Yang and Cheng [18] proposed a CUSUM mean chart to monitor small shifts in the process mean.

In this paper, we propose an improved asymmetric EWMA mean chart (EWMA-AM chart) and a new asymmetric EWMA variance chart (EWMA-AV chart) for variables data to effectively monitor the process mean and variance simultaneously.

To overcome the defects of using the symmetric mean chart and to have superior performance in detecting small shifts in the process mean, a new improved asymmetric EWMA mean chart (EWMA-AM chart) is proposed.

When one compares the out-of-control average run lengths between the EWMA-AM chart (Table 4) and the symmetric EWMA mean chart (Table 5) in Yang et al.

Mean Chart Constant/Range Chart Shifting (Example 2, [ILLUSTRATION FOR FIGURE 5 OMITTED])

Since the mean chart is constant, the environmental sanitation program is still adequate (e.g., disinfectant is effective, no season increase in microorganisms, etc.).

This indicates (mean chart) that the disinfectant is no longer useful in the way it is being used, and/or a seasonal increase in contaminative microorganisms is occurring.

Figure 1 shows an example of a mean chart. This chart comes from a leisure centre - which offers leisure and sports facilities such as squash courts, a swimming pool and a gymnasium to local businesses and the general public.

In a standard mean chart, such as Figure 1, the extent to which the sample means are likely to vary under "normal" circumstances is calculated by measuring the standard deviation of the individual items within each sample, and then using this to predict the variability of the differences between samples, using a formula such as:

This is particularly important for range charts: this means that the range chart which accompanied the mean chart in Figure 1 was flawed because the variable plotted here is very unlikely to be even approximately normally distributed (it had a pronounced skew).

The estimate of the standard deviation calculated from the upper quartile and median is 3.26, whereas the estimate calculated from the variation within the samples using the standard mean chart procedure is 1.8.

Time-series investigation of subsample

mean charts. IIE Transactions 24(5):66-80.