A process monitoring procedure based on a surrogate variable for dichotomous performance variable

A monitoring procedure using a surrogate variable is proposed for a process with a binary performance variable. Using the procedure, every item is inspected on a surrogate variable. When an item is rejected, the latest number of consecutively accepted items up to this point is compared with a predetermined number, r, to decide whether to stop the process for an investigation. The conditional distribution of the surrogate variable given the performance variable is assumed to be normal. A cost model is developed, which incorporates costs of inspection, misclassification, investigation, opportunity, and correction. We develop methods of finding the optimum r value and screening limit and analyze the effects of cost parameters on the optimal solution.