Combined Quality Control Scheme for Monitoring Autocorrelated Process - Tyagi, Dushyant; Yadav, Vipin (Thailand Statistician, 2024)
In statistical process control, the control chart helps to diagnose the presence of variation due to assignable causes so that the process can achieve statistical control. There is no doubt that the process exhibiting autocorrelation degrades the functioning of control chart by producing incessant false signals or responding gradually to out-of-control state. The inefficiency of Shewhart control chart to spot small displacements leads to the application of alternate charting techniques like cumulative sum (CUSUM) and exponentially weighted moving average (EWMA). Both CUSUM and EWMA are helpful in detecting small to moderate displacements in the process. A mixed EWMA-CUSUM (MEC) chart was also proposed to improve the detection ability against the smaller shifts. This paper proposed a combined EWMA-MEC quality control scheme to detect small, moderate and large shifts. We fitted an autoregressive process to the autocorrelated observation and applied the charting technique directly to the residuals. Performance measure average run length (ARL) is used to assess the impact of the proposed scheme. We have evaluated ARL of the proposed scheme and compared it with the ARL of MEC, CUSUM and EWMA control charts. The results indicate that the proposed scheme is more sensitive to detecting small to moderate shifts than the previous schemes. We have also discussed the performance of the proposed scheme for the misdesigned charts, i.e., if the shift is different than the anticipated shift, and found that the proposed scheme performs better for the misdesigned cases than the traditional charts.