Economic design under gamma shock model of the control chart for sustainable operations

The non-uniform sampling scheme and economic statistical design approaches have been successfully applied to determine three parameters of x-bar control charts to monitor a manufacturing process with increasing hazard functions for the last three decades. Nevertheless, a primary assumption for these cost models is that measurements within a sample are independent. However, the conventional supposition may significantly underestimate the type I error probability for the x-bar control chart. Hence, we develop a cost model that combines different researches with the multivariate normal distribution model that given the maximum probability of type I error and the minimum value of power. The optimal parameters of non-uniform sampling interval x-bar control charts are used for the measurements within a sample being correlated. In addition, an industrial example is applied to indicate the solution procedure. Sensitivity analysis is accompanied with input parameters including correlated coefficients as well as process and cost parameters of the model are performed. The genetic algorithm is adopted to reveal the optimal solution of the economic design. The method proposed can be used on related industries to achieve the ability of production monitoring and cost reducing. The human resource consuming and the amount of scraps will be avoided toward the conclusive goals of economic benefit, environmental benefit and social benefit.