Bivariate Survival Model Derived from a Weibull Distribution

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.