A more accurate formulation for a class of models for the economic design of control charts

Abstract

Some of the published models for the economic design of control charts use the expected cost per unit of output as the objective function to be minimized. In these models, the computation of steady-state probabilities that the process is in each possible state does not take into account the effect of the corrective action that may follow a signal from the control chart. As a result, the expected cost per unit is overestimated and the selection of the chart parameters is not optimal. The purpose of this paper is to eliminate this inaccuracy by proposing the exact formulation and to estimate the magnitude of errors resulting from the inaccurate formulation of the objective function. By solving numerical examples of joint design of X and R charts, it is shown that these errors are typically very large and consequently it is imperative to use the exact formulation, proposed in this paper, to avoid inefficient and costly control chart designs. Finally, an additional opportunity for further cost improvements in process control is identified and discussed.