Alternative to Detecting Changes in the Mean of an Autoregressive Fractionally Integrated Process with Exponential White Noise Running on the Modified EWMA Control Chart

The modified exponentially weighted moving-average (modified EWMA) control chart is an improvement on the traditional EWMA chart. Herein, we provide more details about using various values of additional design parameter for detecting small-to-moderate shifts in process mean autoregressive fractionally integrated (ARFI(p, d)) with exponential white noise running thereon. statistical performances two charts were evaluated terms average run length (ARL) obtained by solving integral equations (IEs). This provides exact formula proven existence and uniqueness verified applying Banach’s fixed-point theorem. accuracy proposed ARL was compared derived numerical IE technique out-of-control state. Although their accuracies identical situations long-term memory processes, method required less than 0.01 s to compute whereas took 3–4 s. strengths are that it simple calculate computational time significantly reduced. Comparing standard deviations median lengths yielded same results. Finally, practical examples real-life data corresponding ARFI(p, d) processes provided demonstrate applicability formula.