10 - Experimental Tests for a System Analysis Problem

Abstract

This chapter discusses the procedures for modeling and selecting the working hypotheses in a manner that is consistent with the concept of a system. It is also related with procedures for matching experimental treatments to the mathematical model of the hypothesis. A research problem may be defined as a set of questions assigning unknowns to the cause–effect relationships among variables. The domain of the question is the set of all factors affecting the system. The co-domain is the set of acceptable solutions to the unknowns, as defined in the problem. In system analysis, solutions are expressed as mathematical models of the response functions of the system. Before the experiment takes place, the set of solutions is only a set of hypotheses defined as proposals of mathematical models of the response functions. Testing these models requires testing the coefficients of the mathematical models using the null hypothesis criteria. Critical points of the response curve, such as maximum and minimum values, inflection points, and asymptotic or initial values, are useful indicators for defining a mathematical model of the experimental hypothesis. A pre-experimental selection of mathematical models of the expected response curves of the system is essential for determining the proper experimental treatments. Treatments related to input variables may generate a factorial arrangement. The number and distribution of treatments in the factorial must be chosen to attain the best modulation of the system response functions. When appropriate, the factorial should be nested in the initial states related treatments, which in turn are nested in the treatments related to component variables. Central composite rotatable designs and modifications of these schemes are available for negotiating between the accuracy and the feasibility of experiments.