Approximations for the system hazard function.
Hayne, William John
Esary, James D.
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Methods for approximating the system hazard function are developed for systems which have constant component failure rates. The approximations are applicable to systems which are "highly reliable," e.g., all component reliabilities greater than 0.9 and system reliability greater than 0.95. Three approximations are developed. The first-order approximation is based on the system cuts of least size (smallest cuts). The fix-up approximation is based on the minimal cuts of the system and is an extension of the methods used in NAVWEPS OD 29304. The second-order approximation is a more accurate extension of the first-order approximation. The advantages peculiar to each of these approximations are: (1) first-order: easy to calculate, (2) fix-up: never leads to an overestimate of system reliability, (3) second-order: relatively more accurate.
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