The UCL for any individuals control chart is given by following expression,
UCL=\(\bar{x}+\frac{3\overline{MR}}{d_2}\)

In case of individual measurements, we use moving range of two successive observations as basis of estimating process variability.

The Average run length for any individuals control chart with 3 sigma limits is considerably lower than value of Average run length for any Shewhart control chart.

For any shewhart x bar control chart having 3 ? sigma limits, we have p=0.0027. The average run length is calculated by formula,
\(ARL=\frac{1}{p}=\frac{1}{0.0027}=370\)

The average number of points that must be plotted before a point indicating an out-of-control situation is plotted, is called Average run length of any control chart.

The estimation for process standard deviation is expressed in terms of median of span-two moving ranges by following expression,
\(\widehat{?_3} = 1.047\overline{MR}\)

The estimation of process standard deviation for any individuals control chart is written as,
\(\widehat{?_1}=\overline{MR}/d_2\)
For individuals control chart, n=2. For n=2, we have d₂=1.128. So we get,
\(\widehat{?_1}=\overline{MR}/1.128\).

The center line of any individuals control chart represents value equal to x or process mean for that particular process.

We know that for any individuals control chart,
ARL=\(\frac{1}{1-\beta}\)
Putting values of ?=0.9772, we get ARL=43.96.

The moving range is mostly called as MR of span two because it uses 2 successive observations difference for MR calculation. The span can be increased, MR can be calculated by more than 2 observations.