Modelling (Feb 2024)

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

  • Felipe S. Quintino,
  • Luan Carlos de Sena Monteiro Ozelim,
  • Tiago A. da Fonseca,
  • Pushpa Narayan Rathie

DOI
https://doi.org/10.3390/modelling5010012
Journal volume & issue
Vol. 5, no. 1
pp. 223 – 237

Abstract

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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