Estimation Fuzzy Reliability of the Distribution Data (Topp leone- Kumaraswamy)With Application

Abstract

The process of mixing distributions is one of the vital and important processes that contribute to increasing the flexibility and efficiency of the basic distributions. In this research، a new idea was identified، which is the idea of building a new probability distribution function by the function generating the distributions (Topp - Leone) through the single distribution mode (Kumaraswamy). In the function generated and the derivation of the statistical properties of the resulting new mixed distribution (Kumaraswamy- Topp Leone)، which is characterized by efficiency and flexibility in data representation، as the more parameters of the distribution، the greater the accuracy، reliability and preference، and then estimate the parameters of the aforementioned distribution using the informational standard Bayes estimation methods in light of Different loss functions، and the method of optimization algorithm for the gray wolf (GWO)، the failure times were studied، which are often random and fuzzy mixture in it، and this is expressed in fuzzy numbers، and this leads us to estimate the fuzzy reliability function (Fuzzy Reliability) within certain ranges of belonging to the fuzzy group. Practically applying the (Kum - TL) distribution to the real data obtained from the Ministry of Electricity / South Baghdad Station - Al-Zafaraniya، which numbered (70) engines، representing the operating time of the engine until the failure in order to estimate the expected times of future failures. The results showed that the proposed distribution achieved a clear preference in representing real data. In addition، the results showed the superiority of the (BLS_10) method at all different cut-off levels.