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MIL-HDBK-338 15 OCTOBER 1984 (2) (800) P ( Z > JUJOOzZ) f(z = -0.16) _ 0.3939 " 1600 P (Z > -0.16) " (1600J(0.5636) h(800) = 0.0004 failures/round where P(Z > -0.16) was found from Table A-l and f(z = -0.16) from Table A-2 5.2.2.1.4 EXPONENTIAL DISTRIBUTION This is probably the most important distribution in reliability work and is used almost exclusively for reliability prediction of electronic equipment (Ref. 31). It describes the situation wherein the hazard rate is constant which can be shown to be generated by a Poisson process. This distribution is valuable if properly used. It has the advantages of: (1) single, easily estimated parameter (A) (2) mathematically very tractable (3) fairly wide applicability (4) is additive - that is, the sum of a number of independent exponentially distributed variables is exponentially distributed. Some particular applications of this model include: (1) items whose failure rate does not change significantly with age. (2) complex and repairable equipment without excessive amounts of redundancy. (3) equipment for which the early failures or "infant mortalities" have been eliminated by "burning in" the equipment for some reasonable time period. The failure density function is f(t) = Xe-At (5.29) for t > 0, where A is the hazard (failure) rate, and the reliability function is R(t) = e-*t (5.30) the mean life (0) = 1/A, and, for repairable equipment the MTBF = 6 = 1/A 5.2.2.1.4.1 AIRBORNE FIRE CONTROL SYSTEM EXAMPLE The mean time to failure (MTTF = 8, for this case) of an airborne fire control system is 10 hours. What is the probability that it will not fail during a 3-hour mission? R(3) = e-At = e-t/e = e-3/10 = e-0.3 = o.74 5-13

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