ABSTRACT
The Shewhart chart based on the sample mean X was first developed to monitor a process mean. The chart was then modified to plot the sample range R to monitor a process variance. Each chart was developed assuming that the other process characteristic is in control. The more advanced chart ing procedures such as the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts were later developed based on the same basic assumption. This has led to the design and evaluation of perfor mance of the mean and variance charts separately. This kind of analysis might mislead quality control engineers into making inferences concerning the mean or the variance chart without making reference to the other. Experience with real manufacturing processes has shown that the process variance tends to increase with the process mean. A decrease in the variance when the mean is in control is highly desirable, but if a decrease in the variance is accompanied by a decrease in the mean, then it is highly undesir able. Gan (1995) gave an example of a process with a decrease in the var iance coupled with a change in the mean and showed that this process state is difficult to detect. The mean chart becomes insensitive to the change in the mean because the variance of the sample mean has become smaller. Any detection of a decrease in the variance with the mean appearing to be in control could lead to the false conclusion that the process has improved. In
short, the problem of monitoring the mean and variance is a bivariate one, and both the mean and variance charts need to be looked at jointly in order to make meaningful inferences.
