VSSI X̄ control charts for processes with multiple assignable causes

Abstract

This research investigates the statistical efficiency of variable sample size and sampling interval (VSSI) X̄ control charts under multiple assignable causes. Algorithms for calculating the average run length (ARL) and average time to signal (ATS) of a VSSI X̄ control chart are proposed by employing the Markov chain method. States of a process are defined in vector forms according to the location of a control statistic and the occurrence states of the assignable causes. Initial probabilities and transition probabilities are carefully derived from the definitions of the states. Statistical properties of the proposed control chart are also investigated. Illustrative examples show that the VSSI X̄ control chart is superior to the VSS or VSI X̄ control chart as well as to the Shewhart X̄ control chart in a statistical sense, even under multiple assignable causes. © 2007 IEEE.