The exponentially weighted moving average t chart using auxiliary information (AIB-EWMA-t chart) is an effective approach for monitoring small process mean shifts when the process standard deviation is unstable or poorly estimated. To further enhance the sensitivity of the AIB-EWMA-t chart, in this study, we propose an AIB generally weighted moving average (GWMA) t chart (AIB-GWMA-t chart) to monitor the process mean. The existing EWMA-t, GWMA-t, and AIB-EWMA-t charts are special cases of the AIB-GWMA-t chart. Numerical simulation studies indicate that the AIB-GWMA-t chart performs uniformly and substantially better than the EWMA-t and GWMA-t charts in terms of average run length. Moreover, the AIB-GWMA-t chart with large design and adjustment parameters also outperforms the AIB-EWMA-t chart when the correlation coefficients are within a certain range. An illustrative example is provided to highlight the efficiency of the proposed AIB-GWMA-t chart in detecting small process mean shifts.
The generally weighted moving average variance (GWMAV) chart is effective in detecting increases in process variance when only individual observations are available. Recently, the combination of exponentially weighted moving average and cumulative sum (CUSUM) charts for the effective detection of small process shifts has emerged. Inspired by the features, we propose the mixed GWMAV-CUSUM chart and its reverse order CUSUM-GWMAV to enhance the detection ability of the GWMAV chart and compare with the existing counterparts. Numerical simulation revealed that the mixed GWMAV-CUSUM and mixed CUSUM-GWMAV charts are sensitive to small upward shifts in the process variance and efficient structures compared with their prototypes and their separate charts, that is, GWMAV and CUSUM charts. An industrial dataset was used to illustrate the application of the proposed mixed charts.
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