A Thesis Submitted to

Council of The Faculty of Administration and Economics/
Karbala University as Partial fulfillment of the
Requirements for the Degree of Master of Science in

Statistics

Presented by researcher
Mustafa Talib Abd Ali
Supervised By

Prof. Dr. Awwad Kazem Shaalan Al-Khalidi

This thesis aimed to use the Half-normal distribution as a model for failure by estimating the parameter and reliability function of this distribution using several Methods, namely (Maximum likelihood method, method of moments, the method of least squares, the method of weighted least squares, the method of Precintile estimator).

As a comparison was made between the estimates of the reliability function of these methods by employing the simulation method by the method of (Monte Carlo) and for the purpose of comparing between these methods, the statistical measure was used Mean Square Error Integral. Through the presentation of the results, it was reached that the values of the mean of the squares of the integral error IMSE convergence of all estimation methods at different sample sizes with preference for the method of greatest possibility, which indicates the appropriateness of these methods in estimating the reliability function of the HN distribution.

Then goodness of fit tests were conducted with a sample of real data that represent the failure times of some machines in the State Company for Electrical Industries using the program (Mathematica 12.2) and it was found that the failure times are subject to the Half-normal distribution and using the method of maximum likelihood, an estimate of the parameter and the reliability function of the Half-normal distribution was made using real dat

A Thesis Submitted to

Council of The Faculty of Administration and Economics/
Karbala University as Partial fulfillment of the
Requirements for the Degree of Master of Science in

Statistics

Presented by researcher
Mustafa Talib Abd Ali
Supervised By

Prof. Dr. Awwad Kazem Shaalan Al-Khalidi

This thesis aimed to use the Half-normal distribution as a model for failure by estimating the parameter and reliability function of this distribution using several Methods, namely (Maximum likelihood method, method of moments, the method of least squares, the method of weighted least squares, the method of Precintile estimator).

As a comparison was made between the estimates of the reliability function of these methods by employing the simulation method by the method of (Monte Carlo) and for the purpose of comparing between these methods, the statistical measure was used Mean Square Error Integral. Through the presentation of the results, it was reached that the values of the mean of the squares of the integral error IMSE convergence of all estimation methods at different sample sizes with preference for the method of greatest possibility, which indicates the appropriateness of these methods in estimating the reliability function of the HN distribution.

Then goodness of fit tests were conducted with a sample of real data that represent the failure times of some machines in the State Company for Electrical Industries using the program (Mathematica 12.2) and it was found that the failure times are subject to the Half-normal distribution and using the method of maximum likelihood, an estimate of the parameter and the reliability function of the Half-normal distribution was made using real dat