Performance of Side Sensitive Group Runs Chart based on Exact and Random Process Shifts

Abstract

A control chart is a crucial statistical tool that is typically used to monitor a process, in an effort to reduce variation. It is necessary to practically evaluate the overall performance of a control chart. Evaluation reveals the effciency of a control chart to detect a process shift. This influences practitioners' decisions on the choice of a control chart. The usual practice taken to evaluate the performance of a control chart is to use the average run length (ARL). The assumption for using the ARL as a performance measure is that the shift size is known in advance. Determining the shift size can be restrictive, particularly in the case practitioners do not have prior knowledge about the process. In view of this, the expected ARL (EARL) is employed as a performance measure for the random process mean shift. In this article, the overall performance of the side sensitive group runs (SSGR) chart is investigated in terms of EARL. Moreover, the optimal design for the SSGR chart based on minimising the EARL is proposed.