VSSI (X)over-bar control charts for processes with multiple assignable causes

This research investigates the statistical efficiency of variable sample size and sampling interval (VSSI) (X) over bar control charts under multiple assignable causes. Algorithms for calculating the average run length (ARL) and average time to signal (ATS) of a VSSI (X) over bar 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 (X) over bar control chart is superior to the VSS or VSI (X) over bar control chart as well as to the Shewhart (X) over bar control chart in a statistical sense, even under multiple assignable causes.