Semicircle Control Chart for Variables Data

On t and EWMA t charts for monitoring changes in the process mean

“…For scenarios in which (A1) is reasonable but (A2) is violated, control charts for asymmetrical distributions have been developed; see Choobineh and Ballard 8 , Bai and Choi 9 , Castagliola 10 , Chang and Bai 11 , Chan and Cui 12 , Shore 13 , Khoo et al 14 , and a properly designed EWMA control chart is also robust to the failure of (A2) 15 . Surprisingly, very little has been done when (A3) fails, with some exceptions like Chao and Cheng 16 and Chen and Cheng 17 , where the authors study monitoring process mean and standard deviation simultaneously using only one chart. Assumption (A3) may fail when there are not enough reliable data around to estimate the process standard deviation accurately or when the process standard deviation becomes unstable.…”

Fuzzy MaxGWMA chart for identifying abnormal variations of on-line manufacturing processes with imprecise information

“…In the sense of simultaneously monitoring the shifts of the process mean and variance, Chan et al (1990) introduced a single chart with the mean and variability plotted separately to identify the shifts; Domangue and Patch (1991) proposed an omnibus EWMA chart; Gan (1995) recommended a joint scheme consisting of a two-sided EWMA mean chart and a two-sided EWMA variance chart and found that it can perform well for several out-of-control circumstances; Chao and Cheng (1996) came up with a semicircle chart for joint monitoring the shifts of process mean and variance; Gan (1997) presented a two-dimensional chart with an elliptical incontrol region for the sample variance EWMA (s 2 -EWMA) against the sample mean EWMA ( x-EWMA). On the basis of maximum statistic values, Chen and Cheng (1998) first developed a Maxtype chart which effectively controls both process mean and variability on a single chart; Xie (1999) further examined numerous EWMA-type control charts and concluded that the MaxEWMA chart outperforms others in detecting small shifts of the process mean and variability as well as in identifying the source and the direction of an out-of-control signal.…”

Single Variables Control Charts: an Overview

“…The T chart suffers from the weakness of not being able to tell which parameter has shifted when an out-of-control signal is issued. Chao and Cheng 9 developed a single control chart called the semicircle control chart. This chart uses a semicircle to plot a single plotting character to indicate the position of the mean and standard deviation by plotting the two parameters against each other.…”