أختيار افضل طريقة تقدير معولية نيتروسوفيك-(CasCade) مع تطبيق عملي

Rp-Choosing the Optimal Method for Estimating Neutrosophic Reliability: A Practical Application.pdf

In this thesis, a new distribution is proposed that is flexible in dealing with data with uncertainty and uncertainty by transforming the traditional Shukla distribution into a double neutrosophic Shukla distribution (DUS- Neutrosophic Shukla). Neutrosophic uncertainty was applied to the sample data first and then to the parameters of the original distribution in three stages:
Stage 1: Transforming the traditional Shukla distribution into a neutrosophic distribution with data using a neutrosophic random variable (XN). Here, the data are treated even if they are not fully defined through a neutrosophic probability density function that allows handling the uncertainty in the data.
Stage 2: Transforming the traditional Shukla distribution into a neutrosophic distribution with parameters using neutrosophic parameters (ϴN, αN) based on the Florentin Smarandache approach. This transformation takes into account the uncertainty and uncertainty in the distribution parameters, allowing a broader handling of data of an uncertain nature.
Stage 3: Using the DUS transformation to find a dual neutrosophic probability distribution with the data and parameters, which results in a new probability density function and cumulative function for the proposed distribution. This distribution allows data processing while incorporating all forms of uncertainty. The study concluded that the proposed distribution is more flexible and efficient in handling real-world uncertain data compared to traditional distributions, making it a valuable tool for analyzing complex data across various field.
Three methods were used to estimate the reliability of the Cascade(3+1) system under the proposed distribution: the Genetic Algorithm (GA), the Humpback Whale Algorithm (HWA), and the Grey Wolf Optimizer (GWO). This was carried out from two perspectives:
First — Experimental Aspect:
Monte Carlo simulation experiments were conducted using the Pooled Integrated Mean Squared Error (PIMSE) as a statistical indicator. The results showed that the Grey Wolf Optimizer (GWO) outperformed the other algorithms in estimating the neutrosophic reliability of the Cascade system under the DUS Neutrosophic Distribution (DUSDNS) across all sample sizes, especially for large samples (75, 100). The Humpback Whale Algorithm (HWA) ranked second and performed better with small sample sizes (25), while the Genetic Algorithm (GA) showed the lowest level of performance.
Second — Real Data Application:
Expert estimation data regarding inspection and failure policies were obtained from specialists at the State Company for Grain Milling. The experts provided data on the failure times of three milling machines at the Karbala Silo, with each machine contributing 25 measurements, totaling 75 observations. The Grey Wolf Optimizer (GWO) was applied to this dataset. The findings revealed that the system reliability R₂ increases over time, with the truth degree of reliability increasing, the indeterminacy degree decreasing, and the falsity degree decreasing as well. Similarly, the marginal reliability Rd also increased, accompanied by an increase in its truth degree, a decrease in the indeterminacy degree, and a decrease in the falsity degree.

For the marginal reliability R₂, its truth degree decreases, the indeterminacy degree decreases, and the falsity degree also decreases. In all cases, the falsity degree tends to decrease.Regarding the system reliability R₃, it increases over time, with its truth degree increasing, the indeterminacy degree decreasing, and the falsity degree decreasing as well.As for the marginal reliability R₃, it decreases, with its truth degree decreasing, the indeterminacy degree increasing, and the falsity degree decreasing.Thus, the system operates at its highest truth degree of reliability, reaching 0.95041, with an indeterminacy degree of 0.98581, and a falsity degree equal to zero.