Auxiliary Information Based Variable Sampling Interval EWMA Chart for Process Mean Using Expected Average Time to Signal

An exponentially weighted moving average (denoted as EWMA) chart is quite effective to detect small to moderate shifts. The adoption of the variable sampling interval (denoted as VSI) technique into the auxiliary information based EWMA chart (denoted as AIB-VSIEWMA) significantly improves the efficiency of the auxiliary information based EWMA (denoted as AIB-EWMA) chart in detecting small and moderate shifts, using the average time to signal (ATS) criterion when the precise shift size which must be detected quickly can be specified. However, in many industrial processes, the aforementioned size of the shift cannot be specified, particularly when practitioners have no prior knowledge about the process. This paper adopts the expected ATS (EATS) criterion based on the Markov chain approach to assess the efficiency of the AIB-VSIEWMA chart when the precise size of the shift cannot be specified. The AIB-VSIEWMA chart is compared with the AIB-EWMA chart using the ATS and EATS performance criteria. It is revealed that the AIB-VSIEWMA chart outperforms the AIB-EWMA chart as the former provides quicker detection of process shifts.