abstract

In this thesis, a recent idea was identified, which is the idea of ​​building the probability function of the new proposed distribution (exponential – frecht) by mixing two single distributions, namely the exponential distribution and the frecht distribution by using a parameter known as the mixing ratio parameter to result in the mixed probability distribution (exponential – frecht), which is characterized by With flexibility, efficiency and preference over individual distributions in representing data, the message also aimed to study failure times, in which randomness and fuzziness are often a mixture of them, and are expressed in fuzzy numbers, which means estimating the fuzzy reliability function for it and under certain affiliation ranges for the fuzzy groups.

To achieve this, the thesis was divided into two aspects (theoretical and applied) and the theoretical aspect included generating random data using the method of rejection and acceptance, for different sizes of samples, as well as choosing different values ​​for the distribution parameters by four models, with the aim of giving a clear idea of ​​the measures and their behavior in the event these values ​​change , And the statistical scale averaging the squares of error was used to compare the methods used to estimate the fuzzy reliability function in this message.

The study came out with several results, the most important of which is the expansion of the use of new types of mixed distributions and the recommendation that the study outputs be approved by the department from which the data were collected .