Failure of fiber bundles with local load sharing

We develop a recursion-relation approach for calculating the failure probabilities of a fiber bundle with local load sharing. This recursion relation is exact, so it provides a way to test the validity of the various approximate methods. Applying the exact calculation to uniform and Weibull threshold distributions, we find that the most probable failure load coincides with the average strength as the size of the system N{→}{∞}. {} 1996 The American Physical Society.