Time and magnitude monitoring using Weibull based Max-EWMA chart

To monitor time and magnitude, different types of control charts have been proposed in the literature. This article proposes a new maximum exponentially weighted moving average (Max-EWMA) control chart by assuming Weibull distribution. The test-statistic of the Max-EWMA chart consists of two EWMA statistics, where one statistic is used for monitoring magnitude while the other to monitor time interval between events. The performances of the proposed chart is assessed on the basis of run length characteristics like, average run length (ARL), standard deviation of the run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, real data sets are also considered to show the applications of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small shifts.