ESTIMATION OF THE RELIABILITY OF THE NITROSOPHYC (CASCADE) DISTRIBUTION (DUS-DNS) USING THE GREY WOLF ALGORITHM WITH A PRACTICAL APPLICATION

Abstract

In this research, a new distribution is proposed that is flexible in dealing with data with uncertainty by transforming the traditional Shukla distribution into a double neutrosophic Shukla distribution (DUS). The neutrosophic uncertainty was applied to the sample data first and then to the parameters of the original distribution The proposed distribution was found to be more flexible and efficient in dealing with real data characterized by uncertainty compared to traditional distributions, making it an important tool for analyzing complex data in multiple fields.. The Grey Wolf algorithm was used to estimate the reliability of the Cascade system under the proposed distribution (Grey Wolf Optimizer - GWO), by applying real data to estimate the reliability of the CASCADE nitrosophic system for the distribution (DUS-DNS). Estimated data were used for the inspection and breakdown policy by experts in the General Company for Grain Milling, by seeking the help of experts in the company to obtain data related to the breakdown times of the milling machines. Data was obtained representing the number of days of breakdown of three grain milling machines in the Karbala Silo for each machine (25) The total number of measurements is (75) observations, and the Grey Wolf algorithm was applied to them. It was found that the reliability of the system R_2 increases with the increase of time, and the degree of accuracy of the reliability of the system 2R increases, and the degree of neutrality decreases, while the degree of error decreases. Likewise, the marginal reliability R(1) also increases, and the degree of accuracy of the marginal reliability R(1) increases, The degree of neutrality decreases, while the degree of error decreases, while the marginal reliability R(2) has a degree of correctness decreasing, and the degree of neutrality decreases, and the degree of error decreases. In all cases, the degree of error decreases. And the reliability of the system R_3 increases with increasing time, and the degree of correctness of the reliability of the system 3R increases, and the degree of neutrality decreases, , while the degree of error decreases. The marginal reliability R(3) also decreases, and the degree of accuracy of the marginal reliability R(3) decreases, and the degree of neutrality increases, while the degree of error decreases. The system operates with the highest degree of accuracy for reliability of (0.95041) and a degree of neutrality of (0.98581) and an error amount equal to zero.