Constrained optimal design of X¯ Control Chart for correlated data under Weibull Shock Model with multiple assignable causes

Abstract

An appropriate technique for monitoring a stochastic system is to utilize the control charts. In statistical process, control a drift in characteristics of output may be due to one or several assignable causes. In the establishment of $\overline{X}$ charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice there are many cases where 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 $\overline{X}$ control chart under Weibull shock model with multiple assignable causes and correlated samples have not been presented yet. Based on the optimization of the average cost per unit of time and taking into account the 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.

Keywords:

• Economic statistical design
• $\overline{\mathrm{X}}$ control chart
• Multiple assignable causes
• Weibull shock model
• Correlated data