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

6.3.1.2.

Individuals Control Charts

Moving range used to derive upper and lower limits
 
 
 
 
 
 
 
 
 
 
 
 

Individuals control limits for 
an observation
 
 
 
 
 
 
 
 
 
 
 
 
 

Limits for the moving range chart
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Example of individuals chart
 
 
 
 

 

Samples are Individual Measurements

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.i. 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. 

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

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

 

This yields the parameters below 

.
The control chart is given below 

 

On both charts the process is in control, since none of the plotted points fall outside eithe the UCL or LCL. 

Another way to construct the individual chart is by using a standard deviation based on a historical data set (if available). Then we can obtain the chart from