Evaluating Sensitivity of Double EWMA Chart for ARL Under Trend SAR(1) Model and Applications

The goal of this study is to offer the precise average run length (ARL) on the Double Exponentially Weighted Moving Average (double EWMA) control chart for the data underlying the first-order seasonal autoregressive (SAR(1)L) with trend model. A comparison was made between the explicit formula and the computed ARL obtained using the numerical integral equation (NIE) approach, employing four quadrature methods: the midpoint, Simpson’s, trapezoidal, and Boole’s rules. The comparison was based on accuracy percentage (%Acc) and computation time (in seconds). The results showed that there was not much variation in accuracy between the ARL results of the explicit ARL and ARL via the NIE method. The findings indicate that the explicit ARL and NIE approaches produce very consistent accuracy values; however, the explicit formula is significantly more rapid (instantaneous compared to 1.5–26 seconds). The advantage of the double EWMA chart compared to the extended EWMA chart in identifying process changes is demonstrated, encompassing evaluations under both one-sided and two-sided setups with varied LCL values. The results are additionally corroborated by sensitivity measures (AEQL, PCI, RMI) and checked with actual durian export data, guaranteeing that the conclusions are firmly established in both simulated and empirical evidence.