Jointly optimal design of perfect maintenance policy and CUSUM control chart

For quality control and maintenance management of small process shift, jointly optimal design of perfect maintenance policy and CUSUM control chart is put forward, in which four scenarios of production process are considered, quality loss cost is introduced into total cost and quality loss functions are defined based on the parameters of CUSUM chart. The cost caused by the downtime for detection and/or maintenance is also proposed. By minimizing the expected total cost per unit time, a model is established to search the optimal combination of decision variables to realize the joint economic design of CUSUM control chart and maintenance policy. Pattern-search algorithm is used to find the solution. Finally, a numerical case is shown to illustrate the proposed methodology and sensitivity analysis is conducted.