A double generally weighted moving average exceedance control chart

Since the inception of control charts by W. A. Shewhart in the 1920s they have been increasingly applied in various fields. The recent literature witnessed the development of a number of nonparametric (distribution-free) charts as they provide a robust and efficient alternative when there is a lack of knowledge about the underlying process distribution. In order to monitor the process location, information regarding the in-control process median is typically required. However, in practice this information might not be available due to various reasons. To this end, a generalized type of nonparametric time-weighted control chart labelled as the Double Generally Weighted Moving Average (DGWMA) based on the exceedance statistic (EX) is proposed. The DGWMA-EX chart includes many of the wellknown existing time-weighted control charts as special or limiting cases for detecting a shift in the unknown location parameter of a continuous distribution. The DGWMA-EX chart combines the better shift detection properties of a DGWMA chart with the robust in-control performance of a nonparametric chart, by using all the information from the start until the most recent sample to decide if a process is in-control (IC) or out-of-control (OOC). An extensive simulation study reveals that the proposed DGWMA-EX chart, in many cases, outperforms its counterparts.