When subgroups are selected in a way that minimizes the opportunity for variation within a subgroup and maximizes the opportunity to detect variation…

The method described is the definition of a rational subgroup. In Statistical Process Control (SPC), rational subgroups are formed by collecting samples over a very short time, under conditions that are as consistent as possible. This minimizes the variation within the subgroup, ensuring it represents only the inherent, common-cause variation of the process. The subgroups themselves are then taken at spaced intervals (e.g., hourly). This strategy maximizes the chance of detecting variation between subgroups, which would indicate the presence of a special (or assignable) cause, making the control chart a sensitive tool for process monitoring.

A. random: Random sampling over a long period would mix common and special cause variation within the subgroup, making the control limits wider and the chart less sensitive to process shifts.

B. assignable: An assignable cause is a source of special cause variation that can be identified and removed; it is not a method of subgrouping.

C. controlled: "Controlled" describes the state of a process that is stable and exhibits only common cause variation (i.e., in a state of statistical control), not a sampling strategy.

1. Montgomery

D. C. (2013). Introduction to Statistical Quality Control (7th ed.). John Wiley & Sons. In Section 6.2.2

"Rational Subgroups

" it states

"The subgroups 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." (p. 231).

2. The Certified Quality Engineer Handbook (4th ed.). (2017). ASQ Quality Press. Chapter 21

"Statistical Process Control (SPC)

" explains

"The principle of rational subgrouping is to structure the subgroups in a way that the sources of variation are either in the subgroups or between them... The goal is to minimize the amount of variation within a subgroup and maximize the variation between subgroups." (p. 298).

3. DeVor

R. E.

T. H. Chang

and J. W. Sutherland. (2007). Statistical Quality Design and Control: Contemporary Concepts and Methods (2nd ed.). Prentice Hall. Chapter 5

"The Control Chart for Variables

" discusses that rational subgroups are chosen so that within-group variation represents the "natural" or "chance" variability

while between-group variation can reveal "assignable" causes. (pp. 188-189).