Bicriterion design of process control charts

In this paper, the authors develop a bicriterion approach to the design of process control charts through the use of a multi-attribute utility function. This approach accounts for both the multi-objective aspect (involving minimization of expected administrative cost and maximization of outgoing quality) and the uncertainty/risk aspect (involving uncertainty in the process output) of the problem. As such, the approach allows for several advantages over current design methodologies, including the elimination of a dichotomous view of quality. To illustrate the new methodology, the authors present a specific model for the joint design of an nX chart and an R chart. Results are given for a hypothetical situation involving various utility functions. The results concerning the optimal design for the control charts are robust with respect to the forms (e.g., linear, concave, or convex) of the individual attribute utility functions over the cost and quality attributes. However, the respective weights attached to these individual attribute utility functions within the overall utility function have a significant impact on the optimal design.