On monitoring process variance with individual observations

Effective Control Charts for Monitoring Multivariate Process Dispersion

“…also showed that a two‐sided equal‐tail‐probability exponentially weighted moving average (EWMA) chart for monitoring the variance (MacGregor and Harris) is ARL‐biased. Similar results for the case of individual observations (i.e., when the subgroup size n = 1) were also reported in Yeh et al . In addition, Lowry et al .…”

“…12 Recently, Huwang et al 9 also showed that a two-sided equal-tail-probability exponentially weighted moving average (EWMA) chart for monitoring the variance (MacGregor and Harris 13 ) is ARL-biased. Similar results for the case of individual observations (i.e., when the subgroup size n = 1) were also reported in Yeh et al 10 In addition, Lowry et al 14 reported that, when using the R or S chart, it is much more difficult to detect decreases than increases in variance. Similar phenomena for the EWMA chart were also discussed in Huwang et al 9 and Yeh et al 10 Acosta-Mejia 8 proposed combining two one-sided sample-range-based cumulative sum (CUSUM) charts for monitoring both increases and decreases in variance.…”

“…Similar results for the case of individual observations (i.e., when the subgroup size n = 1) were also reported in Yeh et al 10 In addition, Lowry et al 14 reported that, when using the R or S chart, it is much more difficult to detect decreases than increases in variance. Similar phenomena for the EWMA chart were also discussed in Huwang et al 9 and Yeh et al 10 Acosta-Mejia 8 proposed combining two one-sided sample-range-based cumulative sum (CUSUM) charts for monitoring both increases and decreases in variance. Acosta-Mejia et al 15 also proposed a combined chart for monitoring overall changes in variance and showed that their proposed chart outperforms existing two-sided charts.…”

“…For monitoring the variance in the univariate case, as pointed out by Acosta‐Mejia, Acosta‐Mejia et al ., and Yeh et al ., combining two one‐sided charts leads to better performance in detecting overall variance changes than does a two‐sided chart. As stated earlier, our second objective in this paper is to study whether combining the two effective one‐sided charts for detecting multivariate dispersion will do better than the two‐sided charts.…”

“…On the other hand, monitoring decreases in dispersion has received less attention, and only a few control schemes for the univariate case have been proposed. See, for example, Nelson, Acosta‐Mejia, Huwang et al ., and Yeh et al . As modern processes are getting more complicated, quite often, the quality of a manufacturing process or product is characterized by multiple quality characteristics.…”