Stress–Strength Reliability of the Type <i>P</i>(<i>X</i> < <i>Y</i>) for Birnbaum–Saunders Components: A General Result, Simulations and Real Data Set Applications

Abstract

An exact expression for R=P(XY) has been obtained when X and Y are independent and follow Birnbaum–Saunders (BS) distributions. Using some special functions, it was possible to express R analytically with minimal parameter restrictions. Monte Carlo simulations and two applications considering real datasets were carried out to show the performance of the BS models in reliability scenarios. The new expressions are accurate and easy to use, making the results of interest to practitioners using BS models.

Keywords

• Birnbaum–Saunders distribution
• stress–strength reliability
• special functions