Life Lengths and Association: A Dynamic Approach

We give two sets of conditions for the association of a system's component life lengths. The conditions are dynamic in the sense that they are based on evaluating, at any given time t, the effect a failure would have on the system's future behaviour. Of basic importance is the concept “weakened by failures” introduced in the paper. Mathematically the paper is based on martingales in the case of jump processes, or marked point processes.