7.0 The Structure of the Data Analyzed by VAS

The problem formulation described in the previous chapters leads directly to a standard structure for the data that form the basis for the VAS analyses. The structure applies whether the data are associated with physical or social science applications, or with a manufacturing, service or administrative process. It also applies whether the data are extracted from the process using a census, statistical sample, designed experiment, survey, transactional, observational study or a convenience sample.

The fundamental structure of the data attached to any single unit of analysis includes the values associated with the following variables.

• Y – Performance Measurement

• $F_{1}$ – Process Design Factor 1 at $L_{1}$ Levels

• $F_{2}$ – Process Design Factor 2 at $L_{2}$ Levels

• …

• $F_{M}$ – Process Design Factor M at $L_{M}$ Levels

• PT – Time of Production at T Time Periods

7.1 The Data Understood from an Unstructured Viewpoint¶

The data structure presented in Figure 7-1 reflects the data viewed from an “unstructured” perspective with respect to the K process design conditions defined by the M process design factors included in the problem formulation. That is, any relationship among the design factors $F_{1}$-$F_{M}$ is ignored, and the K rational subgroups that the combinations of process design factors create are simply “strung out” as K separate process design conditions. A sample of size $N_{kt}$ is collected within kt^th rational subgroup as highlighted in Figure 7-1.^[28]

7.2 The Data Understood from a Structured Viewpoint¶

When there are multiple process design factors the process design conditions can also be viewed from a structured perspective. This is often referred to as the analysis of the “factorial structure” of the data. This concept is illustrated in Figure 7-2 for the case of two process design factors with the first factor occurring at 2 levels and the second factor occurring at 3 levels. In this case we have a 2x3 factorial structure associated with the 6 process design conditions, and the effects of the process design conditions can be separated into process design factor effects.

7.3 An Example of the Rational Subgrouping Methodology¶

An actual example involving the patient transport process in a large metropolitan hospital illustrates the method of rational subgrouping. There are two process design factors identified in the problem formulation.

• $F_{1}$ – Nursing Floor were the Patient Resides at 3 levels (1, 2, 3)

• $F_{2}$ – Patient Escort Experienced a Problem During Transport at 2 levels (No, Yes)

So there is a total of K = 3x2 = 6 process design conditions. Data were collected over T = 5 days for a total of R = 5x6=30 rational subgroups. A sample of size N = 4 trips was recorded for each rational subgroup. In this case the rational subgroups are being viewed from a structured perspective. The data within the rational subgroups in Figure 7-3 is the time the patient escort spent in the patient’s room preparing the patient for transport to an ancillary testing unit. The data for the rational subgroup defined by “Nursing Floor = 2” and “Problem Encountered = No” for Day = 3 is highlighted.