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MIL-HDBK-338 15 OCTOBER 1984 5.2.2.1.6.1 EXAMPLE OF USE OF WEIBULL DISTRIBUTION The failure times of a particular transmitting tube are found to be Weibull distributed with 0 = 2, and T = 1000 hours (consider r\ somewhat related to MTTF). Find the reliability of one of these tubes for a mission time of 100 hours, and the hazard rate after a tube has operated successfully for 100 hours. 2 e-(o.i) te 0>99 = 0.0002 failures/hour 5.2.2.2 DISCRETE DISTRIBUTIONS 5.2.2.2.1 BINOMIAL DISTRIBUTION The binomial distribution is used for those situations in which there are only two outcomes, such as success or failure, and the probability remains the same for all trials. It is very useful in reliability and quality assurance work. The probability density function (pdf) of the binomial distribution is f(x) = (") pX q V""A' (5.4D 0 0-" n! (n-x)!x! (n-x) q and q = 1-P Where \x) = (n-x)lxl ^d q = 1-p (5.42) f(x) is the probability of obtaining exactly x good items and (n-x) bad items in a sample of n items where p is the probability of obtaining a good item (success) and q (or 1-p) is the probability of obtaining a bad item (failure). The cumulative distribution function (CDF), i.e., the probability of obtaining r or fewer successes in n trials, is given by F(x; r) = I H px >"x) A 0 >* qv"~*' (5.43) 5-17

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