A New Fatigue Life Model Based on the Family of Skew-Elliptical Distributions

Abstract

ABSTRACT Fatigue is structural damage produced by cyclic stress and tension. An important statistical model for fatigue life is the Birnbaum–Saunders distribution, which was developed to model ruptured lifetimes of metals that had been subjected to fatigue. This model has been previously generalized and in this article we extend it starting from a skew-elliptical distribution, the incorporation of the elliptical aspect makes the kurtosis flexible, and the skewness makes the asymmetry flexible. In this work we found the probability density, reliability, and hazard functions; as well as its moments and variation, skewness, and kurtosis coefficients. In addition, some properties of this new distribution were found. Keywords: Birnbaum–Saunders distributionKurtosisLife distributionsMaterial fatigueMomentsReliability analysisSkew-elliptical distributionsSkewnessMathematics Subject Classification: Primary 62E15Secondary 62N05 Acknowledgments This study was carried out with the support of research projects FONDECYT 1050862, FANDES C-13955/10, and DIPUV 42-2004 from the Universidad de Valparaíso, Chile. The authors also wish to thank the Referee and Editor for their very helpful suggestions and editing of this article. In addition, we would like to thank Dr. Héctor Gómez for his useful comments and Michelli Karinne Barros da Silva for the review of this manuscript.