Constrained Optimal Design of bar{X} Control Chart for Correlated Data under Weibull Shock Model with Multiple Assignable Causes and Taguchi Loss Function

A proper method of monitoring a stochastic system is to utilize the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of $bar{X}$  charts, an assumption is made that there is no correlation within the samples. However, in practice, there are many industrial cases in which the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of $bar{X}$  control chart for correlated data under Weibull shock model with modified Taguchi loss function have not been presented yet. Using modified Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling.