Continuous single attribute control chart for Markov-dependent processes

Most of the times, the observations related to the quality characteristic of a process do not need to be independent. In such cases, control charts based on the assumption of independence of the observations are not appropriate. When the characteristic under study is qualitative, Markov model serves as a simple model to account for the dependency of the observations. For this purpose, we develop an attribute control chart under 100% inspection for a Markov dependent process by controlling the error probabilities. This chart consists of two sub-charts. For a given sample, depending upon the state of the last observation of previous sample (if any), one of these two will be used. Optimal values of the design parameters of the control chart are obtained. Chart’s performance is studied by using its capability (probability) of detecting a shift in process parameters.