A further note on the exponentially weighted moving average control charts for monitoring gradual shifts in a process mean

This article provides a historical discussion of exponentially weighted moving average (EWMA) control charts and makes minor modifications. Because the charting statistics are correlated, both the autocovariance and autocorrelations functions are derived; it is determined that the steady-state autocorrelation also diminishes geometrically. Assuming normality of individual observations, two successive EWMA statistics have the bivariate normal distribution with an autocorrelation of lag 1. We then used the bivariate normal density to approximate the type II error probability, thereby obtaining the first-order conditional average run length.