Enhanced generally weighted moving average variance charts for monitoring process variance with individual observations

Abstract

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.

Generally weighted moving average monitoring schemes: Overview and perspectives

“…Note that Ali and Haq 82 did not consider the mixed CUSUM‐GWMA scheme. Next, Huang et al 83 proposed the mixed GWMA‐CUSUM scheme and the reverse version to monitor upward shifts using individual observations. Both of the mixed schemes have better small shifts detection ability than many competitors, including those discussed in Ali and Haq, 43 and Sheu and Lu 42 .…”

Efficient homogeneously weighted dispersion control charts with an application to distillation process

“…Many researchers, in recent years, devoted their studies on monitoring process dispersion using memory control charts. For instance, Abbas et al, [5][6][7] Abbasi and Miller, 8 Zhou et al, 9 Ahmad et al, 10 Castagliola et al, 11 Huang et al, 12 Haq, 13 Hossain et al, 14 Rajmanya and Ghute, 15 Osei-Aning and Abbasi, 16 Lee and Khoo, 17,18 Zaman et al, 19 and the references cited, therein.…”

A novel single composite Shewhart‐EWMA control chart for monitoring the process mean

“…After the introduction of the Shewhart, EWMA and CUSUM schemes, many authors have developed more advanced and enhanced monitoring schemes; see for instance, Daudin, 5 Mosquera and Aparisi, 6 Abbas et al., 7 Abbasi et al., 8 Shamma and Shamma, 9 Lucas and Saccucci, 10 Abujiya et al., 11,12 Zaman et al., 13 Ali and Haq, 14,15 Mabude et al 16 . and Huang et al 17 …”

“…4 Their setback is that, due to their inertia, they are relatively slow in detecting large shifts in the process. After the introduction of the Shewhart, EWMA and CUSUM schemes, many authors have developed more advanced and enhanced monitoring schemes; see for instance, Daudin, 5 Mosquera and Aparisi, 6 Abbas et al, 7 Abbasi et al, 8 Shamma and Shamma, 9 Lucas and Saccucci, 10 Abujiya et al, 11,12 Zaman et al, 13 Ali and Haq, 14,15 Mabude et al 16 and Huang et al 17 An efficient monitoring scheme is expected to detect small to large shifts as quickly as possible. One of the possible techniques to enhance the sensitivity of a monitoring scheme towards small to large shifts is the combination of memoryless and memory-type schemes such as the composite Shewhart-EWMA and Shewhart-CUSUM monitoring schemes (see, for example, Lucas, 18 Klein, 19 Capizzi and Masarotto, 20 Shamsuzzaman et al 21 and Freitas et al, 22 just to cite a few).…”