5.0 The Method of Rational Subgrouping - VAS Documentation Manual

As introduced in Chapter 3, in general cause systems of variation the assignable and common causes of variation are confounded. The separation of the assignable causes from the common causes depends on the method of “rational subgrouping”. A rational subgroup is defined as a unique combination of the “process design conditions” and “production time” producing the empirical data forming the basis for the analysis.

Each design factor $F_{i}$ in the working set of process design factors { $F_{1}$ , $F_{2}$ , … , $F_{M}$ } occurs at $L_{i}$ levels.^[25] So there is a total of K process design conditions included in the problem formulation where

K = L_{1}xL_{2}x\ldots xL_{M}

Data are collected at each of T production times $\left\{ t_{1},t_{2},\ldots,t_{T} \right\}$ for each of the process design conditions so the problem formulation is based on a total of R=KxT rational subgroups.

The basic structure of data organized into the R rational subgroups is illustrated in Figure 5-1 for K process design conditions, T production times, and a sample of size $N_{kt}$ in the kt^th rational subgroup which is highlighted in gray.^[26]

5.1 The Goal of Organizing Data into Rational Subgroups¶

The method of rational subgrouping allows the analyst to answer many important questions related to the causes of variation associated with the process design factors and production time. The goal is to define the rational subgroups so that:

the variation within the subgroups is due, at least approximately, to common causes of variation devoid of any practically significant assignable causes associated with the process design conditions or production time, or ephemeral assignable causes, and
the variation across the subgroups is due to the common causes of variation occurring within the subgroups plus assignable causes associated with the effects of the process design conditions and/or production time.

Once this organization of the data has been successfully accomplished, the Shewhart process behavior charts presented in Part VII and Part VIII are the graphical tools used to analyze the behavior of the rational subgroups sample means and standard deviations across the rational subgroups. These charts separate the effects of the unexplained causes of variation occurring within from the explainable causes of variation occurring across the rational subgroups.

Figure 5-1. The Basic RSG Structure Based on the Problem Formulation

Footnotes¶

Note: If the process design factor $F_{i}$ is a continuous variable, it is grouped into $L_{i}$ levels or bins. The choice of the number of bins is dictated by the analyst.
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Note: From this point on, the rational subgroup sample sizes $N_{kt}$ will be denoted as N to simplify the notation in the figures.
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