EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response

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Abstract
The control limits of an exponentially weighted moving average (EWMA) control chart should vary with time, approaching asymptotic limits as time increases. However, previous analyses of EWMA charts consider only asymptotic control limits. In this article, the run length properties of EWMA charts with time-varying control limits are approximated using non-homogeneous Markov chains. Comparing the average run lengths (ARL's) of EWMA charts with time-varying control limits and results previously obtained for asymptotic EWMA charts shows that using time-varying control limits is akin to the fast initial response (FIR) feature suggested for cumulative sum charts. The ARL of the EWMA scheme with time-varying limits is substantially more sensitive to early process shifts, especially when the EWMA weight is small. An additional improvement in FIR performance can be achieved by further narrowing the control limits for the first twenty observations. The methodology is illustrated assuming a normal process with known standard deviation where we wish to detect shifts in the mean.