Cumulative Damage Models for Failure with Several Accelerating Variables

Abstract

In this paper, we present a method for incorporating several accelerating variables into accelerated test models for failure of materials. We propose a hyper-cuboidal volume approach as an overall accelerating measure, which enables one to extend existing models for one accelerating variable to the case of several. In particular, we extend a general cumulative damage model and the power-law Weibull model for materials failure to the several accelerating variables case. A real-data example is presented, which illustrates the improvement of the proposed methods over existing models.

Key Words:

• Accelerated testing
• cumulative damage
• failure of materials
• inverse Gaussian distribution
• stochastic process
• strength reduction
• function
• tensile strength

Additional information

Notes on contributors

Chanseok Park

Chanseok Park Professor of Mathematical Sciences at Clemson University, Clemson, SC. He received his B.S. in Mechanical Engineering from Seoul National University, his M.A. in Mathematics from the University of Texas at Austin, and his Ph.D. in Statistics in 2000 from the Pennsylvania State University. His research interests include minimum distance estimation, survival analysis, statistical computing, acoustics, and solid mechanics.

W. J. Padgett

W J. Padgett Distinguished Professor Emeritus of Statistics at the University of South Carolina, Columbia, and a Visiting Professor of Mathematical Sciences at Clemson University, Clemson, SC. He received his Ph.D. in Statistics in 1971 from Virginia Polytechnic Institute & State University. He has published numerous papers on nonparametric and parametric inference in reliability theory and applications, and on other topics in statistics and probability, and co-authored four monographs and seven book chapters. He has been an Associate Editor for Technometrics, Journal of Nonparametric Statistics, and Lifetime Data Analysis, among other journals; and has served as a Coordinating Editor for Journal of Statistical Planning and Inference. He is a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics, and is a Member of the International Statistical Institute.