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Getting Started

A • STATISTICAL

A • STATISTICAL DISTRIBUTIONS Weibull(, ): WEIBULL(Beta, Alpha) or WEIB(Beta, Alpha) Probability Density Function f(x) = a – a x a 1 – e x 0 otherwise – a for x Parameters Shape parameter () and scale parameter ) specified as positive real values. Range [0, + ) Mean -- 1 a ā - , where is the complete gamma function (see gamma distribution). Variance 2 ---- 2 2 a ā - 1 -- 1 a ā - 2 – 167

GETTING STARTED WITH ARENA Applications The Weibull distribution is widely used in reliability models to represent the lifetime of a device. If a system consists of a large number of parts that fail independently, and if the system fails when any single part fails, then the time between successive failures can be approximated by the Weibull distribution. This distribution is also used to represent non-negative task times that are skewed to the left. 168

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