A Control Chart Using Copula-based Markov Chain Models

Statistical process control is an important and convenient tool to stabilize the quality of manufactured goods and service operations. The traditional Shewhart control chart has been used extensively for process control, which is valid under the independence assumption of consecutive observations. In real world applications, there are many types of dependent observations in which the traditional control chart cannot be used. In this paper, we propose to apply a copula-based Markov chain to perform statistical process control for correlated observations. In particular, we consider three methods to obtain the estimates of upper control limit (UCL) and lower control limit (LCL) for the control chart. It is shown by simulations that Joe’s parametric maximum likelihood method provides the most reliable estimates of the UCL and LCL compared to the other methods. We also propose simulation techniques to compute the average run length (ARL) of the proposed charts, which can be used to set the UCL and LCL for a given value of ARL. The piston rings data are analyzed for illustration.