Economic Design of Control Charts with Different Control Limits for Different Assignable Causes

The use of multiple control limits and multiple corresponding levels of response for processes is an effective way for statistical process control when different assignable causes exist which lead to different out-of-control states of the processes, and different restoration procedures. This paper examines the optimal economic design of such process control charts. The exact mathematical model is developed and the expected cost per time unit function is derived. The costs associated with the statistical process control are minimized by means of an optimization procedure involving a quasi-Newton method and a Fibonacci lattice search. Sensitivity analysis performed on a large number of numerical examples reveals key relationships between model parameters. A comparison between the proposed control chart and an approximate matched single-cause chart shows that the former can be a significant improvement over the latter. Several model extensions and managerial implications are also discussed.