SELECTION OF SAMPLING INTERVAL AND ACTION LIMIT FOR DISCRETE FEEDBACK ADJUSTMENT

An important problem in process adjustment using feedback is how often to sample the process and when to apply an adjustment. Schemes designed to minimize the overall cost were developed by Box and Kramer, but unfortunately it is not always easy to assign values to the individual costs required to define such schemes. These are the costs of making an adjustment, of taking an observation, and of being off target. In this article, charts are provided in which the same schemes are alternatively characterized by the mean squared deviation from target they produce, the frequency with which they require observations to be made, and the resulting overall length of time between adjustments. This characterization allows a particular scheme to be chosen by judging the advantages and disadvantages of alternative options in the light of the special circumstances of the application. The schemes are derived on certain assumptions relating, in particular, to the model for the disturbance affecting the process. An investigation is undertaken of the effect of two important kinds of failure of this model. We conclude that the procedures we discuss are reasonably robust against such failures.