loss to the producer and consumer and maximizing the rate of approaching to the ideal operating characteristic (OC) curve when the quality characteristic follows a normal distribution and has lower specication limit. To provide the desired protection for both the producer and the consumer, two constraints are considered that balance both producer and consumer risks by using two specied points on OC curve. The first objective function of this model is constructed based on the total expected loss by incorporating the one-sided minimum specication Taguchi loss function, and the second one is constructed based on conformity to the ideal OC curve by using minimum angle method. Also, the optimal solution of the proposed plans is determined for 10 different scenarios of process parameters. Furthermore, the optimal solution of these plans is determined when only one of the objective functions is considered.