The detection of shifts in autocorrelated processes with MR and EWMA charts

摘要

Since the performance of SPC charts is known to be seriously deteriorated because of autocorralated observations, the detection of an assignable cause is a critical task that most industrial practitioners have to deal with. For this reason, selecting the most appropriate control chart to seperate a shift among autocorrelated observations is a serious problem which needs a thoughtful judgement. In this research, two subclasses of ARIMA models, e.g., AR (1) and IMA (1, 1), were deployed to characterize autocorrelated processes which were categorized into two cases, stationary and non-stationary. The simulation was done to assess how each type of control chart responded to a shift in the form of average run length (ARL) while the factorial analysis was conducted to quantify the impacts of critical factors e.g., AR coefficient (phi), MA coefficient (theta), types of charts and shift sizes on the ARL. For non-stationary case, when shift sizes were small (0.5), the ARL at theta = +1 was significantly higher than the one at theta = −1. However, when the observations were stationary, the above result was valid only when an MR chart was utilized. According to the empirical analysis, another significant finding is that the exponentially weighted moving average (EWMA) was the most potential control chart to monitor both AR (1) and IMA (1, 1) processes since it is sensitive to small and large shift sizes. It is important to note that practitioners should fully understand how SPC charts respond to autocorrelated disturbances with deterministic shifts in order to achieve the highest performance.