Estimating the Reliability Function for some Statistical Distributions According to Neutrosophic Logic with a Practical Application

Thesis submitted to

Council of The College of Administration and Economics at The University of Karbala, Which is Part of The Requirements for Obtaining The Degree of Doctor of Philosophy in Statistics Sciences

Written by

Mariam Mahdi Anad Al-Khazali

Supervised by

Prof. Dr. Shorouk Abdel Reda Saeed Al-Sabbah

Abstract

Neutrosophic logic is a development of fuzzy logic to deal with uncertainty and imprecision in information, and it consists of vectors or elements (true, false, indeterminacy), as the vector of the correct part consists of the data whose validity has been confirmed. While the erroneous part includes data whose existence has been verified to be false, while the unspecified part represents data whose correctness or error cannot be clearly determined. In this thesis, new probability distributions were proposed, namely (the exponential distribution of the neutrosophic transform, the Rayleigh distribution of the neutrosophic transform, Weibull distribution of the neutrosophic transform) using the transformation rule (TLRT) to obtain more flexible distributions in modeling the original (real) data, then converting these distributions to neutrosophic vectors and generating a set of data using the simulation method, which is distributed according to the distributions used and using different values and different sample sizes using… Monte Carlo method, where three distribution models were identified (the Exponential neutrosophic transform, the Rayleigh neutrosophic transform) and five distribution models (the Weibull neutrosophic transform).

The parameters of the proposed distributions were estimated and an estimate of the neutrosophic Reliability function was obtained using estimation methods (maximum potential, ordinary least squares, weighted least squares) and comparison between them using the standard mean square error (MSE) and mean square integral error (IMSE) for the three vectors (true, false, indeterminate). It was concluded that the maximum possibility method is the best in estimation and that the indefinite vector is the best vector to represent the data. As for the applied aspect, the proposed distributions were applied practically to real data. The proposed distributions were applied practically to real data, obtained from a station. Diesels east of Holy Karbala, in which the engine stoppage (malfunction) data is compiled, and that these data represent the working times until failure (malfunction) of the (fuel oil purification) device, represented in hours relative to the month, with the aim of modeling it according to the proposed distributions and then estimating the reliability function using the method MLE and the indefinite vector, which simulation experience has proven superior to other methods.

Estimating the Reliability Function for some Statistical Distributions According to Neutrosophic Logic with a Practical Application

Thesis submitted to

Council of The College of Administration and Economics at The University of Karbala, Which is Part of The Requirements for Obtaining The Degree of Doctor of Philosophy in Statistics Sciences

Written by

Mariam Mahdi Anad Al-Khazali

Supervised by

Prof. Dr. Shorouk Abdel Reda Saeed Al-Sabbah

Abstract

Neutrosophic logic is a development of fuzzy logic to deal with uncertainty and imprecision in information, and it consists of vectors or elements (true, false, indeterminacy), as the vector of the correct part consists of the data whose validity has been confirmed. While the erroneous part includes data whose existence has been verified to be false, while the unspecified part represents data whose correctness or error cannot be clearly determined. In this thesis, new probability distributions were proposed, namely (the exponential distribution of the neutrosophic transform, the Rayleigh distribution of the neutrosophic transform, Weibull distribution of the neutrosophic transform) using the transformation rule (TLRT) to obtain more flexible distributions in modeling the original (real) data, then converting these distributions to neutrosophic vectors and generating a set of data using the simulation method, which is distributed according to the distributions used and using different values and different sample sizes using… Monte Carlo method, where three distribution models were identified (the Exponential neutrosophic transform, the Rayleigh neutrosophic transform) and five distribution models (the Weibull neutrosophic transform).

The parameters of the proposed distributions were estimated and an estimate of the neutrosophic Reliability function was obtained using estimation methods (maximum potential, ordinary least squares, weighted least squares) and comparison between them using the standard mean square error (MSE) and mean square integral error (IMSE) for the three vectors (true, false, indeterminate). It was concluded that the maximum possibility method is the best in estimation and that the indefinite vector is the best vector to represent the data. As for the applied aspect, the proposed distributions were applied practically to real data. The proposed distributions were applied practically to real data, obtained from a station. Diesels east of Holy Karbala, in which the engine stoppage (malfunction) data is compiled, and that these data represent the working times until failure (malfunction) of the (fuel oil purification) device, represented in hours relative to the month, with the aim of modeling it according to the proposed distributions and then estimating the reliability function using the method MLE and the indefinite vector, which simulation experience has proven superior to other methods.