6. Process or Product Monitoring and Control
6.3. Univariate and Multivariate Control Charts
6.3.2. What are Variables Control Charts?

6.3.2.2.

Individuals Control Charts

Samples are Individual Measurements

Moving range used to derive upper and lower limits

Control charts for individual measurements, e.g., the sample size = 1, use the moving range of two successive observations to measure the process variability.

The moving range is defined as

which is the absolute value of the first difference (e.g., the difference between two consecutive data points) of the data. Analogous to the Shewhart control chart, one can plot both the data (which are the individuals) and the moving range.

Individuals control limits for an observation

For the control chart for individual measurements, the lines plotted are:

where is the average of all the individuals and is the average of all the moving ranges of two observations. Keep in mind that either or both averages may be replaced by a standard or target, if available. (Note that 1.128 is the value of d₂ for n = 2).

Example of moving range

The following example illustrates the control chart for individual observations. A new process was studied in order to monitor flow rate. The first 10 batches resulted in

Batch Number	Flowrate x	Moving Range MR
1	49.6
2	47.6	2.0
3	49.9	2.3
4	51.3	1.4
5	47.8	3.5
6	51.2	3.4
7	52.6	1.4
8	52.4	0.2
9	53.6	1.2
10	52.1	1.5
	= 50.81	= 1.8778

Limits for the moving range chart

This yields the parameters below.

Example of individuals chart

The control chart is given below

The process is in control, since none of the plotted points fall outside either the UCL or LCL.

Alternative for constructing individuals control chart

Note: Another way to construct the individuals chart is by using the standard deviation. Then we can obtain the chart from

It is preferable to have the limits computed this way for the start of Phase 2.