Creating a control chart using Moving Range

Control charts are very quickly created by using a standard deviation function for control limits. However, Donald Wheeler, author of Understanding Variation: The Key to Managing Chaos, SPC Press, Inc., suggests that there are problems with standard deviation or standard error because of assumptions about the homogeneity of the data. Instead, he prefers a method using a moving average over an arbitrary period.

In this recipe, we are going to use the same set of rainfall data as the previous recipe, Creating a statistical control chart using standard deviation, to see how the rainfall data for Heathrow varies over time. Instead of using standard deviation of the data to derive the control limits, we will use the moving average (mR) and a statistical constant (2.66 – this value is obtained by dividing 3 by the sample size-specific d2 anti-biasing constant for a subgroup size of n=2).

We will use a 30-year period as our reference for what "Average"...