A method for calculating average run length by the use of Markov Chain

This study is concerned with the development of a methodology for finding the mean action time (or average run length) for the general chart with different zonings, one standard deviation apart, as a function of the changes in the process being controlled. In this methodology we have used the properties of finite state Markov Chain, and the important steady state equations. We considered six states for the transition matrix of the Markov Chain for calculation of ARL. These states were considered as the different zones of the control chart. By the comparison of the run sum control chart with Shewhart and warning limit chart we concluded that the RS control chart has a sensitivity advantage over the other charts in the main range of the shift of the process mean. So to prevent loss of profit form defects in the quality of production we may recommend use of the run sum approach with a small value for the action limit. This approach can be used for most of the factories which are using around the 3σ quality assurance.