Control Charts for Measurements Without Subgrouping (for One Variable)
The control charts given in the preceding chapter can be used when subgroups can be formed. This is not always possible or practical, however. Items coming off an assembly line may be produced at such a slow rate so as to preclude the forming of subgroups. If items are produced every 30 minutes, it would take 1.5 hours to form a subgroup of size 5; by then the process might already have gone out of control. Variables such as temperature and pressure could also not be charted with subgrouping since, for example, a “subgroup” of five temperature readings made in quick order would likely be virtually the same. Thus, nothing could be gained. Clerical and accounting data would also have to be charted using individual numbers rather than subgroups. For example, Walter, Higgins, and Roth (1990) discussed potential applications in accounting, such as charting the days required to process an invoice and charting the weekly payroll.
So in many control chart applications there is no option as to whether or not individual observations will be used. If individual observations can be obtained frequently enough that it would be possible and practical to group them, there is the obvious question of whether or not this should be done. The research of Reynolds and Stoumbos (2004) is relevant to this scenario, as they considered both permanent process changes and transient changes in Stage 2. They made the reasonable ...