Statistics for Environmental Engineers

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These are problems in time series analysis. Models of this kind are explained in Tiao et al. (2000) and Box and Luceno (1997). An exponentially weighted moving average will describe certain patterns of drift. Chapters 51 and 53 deal briefly with some relevant topics.

Once the typical underlying pattern (the inherent variability) has been described, the statistical properties of the deviations of observations from this typical pattern need to be characterized. If the deviations are random, independent, and have constant variance, we can construct a control chart that will examine these deviations. The average value of the deviations will be zero, and symmetrical control limits, calculated in the classical way, can be drawn above and below zero.

The general steps in constructing a control chart are these:

1. Sample the process at specific times (t, t — 1, t — 2,…) to obtain…yt, yt-1, and yt-2. These typically are averages of subgroups of n observations, but they may be single observations.

2. Calculate a quantity Vt, which is a function of the observations. The definition of Vt depends on the type of control chart.

3.    Plot values Vt in a time sequence on the control chart.

4.    Using appropriate control limits and rules, plot new observations and decide whether to take corrective action or to investigate.

Kinds of Control Charts

What has been said so far is true for control charts of all kinds. Now we look at the Shewhart
5 chart (1931), cumulative sum chart (Cusum), and moving average charts. Moving averages were used for smoothing in Chapter 4.

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