A renewal theory approach is proposed to derive the cost model for multiple dependent subprocesses. The optimal individual Y control chart and multiple cause-selecting control chart are thus constructed to monitor the overall product quality and specific product quality contributed by the multiple dependent subprocesses. They can be used to maintain the process with minimum cost and effectively distinguish which component of the subprocesses is out of control. The optimal design parameters of the proposed control charts can be determined by minimizing the cost model using a simple grid search method. An example is given to illustrate the application of the optimal individual Y control chart and multiple cause-selecting control chart.
Quality and Reliability Engineering International, 14(5), 347-355