A Markov-based control chart for dependent binary data

There are different statistical approaches for monitoring proportion when the observations are binary. Usually, it is considered that the data are independent. But there are situations in which the data are intrinsically correlated. In this paper, two Markov-based charts, the Markov EWMA and the Markov Shewhart, are presented as reasonable charts for dependent binary observations and a new method named Markov CUSUM chart is developed. It is shown that the one-sided Markov CUSUM chart has better performance than the two other charts in most situations by calculating ARL values. However, the significant extension of this paper over past works is in providing an effective first-order Markov model for dependent data based on individual binary observations.