Stress-strength reliability for general bivariate distributions | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 24, Issue 4, 2016, Page 617-621 PDF (341.39 K) | ||||
| DOI: 10.1016/j.joems.2016.01.005 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Alaa H. Abdel-Hamid | ||||
| Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt | ||||
| Abstract | ||||
| 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. | ||||
| Keywords | ||||
| General bivariate distribu- tion; Parametric estimation of parameters and stress- strength reliability; Govindarajulu’s non-par- ametric interval bounds of R | ||||
|
Statistics Article View: 18 PDF Download: 5 |
||||
