تَقدِيرات دالَة المُعَّوَلية لِتوزيع بُواسُون مع تطبيق عملي

Estimation of reliability function for Poisson distribution With practical application

Abstract :

The technological development and the use of complex electronic systems in various fields led many researchers to study the Reliability. Therefore, the study of the Reliability and linkage between the theoretical and practical aspects is of great importance because it is the indicator to show the efficiency and ability of the machine to work without breaks for a period of time Long for the purpose of increasing production of both quality and quantity. Since the number of failures is subject to the distribution of Poisson, the study focused more on the study of the Poisson processes by two types the homogeneous(HPP) and non-homogeneous (NHPP), and the absence of a general trend in the number of failures vs. time t It was appropriate to analyze data using the Poisson regression. This study was concerned with estimating the reliability function in the case of data distributed of Poisson distribution in comparison to three methods of estimation methods, namely the Poisson regression method as a regression method, and the Maximum Likelihood method as a traditional method, and Kaplan-Meier method as a method of nonparametric. For the purpose of applying the theoretical dimensions of the estimation methods, the Monte Carlo method was used using a programming language R (version 3.3.2), and several experiments were carried out by producing a random sample with a Poisson distribution based on sample sizes equal to (n =10,20,30,40 ,50,100). The replicates for each experiment were L = 5000. The estimation methods were compared by using Mean Squares Error and were reached with generally concluded that the maximum Likelihood estimator was the best of these estimates because it had the lowest mean error squares compared to other capabilities, it means, the reliability estimation of the data distributed by the Poisson distribution the maximum Likelihood method is best for all sample sizes, followed directly by the Poisson regression method and for all sample sizes. As for the practical side has made Chi Square test was first on available data that represent the number of failures of some of the machines in Dar Al- Warith for printing and publishing in the holy city of Karbala using a statistical program (Easy fit) shows that the number of failures are distributed (Poisson distribution), and they trace non homogenous poison processes, and because the Maximum Likelihood for the reliability function is the best of these capabilities after an estimated contraction according to a pilot aspect in this research has been the estimated these machines account under study for the purpose of identifying efficiency and behavior with time, as a function account reliability way to measure based on the Mean Time Between Failures (MTBF) .