Estimate of the reliability of the (Topp-leone) distribution with practical application

Thes is submitted to

The Council of the College of Administration and Economics at the University of Karbala, which is part of the requirements for obtaining a Master of Science degree in Statistics

By

Hayder Rassol Naeem

Supervision  Under

Prof. Shrook A.S.AL-Sabbah

Abstract

In this thesis, one of the most important failure models widely used in reliability function studies and life tests when society is heterogeneous is studied, which is the Topp-Leone distribution. The reliability function of the most simple distribution, which is the Topp-Leone distribution in the presence of a shape parameter, taking into account the case of the possibility of determining the affiliation of the individual to the micro-community, as three of the important methods were used to estimate the reliability function, which is the Maximum Likelihood Method, the estimators method Partial Estimates Method, and Shrinkage method.    A comparison was made between the preference of these methods on the experimental side by means of simulation using Matlab program by the Monte Carlo method, and several experiments were conducted using one of the important statistical measures, the Mean Square Error (MSE), and it was generally concluded that The method of maximum likelihood is the best among the other used methods, as it was found that the larger the sample size, the more proving that the method of the maximum likelihood is the best among the methods because it has the least average error squares on the experimental side, but on the applied side, where data for the sonar device was fetched from Al-Rifai Hospital and applied The best method was estimated in the third chapter, where the average reliability of the data used was shown.

Estimate of the reliability of the (Topp-leone) distribution with practical application

Thes is submitted to

The Council of the College of Administration and Economics at the University of Karbala, which is part of the requirements for obtaining a Master of Science degree in Statistics

By

Hayder Rassol Naeem

Supervision  Under

Prof. Shrook A.S.AL-Sabbah

Abstract

In this thesis, one of the most important failure models widely used in reliability function studies and life tests when society is heterogeneous is studied, which is the Topp-Leone distribution. The reliability function of the most simple distribution, which is the Topp-Leone distribution in the presence of a shape parameter, taking into account the case of the possibility of determining the affiliation of the individual to the micro-community, as three of the important methods were used to estimate the reliability function, which is the Maximum Likelihood Method, the estimators method Partial Estimates Method, and Shrinkage method.    A comparison was made between the preference of these methods on the experimental side by means of simulation using Matlab program by the Monte Carlo method, and several experiments were conducted using one of the important statistical measures, the Mean Square Error (MSE), and it was generally concluded that The method of maximum likelihood is the best among the other used methods, as it was found that the larger the sample size, the more proving that the method of the maximum likelihood is the best among the methods because it has the least average error squares on the experimental side, but on the applied side, where data for the sonar device was fetched from Al-Rifai Hospital and applied The best method was estimated in the third chapter, where the average reliability of the data used was shown.