مقارنة بعض طرائق تقدير المعلمة والمعولية لانموذج ريلي للفشل لبيانات تامة وبيانات تحت المراقبة من النوع الاول باستخدام المحاكاة == A Comparison of Some Estimation Methods of Parameter And Reliability of Rayleigh Failure Model For A Complete Data And Type One Censored Data By Using Simulation
Author name:
صبا صباح احمد الجميلي
Supervisor name:
عبد المجيد حمزة الناصر
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Master
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3782 - p.pdf
Abstract:
تعرض الكثير من الباحثين الى انموذج ويبل للفشل (Weibull Failure Model) وتطبيقاته المختلفة كونه احد نماذج الفشل الشائعة الى جانب اهميته في حقل المعولية واختبارات الحياة. فـي هـذا البحث تـم تقديـر معلمــة القياس ودالـة المعوليـة لانموذج ريلـي للفشـل (Rayle | Weibull Failure Model and its different applications have been studied by many researchers, since it is one of the well known failure models in addition to its importance in the reliability field and life tests.This research estimated the scale parameter and reliability function for Rayleigh Failure Model, which is one of the well known failure model in the reliability field and life tests and the signal analysis.The research focused on the comparison between some of the well known estimation methods (classical and Bayesian) for the scale parameter and reliability function of this model by using the Maximum likelihood, Moments, White and Standard Bayes estimation methods.The methodology of the research depends on theoretical study, the methods of classical and Bayesian estimation has been determined elaborately to arrive to the estimations forms of reliability.Also this research depends on an experimental study by designing number of simulation experiments using various values of parameters and sample sizes, this experiment replicated to get high homogeny for the comparison among the estimation methods.Two kinds of data are used in the research : 1 - Complete Data.2 - Time - Censored Data. The researcher suggested two Bayesian methods for estimation in case of complete data; the first is a loss function obtained by compressing the well known square loss function which called it (The Compressed Bayes Method), and the second is a prior function which is called (The Developed Bayes Method). The comparison between the two proposed methods is done to show the effect of Bayesian estimator, then a comparison done between the best proposed methods with the best well known methods to show which estimator is the more accurate to be used for estimation the scale parameter and reliability function for Rayleigh failure model.The results of these experiments show that White method is the best from the other methods which are used in this research in estimating the scale parameter and reliability function, and the results show that the proposed Compressed Bayes method is better than the Standard Bayes and the Maximum Likelihood methods, while the proposed Developed Bayes method verified that it is better than the Moment method in estimating the scale parameter and the reliability function; and better than the Maximum Likelihood estimation method in estimating the reliability function, and using any of the proposed methods (Compressed Bayes, Developed Bayes) is better than the Standard Bayes method. In case of censored data the simulation experiments proved that the Maximum Likelihood estimation method is better than the Standard Bayes estimation method. A comparison of preference estimation methods is done by using the two standards; Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE).
