Markov Chain Method for Monitoring Mean Vector in Multivariate Cumulative Sum Control Chart

In many quality conical settings, the manufacturing process may have two or more correlated variables. The usual practice has been to maintain a separate (univariate) chart for each characteristic. Unfortunately, this could result in some false (out-of-control) alarms when the characteristics are highly correlated. Therefore. the purpose of this work is to apply MCUSUM scheme to simultaneously monitor the quality characteristics that can identify a change in mean vector of steel manufacturing process, machining process and detergent production process. Results obtained by Markov Chain procedure gave the desired in-control Average Run Length as 250, 200, 200 and the decision limit (h) as 3.97, 4.86 6.64 respectively.  While the graphical results showed that the 3^rd,11th and 6^th sample respectively are the point at which out-of-control signal set in.  Hence, the ability of the MCUSUM chart to detect small to moderate shift in the mean vector was demonstrated.

 

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