TABLE OF CONTENTS This monograph is about "empirical modeling of a response variation". In this introductory chapter we elaborate on this concept and explain its various components.
Scientific and engineering modeling aims to capture the variation of a "response". The latter refers to any characteristic, or variable, where variation has been observed, and this variation is the subject of a scientific or engineering research effort. As the word implies, a "Response" is the "reaction" of an investigated characteristic to the effects exercised on it by external factors. The scientific or engineering investigation attempts to model this relationship via some mathematical expression (or a set of mathematical expressions).
Consider fatigue-life of a product that experiences stress. Fatigue-life may serve as a response and research effort is exercised to learn how it "responds" to stress. This "learning effort" result in our ability to characterize fatigue-life behavior and subsequently model the variation observed in fatigue-life in terms of variation in the observed (or applied) stress. Similarly, an electronics-engineer would never be able to design a product without the prior research effort that culminated in modeling a response of interest in terms of design factors that affect it. For example, the voltage of an electric circuit expressed in terms of the electric resistance or capacity of components embedded in the circuit.
"Variation" is another term that needs clarification. There are two components to this term: "Systematic variation" and "Random variation". Most responses that we may wish to model exhibit both sorts of variation. Let us address...
