Statistics for Environmental Engineers

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Comparison of the Charts

Shewhart, Cusum, Moving Average, and EWMA charts (Figures 12.1 to 12.3) differ in the way they weight previous observations. The Shewhart chart gives all weight to the current observation and no weight to all previous observations. The Cusum chart gives equal weight to all observations. The moving average chart gives equal weight to the к most recent observations and zero weight to all other observations. The EWMA chart gives the most weight to the most recent observation and progressively smaller weights to previous observations.

Figure 12.1 shows a Shewhart chart applied to duplicate observations at each interval. Figures 12.2 and 12.3 show Moving Average and EWMA, and Cusum charts applied to the data represented by open points in Figure 12.1. The Cusum chart gives the earliest and clearest signal of change.

The Shewhart chart needs no explanation. The first few calculations for the Cusum, MA(5), and EWMA charts are in Table 12.1. Columns 2 and 3 generate the Cusum using the target value of 12. Column 4 is the 5-day moving average. The EWMA (column 5) uses Я = 0.5 in the recursive updating formula starting from the target value of 12. The second row of the EWMA is 0.5(11.89) + 0.5(12.00) =

12.10, the third row is 0.5(12.19) + 0.5(12.10) = 12.06, etc.

No single chart is best for all situations. The Shewhart chart is good for checking the statistical control of a process. It is not effective unless the shift in level is relatively large compared with the variability.

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