Economic development of specifications for 100% inspection based on asymmetric quality loss functions

As a means of providing protection for both the producer and the consumer, for example as in airport security, 100% inspection plays an important role in today's environment. The same is true for some industrial or other decision-making processes where the consequences of excessive deviations from target values are very high. Motivated by Deming's “all or none” inspection rule and associated philosophy for quality improvement, we develop an inspection strategy by considering the costs to both the producer and the customer, and thus to the whole system. A general optimization model is formulated to determine whether 100% inspection is to be performed or no inspection to be performed. If complete inspection is chosen then the optimal specification limits can be determined at the same time. Specifically, we consider two types of asymmetric quality loss functions for the “target the best” quality characteristic: the asymmetric quadratic quality loss function, and the asymmetric piecewise linear loss function. For each loss function, we propose an optimization model to determine the optimal process mean and specification limits. Numerical examples are given to illustrate the proposed models that can be used to improve the quality of the output of any process.