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MIL-HDBK-338 15 OCTOBER 1984 5.2.2.1.6 WEIBULL DISTRIBUTION The Weibull distribution is particularly useful in reliability work since it is a general distribution which, by adjustment of the distribution parameters, can be made to model a wide range of life distribution characteristics of different classes of engineered items. One of the versions of the failure density function is f(t) n \ i? ) exp - 1 -jj- \ (5.37) where /3 is the shape parameter >7 is the scale parameter or characteristic life (life at which 63.2% of the population will have failed) y is the minimum life In most practical reliability situations, y is often zero (failure assumed to start at t = 0) and the failure density function becomes nt) = % * 0 (tW exp 4 (5.38) and the reliability and hazard functions become .0 R(t) exp # h(t) = m ff t\0-i (5.39) (5.40) Depending upon the value of j8, the Weibull distribution function can take the form of the following distributions as follows, /3<1 0= 1 0= 2 0= 3.5 Gamma Exponential Lognormal Normal (approximately) Thus, it may be used to help identify other distributions from life data (backed up by goodness of fit tests) as well as being a distribution in its own right. Graphical methods are used to analyze Weibull failure data and are described in Section 8. 5-16

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