There are a lot of techniques for obtaining new statistical distributions. Weibull distribution is one of the most capable statistical distribution in modeling strength data sets. Basic principle of gaining new distribution is increasing modelling efficiency. In this study a new distribution is proposed by taking the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution of which marginal distributions are Weibull distribution. Specifications and characteristics of this new distribution are studied. The structure of the proposed distribution is discussed statistically and the parameter estimation for the new distribution is made by known methods. In addition, reliability analysis has performed. Efficiency on the statistical modeling of the new distribution can be detected by using data sets in literature. The new distribution which is proposed in this study, is compared with Weibull distribution, which is the most known strength statistical distribution, in modeling efficiency. The Kolmogorov Smirnov test statistics was used as a compare method in modeling efficiency of distributions. In Kolmogorov Smirnov test statistics there is a p-value statistic which can be used as explanation rate of the dataset in the model. According to this statistic, modelling efficiency of Weibull Distribution can be improved by 20%. It is concluded that this new distribution offers a model that can be used effectively in strength datasets. With this approach, other statistical distributions modelling efficiency can be improved. Therefore, any researcher who wants to work with a specific distribution, but does not have enough goodness of fit, can increase efficiency with this method.
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