Optimal Cusum schemes for monitoring variability

Cumulative Sum (Cusum) Control Schemes are widely used in industry for process and measurement control. Most Cusum applications have been in monitoring shifts in the mean level of a process rather than process variability. In this paper, we study the use of Markov chain approach in calculating the average run length (ARL) of a Cusum scheme when controlling variability. Control statistics S and S 2 , where S is the standard deviation of a normal process are used. The optimal Cusum schemes to detect small and large increases in the variability of a normal process are designed. The control statistic S 2 is then used to show that the Cusum scheme is superior to the exponentially weighted moving average (EWMA) in terms of its ability to quickly detect any large or small increases in the variability of a normal process. It is also shown that Cusum with control statistics sample variance ( S 2 ) and sample standard deviation ( S ) perform uniformly better than those with control statistic log S 2 . Fast initial response (FIR) Cusum properties are also presented.