Optimal combined set-up and calibration policy

The optimal level to which the mean of a critical variable should be set-up, and the optimal number of repetitions until recalibration, has been jointly determined for the case where the variable is distributed normally and the mean changes linearly with the number of repetitions. It was proven that the optimal set-up level should be below the midpoint between the specification limits by a distance which depends on the slope of change of the mean and on the recalibration cycle, in such a manner that just prior to the recalibration the mean reaches the same distance above the midpoint. A method has been outlined for the numerical evaluation of the optimal number of cycle repetitions, and a general approximation formula was derived, which allows its closed-loop determination. A numerical example and sensitivity analysis are provided.