Abstract: Several components having lifelengths which are not necessarily independent are ``competing'' to fail first. We show that the time and identity of first failure are mutually independent if and only if the cause specific hazard rates of the components are proportional to each other.
Key words and phrases: Competing risks, dependent failure times, joint survival function, proportional hazard functions, cause-specific hazard rate function, bivariate symmetry, absolutely continuous bivariate exponential function, parallel systems.