by Haim Shore (Ben-Gurion University of the Negev, Israel)

This book introduces a new approach, denoted RMM, for an empirical modeling of a response variation, relating to both systematic variation and random variation. In the book, the developer of RMM discusses the required properties of empirical modeling and evaluates how current approaches conform to these requirements. In addition, he explains the motivation for the development of the new methodology, introduces in detail the new approach and its estimation procedures, and shows how it may provide an excellent alternative to current approaches for empirical modeling (like Generalized Linear Modeling, GLM). The book also demonstrates that a myriad of current relational models, developed independently in various engineering and scientific disciplines, are in fact special cases of the RMM model, and so are many current statistical distributions, transformations and approximations.

• Current Models and Modeling Methodologies:
  • Relational Models in Engineering and the Sciences (Monotone Convex/Concave Relationships)
  • Shared Features and “The Ladder”
  • Approaches to Model Systematic Variation
  • Approaches to Model Random Variation
  • The Requirements and Evaluation of Compliance
• RMM — Developing and Evaluating the General Approach:
  • The RMM Model
  • Estimating the Relational Model
  • The RMM Error Distribution
  • Fitting Procedures (for the Error Distribution)
  • Estimating the Error Distribution
  • Special Cases of the RMM Model
  • Evaluating RMM for Compliance
• Modeling Systematic Variation — Applications:
  • Comparative Solutions for Relational Models
  • Reliability Engineering (with Censoring)
  • Software Reliability-Growth Models
  • Modeling a Chemo-Response
  • Forecasting S-Shaped Diffusion Processes
• Modeling Random Variation — Applications:
  • RMM Distributional Approximations
  • Inverse Normalizing Transformations
  • Piece-Wise Linear Approximations
  • General Control Charts
  • Inventory Analysis