Abstract: Correlated data frequently result in misleading process control conclusions; thus, selecting effective control charts is crucial nowadays. The present work presents a mathematical approach to calculate the average run length (ARL) of an adaptive MEWMA (AMEWMA) control chart for the seasonal autoregressive model (SAR(P)L) aimed at identifying autocorrelated process variations in the zero state. The methodology for developing new one-sided and two-sided MEWMA control charts is delineated, and the ARL values derived from the explicit formulas are juxtaposed with the outcomes of four NIE approaches. Furthermore, the accuracy is analyzed by evaluating the standard deviation of run length (SDRL) and mean run length (MRL). At the same time, the control charts’ overall efficacy across all variation levels is assessed using EARL, ESDRL, and EMRL metrics. The findings demonstrated that the AMEWMA control charts surpass the MEWMA and EWMA control charts while $$c_{2}$$ is decreasing. The ARL formula is also employed for seasonal statistics, namely the crude palm oil production index and refined palm oil shipment index.

Keywords: Change-point detection, Average Run Length, zero-state, Seasonal Autoregressive model, adaptive Modified Exponentially Weighted Moving Average, explicit formula

Pages: 144-163