An Extension of the Birnbaum–Saunders Distribution as a Model for Fatigue Failure Due to Multiple Cracks

Abstract

In this article, we propose an extension of the Birnbaum–Saunders distribution to model the more realistic situations where the fatigue failure time of a material is due to the growth of multiple cracks. Properties of the proposed extended Birnbaum–Saunders (EBS) distribution are discussed; hazard function and the change point of the hazard function of this EBS distribution are derived. Maximum likelihood estimates of the unknown parameters as well as the hazard functions for two special cases of the new EBS distribution are also obtained. Finally, Monte Carlo simulations are carried out to assess the performance of the EBS distribution parameters.

AMS Subject Classification:

• Primary 62E15
• Secondary 62H12

Keywords:

• Birnbaum–Saunders distribution
• Hazard function
• Maximum likelihood estimates
• Monte Carlo simulations
• Multiple cracks