Modified EWMA Chart With Restarting Mechanism for Monitoring Serially Correlated Sequential Processes

ABSTRACT In practical applications of statistical process control (SPC), the assumption of data independence among serial process observations is often unrealistic. In the SPC literature, it has been well demonstrated that control charts ignoring the serial data correlation would be unreliable to use. Thus, it is important to develop control charts that can accommodate serial data correlation properly. To this end, one approach is to decorrelate the observed data properly before a control chart is used. However, the related computing burden would be too heavy to be practically feasible if the observed data at the current observation time need to be decorrelated with all previous data. With a cumulative sum (CUSUM) chart, its restarting mechanism has been found helpful to reduce the computing burden substantially by ignoring the observed data collected before the previous restarting time. In many applications, for example, those with unequally spaced observation times, exponentially weighted moving average (EWMA) charts are often preferred since construction of their charting statistics can accommodate the unequally spaced observation times well. But, conventional EWMA charts do not have the restarting mechanism, and thus are difficult to use in cases with serially correlated data. To address this issue, a modified EWMA chart is considered in this paper to include the restarting mechanism in the chart. Numerical studies confirm that the computing time using the modified EWMA chart is dramatically reduced for monitoring serially correlated data while its process monitoring performance is little compromised.