Weibull extensions of the Freund and Marshall-Olkin bivariate exponential models

The physical motivation for the bivariate extensions of the exponential distribution due to Freund (1961) and Marshall-Olkin (1957) is common in engineering applications. The author extends their models to the case where the failure rate of one component changes upon the failure of the other and Poisson fatal shocks cause simultaneous failures of both components in order to derive bivariate extensions of the Weibull distribution. Some special cases, such as bivariate extensions of the linear hazard rate and minimum type distributions, are discussed