Max-EWMA chart for time and magnitude monitoring using generalized exponential distribution

Joint monitoring of time and magnitude is an important issue in many industrial and non-industrial fields and several proposals exist in the literature. The aim of this article is to propose a new maximum exponentially weighted moving average (Max-EWMA) chart assuming generalized exponential distribution for time as well as magnitude. As the test-statistic of Max-EWMA chart consists of two EWMA statistics, it is easy to identify the out-of-control signal raised by the chart. The performance of the chart is evaluated using different run length characteristics including, average run length (ARL), standard deviation of run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, a real data set is also used to show the practicality of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small to moderate shifts.