الفهرس 
الفصل الاوليوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
Mixed distributions are among the important distributions, especially in recent years, due to their role in data modeling and their flexibility and conformity to most data, which results from mixing two or more distributions In this study, two single distributions, namely the Weibull distribution and the Rayleigh distribution, were mixed using the mixing ratio parameter, resulting in the mixed statistical distribution (Weibull - Rayleigh), which is characterized by flexibility and efficiency compared to the single distributions in representing data, and due to the presence of a lot of data that suffers from the problem of inaccuracy in its measurements. It has a different degree of affiliation to its groups; It is called fuzzy data and is expressed in fuzzy numbers, as reliability in light of this fuzzy data is the fuzzy probability that a single unit will remain operational after the passage of time. Therefore, the study aimed to use three methods to estimate the parameters of the mixed distribution (Weibull-Rayleigh) and use these estimates to estimate the fuzzy reliability of the distribution. Some mathematical properties were also studied, such as the aggregate function and the probability density function. Therefore, the thesis was divided into two parts (the experimental and the real), and the experimental side included the use of the simulation method, where the Monte-Carlo method was adopted for the purpose of generating data with different sample sizes and choosing different values for the distribution parameters and with (7) models. The experiment was repeated for the purpose of generating 100 times to achieve the most homogeneity. Through the simulation results, where the statistical measure, the mean squared error, was used to compare the methods used, the results showed that the maximum likelihood method is the best method for estimating the fuzzy reliability of a mixed distribution.As for the real (applied) aspect, data was obtained for the duration of operation of the electric power production engines for the Najibiyah Thermal Power Station in Basra Governorate, and goodness-of-fit tests were applied to this data and it was more consistent with the mixed distribution. The study produced a number of results, the most important of which is the expansion of the use of new types of mixed distributions and the adoption of these results by the ministry from which the data was collected