An expression for the stress-strength reliability R = P( X 1 < X 2 ) is obtained when the vector ( X 1 , X 2 ) follows a general bivariate distribution. Such distribution includes bivariate compound Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the parametric case, the maximum likelihood estimates of the parameters and reliability function R are obtained. In the non-parametric case, point and interval estimates of R are developed using Govin- darajulu’s asymptotic distribution-free method when X 1 and X 2 are dependent. An example is given when the population distribution is bivariate compound Weibull. Simulation is performed, based on different sample sizes to study the performance of estimates.
Abdel-Hamid, A. (2016). Stress-strength reliability for general bivariate distributions. Journal of the Egyptian Mathematical Society, 24(4), 617-621. doi: 10.1016/j.joems.2016.01.005
MLA
Alaa H. Abdel-Hamid. "Stress-strength reliability for general bivariate distributions", Journal of the Egyptian Mathematical Society, 24, 4, 2016, 617-621. doi: 10.1016/j.joems.2016.01.005
HARVARD
Abdel-Hamid, A. (2016). 'Stress-strength reliability for general bivariate distributions', Journal of the Egyptian Mathematical Society, 24(4), pp. 617-621. doi: 10.1016/j.joems.2016.01.005
VANCOUVER
Abdel-Hamid, A. Stress-strength reliability for general bivariate distributions. Journal of the Egyptian Mathematical Society, 2016; 24(4): 617-621. doi: 10.1016/j.joems.2016.01.005
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