Response modeling methodology (RMM) - Exploring the properties of the implied error distribution

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.