Bivariate Survival Model Derived from a Weibull Distribution
- 1 June 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Reliability
- Vol. R-30 (2) , 194-197
- https://doi.org/10.1109/tr.1981.5221031
Abstract
A bivariate survival model is based on an underlying Weibull distribution and extends a bivariate exponential model considered by Freund. The model is motivated by a 2-component system which can function even if one of the components has failed. The components initially have a workload (inverse scale parameter) proportional to λ. Upon the failure of one component, the workload of the remaining component becomes proportional to θλ. where λ > 0. The parameter θ describes the amount of support or antagonism between the two components. The joint pdf of the first failure time and the time between the first and second failures is derived. The likelihood equation achieves its maximum in the interior of the parameter space, but the estimators do not have a closed form. A simulation study was performed to evaluate the performance of the maximum likelihood estimators.Keywords
This publication has 4 references indexed in Scilit:
- A Continuous Bivariate Exponential ExtensionJournal of the American Statistical Association, 1974
- A Competing Risk Model: A One Organ Subsystem Plus a Two Organ SubsystemIEEE Transactions on Reliability, 1973
- Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood EstimatesIEEE Transactions on Reliability, 1970
- A Bivariate Extension of the Exponential DistributionJournal of the American Statistical Association, 1961