An MR-chart is a type of control chart used to process variability (as the moving range of successive observations) when measuring individuals at regular intervals from a process.
When data are individual observations, it is not possible to use the standard deviation or range of subgroups to assess the variability and instead the moving range is an estimate the variability.
Given a series of observations and a fixed subset size, the first element of the moving range is the range of the initial subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next number following the subset in the series. The next element of the moving range is the range of this subset. This process is repeated over the entire series creating a moving range statistic.
The moving range requires:
Each point on the chart represents the value of a moving range.
The center line is the expected value of the range statistic.
The control limits are either:
- A multiple (k) of sigma above and below the center line. Default k=3.
- Probability limits, defined as the probability (alpha) of a point exceeding the limits. Default alpha=0.27%.
If unspecified, the process sigma is the weighted average of the unbiased moving range estimates of sigma based on the range statistics.
You should be careful when interpreting a moving range chart because the values of the statistic are correlated. Correlation may appear as a pattern of runs or cycles on the chart. Some authors (Rigdon et al., 1994) recommend not plotting a moving range chart as moving range does not provide any useful information about shifts in process variability beyond the I-chart.