Optimal parameters of EWMA Control Chart for Seasonal and Non-Seasonal Moving Average Processes

Abstract

The main goal of this paper is to study optimal parameters of an Exponentially Weighted Moving Average (EWMA) control chart for seasonal and non-seasonal Moving Average (SMA and MA) processes. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be large enough, so-called Average Run Length for in-control process (ARL 0). Otherwise, it should be small when the process is out-of-control, so-called Average Run Length for out-of-control process (ARL 1). We obtain explicit formulas of ARL for EWMA chart for Moving Average (MA) process with exponential white noise. In particular, the explicit analytical formulas for evaluating ARL 0 and ARL 1 are able to obtain a set of optimal parameters which depend on a smoothing parameter (λ) and a width of control limit (b) for designing EWMA chart with a minimum ARL 1 value. In addition, the explicit formulas for the EWMA control chart was applied with the practical data of the unemployment rate of Thailand.