Response Modeling Methodology Validating Evidence from Engineering and the Sciences

Abstract

Modeling a response in terms of the factors that affect it is often required in quality applications. While the normal scenario is commonly assumed in such modeling efforts, leading to the application of linear regression analysis, there are cases when the assumptions underlying this scenario are not valid and alternative approaches need to be pursued, like the normalization of the data or generalized linear modeling. Recently, a new response modeling methodology (RMM) has been introduced, which seems to be a natural generalization of various current scientific and engineering mainstream models, where a monotone convex (concave) relationship between the response and the affecting factor (or a linear combination of factors) may be assumed. The purpose of this paper is to provide the quality practitioner with a survey of these models and demonstrate how they can be derived as special cases of the new RMM. A major implication of this survey is that RMM can be considered a valid approach for quality engineering modeling and, thus, may be conveniently applied where theory-based models are not available or the goodness-of-fit of current empirically-derived models is unsatisfactory. A numerical example demonstrates the application of the new RMM to software reliability-growth modeling. The behavior of the new model when the systematic variation vanishes (there is only random variation) is also briefly explored.

Non‐normal Populations in Quality Applications: a Revisited Perspective

“…Again, at most second-degree moments have been used. Most recently, Equation (5) was found 20 to be a special case of the error distribution associated with a new response modeling methodology that has been recently developed 21,22 .…”

Bid management: A systems engineering approach

“…If there are significant amounts of data and information on the bid system and the subsystem areas, such as extensive technical data, staff resource profiles, asset and capital equipment data and various financial models, then it may be possible to employ more sophisticated systems modeling techniques to develop the bid architecture. Possible techniques include object-orientation through unified modeling language (Keng & Qing, 2001), entity relationship diagrams (Chen & Lu, 1997) or the response modeling methodology (Shore, 2004).…”

Response modeling methodology

“…If the model includes a standard normal quantile (as in cases 1, 2 and 6 above), the expected standard normal quantile is first calculated from the fitted model for each order statistic and then the corresponding DF value is calculated (to be inserted into the formula for AD). Table 3 displays AD 2 values calculated for all seven cases. We realize that the best fitted model, by both criteria, is the RMM model, irrespective of whether it is fitted via ML or by percentile matching.…”

“…First, RMM basic model delivers monotone convex relationships with 'convexity intensity' that varies on a continuous spectrum (rather than in discrete steps). One may appreciate this property on inspecting monotone convex scientific and engineering models that have appeared over the years in the literature (refer to Shore 1,2 for examples). We may realize that a major property that differentiates between these models is their level of convexity.…”