Economic design of a two-stage control chart based on both performance and surrogate variables

The traditional approach to economic design of control charts is based on the assumption that a process is monitored using only a performance variable. If, however, the performance variable is costly to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled by using both performance and surrogate variables. In this article we propose a model for economic design of a two-stage control chart which uses a highly correlated surrogate variable together with a performance variable. The process is assumed to be monitored by the surrogate variable until it signals out-of-control behavior, then by the performance variable until it signals out-of-control behavior or maintains in-control signals for a prespecified amount of time, and the two variables are used in alternating fashion. An algorithm based on the direct search method of Hooke and Jeeves is used to find the optimum values of design parameters. The proposed model is applied to the end-closure welding process for nuclear fuel to compute the amount of reduction in cost compared with the current control procedure.