Development of the Optimum Product Specification for an Exponential-Type Quality Characteristic

This paper investigates the problem of determining the most economical product specification (upper specification limit) for an exponential-type quality characteristic using the concept of a truncated quadratic loss function within the framework of a screening inspection scheme. Implementing a tight limit on products may provide a high outgoing quality, but it creates a high rejection cost on the rejected products. In contrast, implementing a loose limit may reduce the rejection cost, but it can result in a low outgoing quality. An immediate problem is then how to trade off these conflicting cost criteria to determine the most economical upper specification limit. This important issue has neither been satisfactorily addressed or received much attention in the literature. This paper presents the concept of the truncated quadratic loss function, applies the concept to screening inspection problems, derives the truncated statistics of interest, and presents the optimization model of the most economical upper specification limit for an exponential-type quality characteristic. A numerical example is presented.