Generalized age-dependent model for estimation of mean survival time in the presence of two competing risks

The paper is motivated towards developing a generalized probability model describing the longevity of a system exposed to paired risks R₁ and R₂ which are dependent. The bivariate exponential model of Freund (1961) with failure times X and Y under risks R₁ and R₂ with a time-independent hazard rate set-up has been generalized by incorporating an additional age factor, t, as a variable. The hazard rates due to R₁ and R₂ have been changed from a to α(t) = αt^α?1, and from β to β(f) = βt^β?1 where α,β > 0 which are Weibull hazard functions for α,β > 1. Further conditions are imposed such that α is changed to α' when R₂ is off and β is changed to β' when R₁ is off. The trivariate distribution of Freund so generalized has again been doubly truncated in the range a  t  b, for a, b > 0; and the conditional distribution of X and Y given t has been used to study the role of the component's age in the context of the system's survival under paired dependent risks in the finite age range.