Response Modeling Methodology Research Articles

Response modeling methodology (RMM)—a new approach to model a chemo-response for a monotone convex/concave relationship

Modeling the variation of a response in terms of the variation transmitted to it by a related factor (or factors) comprises the bulk of the scientific and engineering research effort. Often, we may reasonably assume that the relationship between the response and the affecting factor (or a linear combination of factors) is monotone convex (concave). To model such a relationship, a new Response Modeling Methodology (RMM) has recently been introduced and shown to represent a natural generalization of many theoretical or empirically-derived models, developed over the years in various scientific and engineering disciplines. In particular, many models of chemistry and chemical engineering fall into this category. In this paper, we demonstrate application of the new methodology to the modeling of a chemical response, and discuss extension to non-monotone relationships. It is shown that some well-known and widely used property correlation equations are indeed special cases of the new model. The allied estimation procedures are applied to some published data sets, related to temperature dependence of vapor pressure and solid heat capacity. We assess the effectiveness of the new approach relative to current models.

RESPONSE MODELING METHODOLOGY (RMM)—EXPLORING THE PROPERTIES OF THE IMPLIED ERROR DISTRIBUTION

ABSTRACT Modeling efforts in engineering and the sciences often attempt to describe the relationship between a response and some external affecting factor (or a linear combination of factors), where the modeled relationship is known to be monotone convex (or concave). Recently, a new general model had been developed (in the framework of a new response modeling methodology, RMM), which was demonstrated to be a natural generalization of current mainstream models in many scientific and engineering disciplines, like physics, chemistry, chemical engineering, electric engineering or reliability engineering (hardware and software). The error structure of this model comprises two normal error components, which together define the error distribution associated with the response. In this paper, we derive this error distribution and investigate its properties. We show that widely-used theoretical distributions may be well represented by the new distribution, surprisingly not to be found in textbooks.