Optimal triple sampling X charts for autocorrelated processes

Autocorrelation is a phenomenon in which the characteristics of interest being monitored are dependent. In the presence of autocorrelation, the detection ability of classical control charts deteriorates significantly, and this poses great concerns to practitioners as some processes in real-life settings produce autocorrelated observations. This paper deals with the problem of autocorrelation in Shewhart charts by incorporating the AR(1) and MA(1) models into the classical TS X chart, which is an extension of the Shewhart chart. The performance of the introduced TS X charts for AR(1) and MA(1) is improved by optimizing the parameters of the charts when the incontrol average run length (ARL) of the charts is 370. The TS X chart for AR(1) is found to outperform the DS X chart for AR(1) in the presence of autocorrelation. The performance of the proposed charts is assessed using ARL, standard deviation of the run length (SDRL), average number of observations to signal (ANOS), and standard deviation of the number of observations to signal (SDNOS) criteria. Based on these criteria, the TS X chart for MA(1) is found to surpass the TS X chart for AR(1) as the autocorrelation level increases.