Max‐EWMA chart for time and magnitude monitoring using exponentially modified Gaussian distribution

Abstract

AbstractMonitoring time and magnitude jointly is an attractive field due to their vast applications in different industries. This article presents a new maximum exponentially weighted moving average (Max‐EWMA) chart assuming exponentially modified Gaussian (EMG) distribution for time and magnitude. The reason of considering Max‐EWMA chart is its flexibility in identifying an out‐of‐control signal. Furthermore, the exponentially modifying Gaussian distribution can easily handle the monitoring of schedule time and also suitable for positive and negative magnitude. The performance of the chart is assessed using average run length (ARL), standard deviation of run length (SDRL), and quantiles of the run length distribution. In addition to extensive simulation study, two real data sets are also used to illustrate practical applications. The results indicate that the Max‐EWMA chart for monitoring time and magnitude is suitable for detecting time as well as magnitude shifts.