On the independence of system life distribution and cause of failure

Abstract

Under the competing risks model, we obtain conditions for and consequences of the independence of the system life length and the cause of failure. When the survival distributions are continuous, we consider the situations where the risks are independent as well as they are dependent. In the dependent case, the discussion is limited to two risks with some special bivariate survival distributions. The discussion of discrete model where we assume the survival distributions to be discrete, is limited to two independent risks. This results in two characterizations of geometric distribution. Finally some generalizations of our results to k out of m systems are considered.