Snapshot approach to rational subgroups (Xbar, R chart)

 A fundamental idea in the use of control charts is the collection of sample data according to what Shewhart called the rational subgroup concept.

To illustrate this concept, suppose that we are using an control chart to detect changes in the process mean. Then the rational subgroup concept means that subgroups or samples should be selected so that if assignable causes are present, the chance for differences between subgroups will be maximized, while the chance for differences due to these assignable causes within a subgroup will be minimized.

The rational subgroup concept is very important. The proper selection of samples requires careful consideration of the process, with the objective of obtaining as much useful information as possible from the control chart analysis.


In snapshot approach to rational subgroups, each sample consists of units that were produced at the same time (or as closely together as possible), assuming that five consecutive units are selected.

This approach is used when the primary purpose of the control chart is to detect process shifts. It minimizes the chance of variability due to assignable causes within a sample, and it maximizes the chance of variability between samples if assignable causes are present. 

It also provides a better estimate of the standard deviation of the process in the case of variables control charts. This approach to rational subgrouping essentially gives a snapshot of the process at each point in time where a sample is collected.



Figure 5.10a, shows process for which the mean experiences series of sustained shifts and the corresponding observations obtained form this process at the points in time along the horizontal axis, using snapshot approach. 

Note that although the process mean is shifting, the process variability is stable (refer 5.10 b) Furthermore, the within-sample measure of variability is used to construct the control limits on the chart. Note that the chart in Figure 5.10b has points out of control corresponding to the shifts in the process mean.


Reference:

Chapter 5, of SQC by Montgomery.

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