Estimating the reliability of type II censored data using the Topp-Leone generator.

A thesis submitted to the council  of the College of Administration and Economics at the University of Karbala  as partial fulfillment  of the requirements for the degree Doctor of Philosophy in Statistics

By

Abdul Amir Taima Bandar

Supervision  UnderProf. Dr. Shrook Abdulredha Saeed

Abstract

Studying the reliability of machines and knowing their efficiency and comparing different types of them, in order to reach the best and formulate economic policies through them, is of great importance in most recent research and studies. Leone) and by putting the exponential distribution – Weibull in the generated function and finding the characteristics of the resulting distribution (Topp – Leone – Exponential–Weibull), also experimental data were generated by the cumulative distribution function by the Monte-Carlo method using four different large sample sizes (n = 200), (n = 100), medium (n = 50), small (n = 25) and different values ​​of parameters at each sample size. The reliability function of the experimental data was estimated by three methods (maximum likelihood, least squares, moments). The preference of the maximum likelihood  method in general over the other two methods, based on the integral mean squares error (IMSE) criterion. On the application  side, real censored data of the second type (observing the number of failed units predetermined during time t) were used. It was obtained from the Ministry of Health – Dhi Qar Health Department about neopolar devices and recording their defect . A comparison was made between the basic distributions (Exponential- Weibull) and the resulting distribution to find out the most efficient of them. The study concluded that the proposed distribution achieved an advantage over the basic distributions by some comparison criteria .

Estimating the reliability of type II censored data using the Topp-Leone generator.

A thesis submitted to the council  of the College of Administration and Economics at the University of Karbala  as partial fulfillment  of the requirements for the degree Doctor of Philosophy in Statistics

By

Abdul Amir Taima Bandar

Supervision  Under

Prof. Dr. Shrook Abdulredha Saeed

Abstract

Studying the reliability of machines and knowing their efficiency and comparing different types of them, in order to reach the best and formulate economic policies through them, is of great importance in most recent research and studies. Leone) and by putting the exponential distribution – Weibull in the generated function and finding the characteristics of the resulting distribution (Topp – Leone – Exponential–Weibull), also experimental data were generated by the cumulative distribution function by the Monte-Carlo method using four different large sample sizes (n = 200), (n = 100), medium (n = 50), small (n = 25) and different values ​​of parameters at each sample size. The reliability function of the experimental data was estimated by three methods (maximum likelihood, least squares, moments). The preference of the maximum likelihood  method in general over the other two methods, based on the integral mean squares error (IMSE) criterion. On the application  side, real censored data of the second type (observing the number of failed units predetermined during time t) were used. It was obtained from the Ministry of Health – Dhi Qar Health Department about neopolar devices and recording their defect . A comparison was made between the basic distributions (Exponential- Weibull) and the resulting distribution to find out the most efficient of them. The study concluded that the proposed distribution achieved an advantage over the basic distributions by some comparison criteria .