4.0 Fundamental Concepts Associated with the Process

Part IV. The Structure of Cause Systems of Variation in Analytic Studies

There is a fundamental structure that is common to many of the processes producing the data in applications encountered in practice. The VAS methodology is based on exploiting this common structure so the methodology applies to a wide variety of applications in both the physical and social sciences in business, science and industry. The fundamental concepts associated with this common structure are described in the following sections.

4.1 The Unit of Analysis - UOA¶

The “unit of analysis” (UOA) is the product or service entity produced by the primary process to which all data relevant to the process under study are attached. The unit of analysis may be a single entity or product produced by the process. For example, with respect to the process for producing cups filled with yogurt, the filled cup is the unit of analysis, and the fill weight is response variable attached to the cup. But single entities or products may also be aggregated into a “production batch” which becomes the unit of analysis. For example, the fundamental products in a new car loan process are the individual car loan contracts. The fundamental response variable is binary – the contract is in default or not in default at any specific point in time. The individual contracts may be grouped by month forming a production batch which becomes the unit of analysis, and the fraction of contracts in default in the production batch is the response variable.

4.2 Performance Characteristics – PC¶

A performance characteristic (PC) is a measurable property of the process or the unit of analysis. For example, in the process producing cups filled with yogurt, the performance characteristic of interest is the gross weight (GW) of the filled cup. In the new car loan process the performance characteristic is the fraction of contracts in default in the production batch.

4.3 Performance Measurements – PM¶

In any application the performance characteristics of interest must be measured. The observed measurement of the performance characteristic is referred to as the “performance measurement” (PM) which is the “response variable” of interest. For example, in a cup filling process the gross weight (GW) of a filled cup is measured using a digital weight scale. The filled cup is placed on the scale and the measured value Y is recorded. Y is the observed performance measurement which is an estimate of the performance characteristic.^[23]

4.4 Process Design Factors – PDF¶

One of the key principles in the VAS methodology is that the important assignable causes of variation are associated with the design of the process under study. Therefore, the analysis of the design of the process is an essential step in the analytic methodology. This analysis is often accomplished by creating a process design diagram.

The analysis of the design of the process under study identifies $M'$ “process design factors” $\left\{ F_{1}',F_{2}',\ldots,F_{M'}' \right\}$. Each factor occurs at a fixed number of levels. That is, factor $F_{i}'$ occurs at $L_{i}'$ levels. If the process design factor is continuous, it is converted into a categorical variable by redefining the factor using bins. For example, the factor “Age” which is measured on a continuous scale might be placed into five “year categories” or bins {<21, 21-30, 31-40, 41-50, >50}.

4.5 Process Design Conditions – PDC¶

The combinations of the levels of the process design factors create

unique production environments which are referred to as “process design conditions” (PDC) producing the performance measurements forming the basis for the analysis.

4.6 Production Time – PT¶

Many classical statistical theories and methods of analysis are based on the assumption that the properties of the deterministic and stochastic components of the cause system of variation under study are fixed and do not change over time.^[24] Professor George Box referred to such a system as a “fixed frame”. Most physical and social processes encountered in practice, however, are dynamic, operating over time. And, typically the properties and behavior of the process change over time in both predictable and unpredictable ways. Therefore, in analytic studies, there is a temporal component associated with the cause system of variation. This means that, in addition to the “process design conditions”, there is also a “production time” variable (PT) associated with each unit of analysis. That is, the units of analysis within each process design condition are produced at discrete time points $\left\{ t_{1},t_{2},\ldots,t_{T} \right\}$.

Production time is called out separately from the process design factors because it plays a special, and fundamentally different, role in analytic studies. The production time is associated with the temporal changes occurring in the behavior of the cause system of variation. These changes can be of a global nature affecting all $K'$ process design conditions simultaneously, or these changes may be local, that is specific to individual process design conditions. They can also be ephemeral or fleeting changes.

4.7 Unknown or Ignored Process Design Factors¶

In practice it is often the case that it is not possible to observe units of analysis produced under all of the possible $K'$production conditions. For example, we may be ignorant of, or may choose to ignore, some of the $M'$ design factors. That is, based on the analysis of the design of the process under study, we may only recognize a subset of M design factors {$F_{1}$, $F_{2}$, … , $F_{M}$} out of the $M'$ possible design factors $\left\{ F_{1}',F_{2}',\ldots,F_{M'}' \right\}$. This leaves $G = M' - M$ factors $\{ F_{1}^{*},F_{2}^{*},\ldots,F_{G}^{*}\}$ which are either “unknown” or “ignored” in the problem formulation. We stress here that it is a critical, but subtle, practical point to understand that while the design factors $\{ F_{1}^{*},F_{2}^{*},\ldots,F_{G}^{*}\}$ are not included in the problem formulation, they still possibly affect the variation in the performance measurement. Simply ignoring a process design factor does not make its effect go away. Therefore, the possible effects of unknown or ignored process design factors must be accounted for in any statistical model used to describe the data, the methods of analysis used to organize and analyze the data, the inferences or predictions drawn from the data, and in the understanding of the risks incurred in acting on the predictions.

4.8 The “Working Set” of Process Design Factors¶

Each design factor $F_{i}$ in the selected set {$F_{1}$, $F_{2}$, … , $F_{M}$} derived from the problem formulation occurs at $L_{i}$ levels. So there is a total of K process design conditions included in the problem formulation where

This set of process design factors, and process design conditions is referred to as the “working set” of process design factors and process design conditions

.