Simultaneously considered the properties of cost and quality for a control chart design with a gamma shock model and correlated data

Recently, both the non-uniform sampling scheme and economic statistical design approaches have been successfully applied to determine three parameters of X̅ control charts (including sample size, sampling interval between successive samples, and the control limits) for monitoring a manufacturing process with increasing hazard functions. Nevertheless, a primary assumption for these cost models is that measurements within a sample are independent. However, the conventional supposition may underestimate significantly the type I error probability for an X̅ control chart. Hence, in this investigation, we develop a cost model that combine Rahim and Banerjee´s cost model with Yang and Hancock´s multivariate normal distribution model under maximum probability of type I error and minimum value of power to search the optimal parameters of non-uniform sampling interval X̅ control charts for the measurements within a sample being correlated. In addition, an industrial example is applied to indicate the solution procedure. Meanwhile, a genetic algorithm is adopted.