The economic design of multivariate acceptance sampling plans

A total expected cost model for multivariate acceptance sampling is developed. The components of cost included in the model are presented in two phases: the cost of making the quality control decision (sampling inspection) and the cost of implementing the quality control decision (accept the inspection lot, scrap the lot, or screen the lot). Several variables are to be controlled within their given specification limits, where the sample mean for each of the variables in the criterion by which lot acceptance for that variable is determined. The decision variables are the sample size and the lower and upper control limits for each of the characteristics subjected to the control. The pattern search is used to determine the values of the decision variables which minimize the total expected cost of quality control per inspection lot submitted for control.

The lot mean, sample mean, and individual unit measurements for each of the quality characteristics are considered to be random variables. Sensitivity analysis is performed to determine the robustness of the model to changes in the form of the distributions on the lot means given that the desired mean and variance of these distributions has been accurately estimated.