Open Journal of Statistics, 2021, 11, 1072-1096 https://www.scirp.org/journal/ojs ISSN Online: 2161-7198 ISSN Print: 2161-718X DOI: 10.4236/ojs.2021.116064 Dec. 29, 2021 1072 Open Journal of Statistics Step-by-Step Building of a Four Dimensional Fatigue Compatible Regression Model including Frequencies Enrique Castillo 1,2 , Alfonso Fernández-Canteli 3 , Sergio Blasón 4,5 , Golta Khatibi 6 , Bernhard Czerny 6 , Mohammad Zareghomsheh 6 1 Spanish Royal Academy of Engineering, Madrid, Spain 2 Spanish Royal Academy of Sciences, Madrid, Spain 3 Department of Construction and Engineering Manufacturing, Polytechnic School of Gijón, University of Oviedo, Campus de Viesques, Asturias, Spain 4 Bundesanstalt für Materialforschung und Prüfung (BAM), Berlin, Germany 5 Department 9-Component Safety, Division 9.4, Weld Mechanics, Berlin, Germany 6 Christian Doppler Laboratory for Lifetime and Reliability of Interfaces in Complex Multi-Material Electronics, Chemical Technologies and Analytics, Vienna, Austria Abstract The purpose of this research is to develop a model, with emphasis on compa- tibility conditions and model building, valid for high cycle fatigue design components such as wind turbines, automobiles, high speed railways and aeronautical material. In this work, we have added the frequency as one more variable to an existing fatigue model that already includes maximum stress, stress ratio and lifetime. As a result, a model and estimation method has been proposed and a random variable V has been identified, which, allows the ac- cumulated damage and the probability of failure to be assessed for any load history in terms of stress levels, stress ranges and frequencies. Finally, the model is validated using a large set of real experimental data. Keywords Compatibility Conditions, Cumulative Damage, Frequency Effect, Functional Equations, Regression Model 1. Introduction The current structural integrity concept in the fatigue design in aeronautics, elec- How to cite this paper: Castillo, E., Fer- nández-Canteli, A., Blasón, S., Khatibi, G., Czerny, B. and Zareghomsheh, M. (2021) Step-by-Step Building of a Four Dimensional Fatigue Compatible Regression Model in- cluding Frequencies. Open Journal of Sta- tistics, 11, 1072-1096. https://doi.org/10.4236/ojs.2021.116064 Received: November 26, 2021 Accepted: December 26, 2021 Published: December 29, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access