An integrated Markov chain model for the economic-statistical design of adaptive multivariate control charts and maintenance planning

In this paper, the mean of a process with several quality characteristics is monitored using a multivariate control chart which is a variable parameter (Vp) chi-square control chart with two types of sampling schemes. For this purpose, using the property of Markov chains, an integrated model is developed that coordinates the decisions related to the economic-statistical design of the control chart and maintenance planning. In the case of failure, the system will shut down automatically and a corrective maintenance activity will be performed immediately. Preventive maintenance activity is implemented when an out-of-control state is correctly identified. To evaluate the economic efficiency of the proposed model, a comparison between its optimum cost and the optimum cost of a multivariate exponentially weighted moving average (MEWMA) control chart and also a model that applies a chi-square control chart with fixed parameter is provided. Moreover, constraints related to ARL(0) and ARL(1) have been taken into account to ensure the statistical performance of the model. The results of the numerical analyses show a significant improvement in the cost per time unit.