Optimal design and evaluation of adaptive EWMA monitoring schemes for Inverse Maxwell distribution

Abstract

Monitoring schemes have been successfully implemented when the underlying data follows a non-normal distribution like the Inverse Maxwell (IM) distribution. The article proposes a new adaptive exponentially weighted moving average (AEWMA) scheme, namely the AIMEWMA, to monitor the IM distributed process. The design parameters of the AIMEWMA scheme are determined via a Markov chain model and its performance is analyzed by its run length (RL) characteristics. The overall model ability is examined using some popular performance tools. The results show that, for most of shifts, the AIMEWMA scheme is more efficient than other available competitors. Moreover, some guidelines regarding the selection of the most effective scheme in practice have been discussed. The applicability of the new scheme is also presented on a real data set.