Using  Some of Robust and Non parametric Methods to estimate Reliability function  (practical  Study)
A Thesis Submitted to
Council of The college of Administration and Economics at the
Kerbala University
As a Part of the Requirements for  obtaining  a master Degree
in Statistics

By
Thaer  Hashim Abd ulmubttale
Supervised By
Assist.Prof.Dr
Jassim Nassir Hussein

ABSTRACT:

     The reliability function is defined as the probability of completion of any part of the system over a specified period of time and in the same circumstances. The reliability study must identify the reliability function and the aggregate function of failure as well as identify the appropriate distribution.

  Many of the facilities, including the textile section of the General Company for Textile Industries in Wasit, lack a practical evaluation, which causes continuous stops in the machines in addition to the data problems. Therefore, the purpose of this thesis is to estimate the reliability function of the second type monitoring data subject to Raleigh distribution (Rayle) through some robust estimation methods and non-learning methods, and to choose the best method of estimation using Mean Square Error.

  The problem of the message is that there are many methods for estimating the reliability function but often the most suitable conditions are not available these methods in data such as the presence of abnormal values ​​or extreme or not knowing the proper distribution of this data so you need to modalities through which to deal with this problem.  Four estimation methods were used: the Bayes hippocampus method, the H (H) estimator method, the experiment method and the Kernel  method. These estimation methods were derived to arrive at their ability formulas.

   A comparison of these capabilities was performed using simulations. Simulation experiments were carried out using different sample sizes and repeated  The results were compared with one of the most important statistical measures, the mean error squares (MSE). The best method of estimation was obtained.  For textile industries in Wasit which If the machine is taken from a machine of size (250) machine, and after the distribution was confirmed by a good match test, the reliability function was estimated using the best method reached by the researcher through the experimental side, M) Hippocampus It has been shown that the estimation of the reliability function decreases gradually over time and this is consistent with the characteristics of this function.