An Accurate Approximation to 3-Parameter Weibull Sum Distribution

ABSTRACT: Sum of 3-parameter Weibull is used in communications systems engineering, in reliability engineering and failure analysis. Unfortunately, closed form expressions do not exist for the distribution of 3-parameter Weibull sum. So far no approaches have been proposed for approximation of 3-parameter Weibull sum. An accurate approximation to Rayleigh (2-parameter Weibull with shape parameter equal two) sum is proposed by Jeremiah and Beaulieu, and a simple precise approximation to 2-parameter Weibull sum based on general Gamma distribution is proposed, but this approximation cannot be generalized to a 3-parameter Weibull distribution. In this letter, we present an accurate approximation to a 3-parameter Weibull sum distribution that is based on Generalized Extreme Value (type ) RV.