Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model

Abstract

ABSTRACTThis paper aims to derive explicit analytical solutions for Average Run Length (ARL) of CUSUM chart for the SARFIMA(P,D,Q)S process with exponential white noise. Measurement of performance was done with the ARL in terms of percentage error and CPU time. The results obtained from the explicit formulas were compared focusing on the performance using the numerical integral equation (NIE) method. Both methods had similarly excellent agreement with the percentage error at less than 0.25%. Meanwhile, the explicit formulas consumed less CPU time than the NIE method. It is clear that the explicit formulas are a good alternative in real applications.