A key element in implementing a control chart for a process is the determining of the subgroup to be used for sampling the data to be charted. Our text discusses subgroup rationale from the standpoint of picking a correct orientation for sampling; under different scenarios using some combination of time, operator, or machine. Choosing the right rational subgroups allows our control charts to directly signal when and where something is wrong in our processes. Choosing the wrong subgroup can cause our charts to not be able to detect the types of out of control conditions we need to see. Another way to think about rational subgroups is to work to identify a sampling plan that makes the variation within the subgroups much smaller than the variation across subgroups particularly important because it is the variation across groups that will be used to spot special causes in our process data.

Think of the scenario where UCF confers degrees to over ten thousand undergraduate students every year. The grade point average (GPA) of each of these students could be considered a continuous random variable that is an output of the education process for each of those graduates. If the administration wanted to know if the output GPA should be considered under statistical control, we could design control charts to be used for that purpose. If you chose students at random across the university, you would likely embed significant variation within your selected subgroups. If that variation is too large, it could invalidate the control chart as a tool for this application because it would not be sensitive enough to properly identify and signal out of control conditions. Alternatively, you could develop different control charts for samples pulled from different sub-populations so that the variation within the samples would be lessened.

Discuss how you would stratify your sampling to minimize noise in your subgroups? How would you select appropriate rational subgroup types and sizes for your analysis? What kind of questions would your selection be able to answer, and at what level of detail? Discuss any advantages or disadvantages you see in your choices.