EWMA Control Charts for the Smallest and Largest Observations

A NewS2-EWMA Control Chart for Monitoring the Process Variance

“…The properties and design strategies of the EWMA control chart for the mean (introduced by Roberts 1 ) have been thoroughly investigated by Robinson and Ho 2 , Crowder 3,4 , Lucas and Saccucci 5 and Steiner 6 . The use of the EWMA as a tool for monitoring the process variability has received attention by Wortham and Ringer 7 , Sweet 8 , Ng and Case 9 , Crowder and Hamilton 10 , Hamilton and Crowder 11 and MacGregor and Harris 12 , Gan 13 , Amin et al 14 , Lu and Reynolds 15 and Acosta-Mejia et al 16 . The goal of this paper is to present a new EWMA-type control chart for monitoring the variance of the process.…”

Statistical Control of Multiple-Stream Processes: A Literature Review

“…(I cannot fully agree with this point though, because a similar adjustment could be applied to the other methods, simply by considering the range of these adjusted observations instead of the range of the raw observations). Amin et al (1999) proposed an EWMA chart for the largest and smallest observations in each sample (the MaxMin EWMA chart). This chart can serve to simultaneously monitor the mean and variability of univariate processes, but serves as well to monitor multiple-stream processes, being sensitive to changes in the overall process mean, in the inter-stream dispersion (as when individual streams shift) or both.…”

“…For example, how would the methods in Liu et al (2008) extend to the case of processes with a common component exhibiting autocorrelation? How would the MaxMin EWMA chart by Amin et al (1999) perform in the case of an MSP with two sources of variation? Or in which conditions (for which values of the ratio between variance components) does it perform well?…”

“…They reported that the chart has been successfully applied in the nylon fibers industry to monitor 100 similar 8-stream processes. Amin et al (1999) analysed the performance of the chart and compared it with a pair of EWMA charts, a two-sided EWMA chart for N x and a one-sided EWMA chart for ln.S 2 /. For shifts only in the mean, the joint charts perform better; with a slight increase in the standard deviation, the difference in performance reduces and for larger increases in the standard deviation the MaxMin EWMA chart outperforms the joint scheme.…”

Statistical Surveillance. Optimality and Methods

“…In the latter the probability of signaling in the wrong chart is evaluated. Monitoring of the maximum and the minimum in samples for detection of change in the mean and/or the variance is suggested by Amin et al (1999).…”