Robust economic-statistical design of the EWMA-R control charts for phase II linear profile monitoring

Control charts are powerful tools to monitor quality characteristics of services or production processes. However, in some processes, the performance of process or product cannot be controlled by monitoring a characteristic; instead, they require to be controlled by a function that usually refers as a profile. This study suggests employing exponentially weighted moving average (EWMA) and range (R) control charts for profile monitoring, simultaneously. For this purpose, the parameters of these control charts should be determined in a way that the expected total cost is minimized. In order to evaluate the statistical performance of the proposed model, the in-control and out-of-control average run lengths are applied. Moreover, the existence of uncertain parameters in many processes is a barrier to attain the best design of control charts in practice. In this paper, the economic-statistical design of control charts for linear profile monitoring under uncertain conditions is investigated. A genetic algorithm is used for solving the proposed robust model, and the Taguchi experimental design is employed for tuning its parameters. Furthermore, the effectiveness of the developed model is illustrated through a numerical example.