Stress-strength reliability for general bivariate distributions
An expression for the stress-strength reliability R=P(X1<X2) is obtained when the vector (X1, X2) follows a general bivariate distribution. Such distribution includes bivariate compound Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the parametric case, the maxi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X16000213 |
| _version_ | 1811235579592966144 |
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| author | Alaa H. Abdel-Hamid |
| author_facet | Alaa H. Abdel-Hamid |
| author_sort | Alaa H. Abdel-Hamid |
| collection | DOAJ |
| description | An expression for the stress-strength reliability R=P(X1<X2) is obtained when the vector (X1, X2) 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 Govindarajulu's asymptotic distribution-free method when X1 and X2 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. |
| first_indexed | 2024-04-12T11:54:25Z |
| format | Article |
| id | doaj.art-0723a2708092420f81d47abe4008e38b |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-04-12T11:54:25Z |
| publishDate | 2016-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-0723a2708092420f81d47abe4008e38b2022-12-22T03:34:03ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-10-0124461762110.1016/j.joems.2016.01.005Stress-strength reliability for general bivariate distributionsAlaa H. Abdel-HamidAn expression for the stress-strength reliability R=P(X1<X2) is obtained when the vector (X1, X2) 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 Govindarajulu's asymptotic distribution-free method when X1 and X2 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.http://www.sciencedirect.com/science/article/pii/S1110256X16000213General bivariate distributionParametric estimation of parameters and stress-strength reliabilityGovindarajulu's non-par-ametric interval bounds of R |
| spellingShingle | Alaa H. Abdel-Hamid Stress-strength reliability for general bivariate distributions Journal of the Egyptian Mathematical Society General bivariate distribution Parametric estimation of parameters and stress-strength reliability Govindarajulu's non-par-ametric interval bounds of R |
| title | Stress-strength reliability for general bivariate distributions |
| title_full | Stress-strength reliability for general bivariate distributions |
| title_fullStr | Stress-strength reliability for general bivariate distributions |
| title_full_unstemmed | Stress-strength reliability for general bivariate distributions |
| title_short | Stress-strength reliability for general bivariate distributions |
| title_sort | stress strength reliability for general bivariate distributions |
| topic | General bivariate distribution Parametric estimation of parameters and stress-strength reliability Govindarajulu's non-par-ametric interval bounds of R |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X16000213 |
| work_keys_str_mv | AT alaahabdelhamid stressstrengthreliabilityforgeneralbivariatedistributions |