مقارنة مقدرات بيز لدالة المعولية لانموذج ويبل للفشل باستعمال دوال خسارة مختلفة مع تطبيق عملي == A Comparison of Bayes Estimators For Reliability Function of Weibull Failure Model By Using Different Loss Functions With Practical Application
Author name:
صبا صباح احمد الجميلي
Supervisor name:
لميعة باقر جواد الجواد
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T4200 - p.pdf
Abstract:
Weibull failure model considered being one of the well known failure models because of its different applications in addition to its importance in the reliability field and life tests.This thesis focused on a comparison of standard Bayes estimators for reliability function of the two parameters Weibull distribution by usingsix different loss functions, three of them have been suggested by the researcher.And for that, the methodology of this thesis depended on the following methodologies : - First : - Theoretical study, the standard Bayesian estimations has been derivatives elaborately to reach the Bayes estimators forms for the reliability function of Weibull distribution by using symmetric and asymmetric loss functions which been explained elaborately, and these are quadratic loss function, logarithm loss function and precautionary loss function to reach to the standard Bayes estimators which called quadratic Bayes estimator (QB), logarithmic Bayes estimator (LB) and precautionary Bayes estimator (PB)) respectively. And those loss functions have been Modified by suggested three modified loss functions counterpart to the functions above to reach proposed estimators which called (modified quadratic Bayes estimator (MQB), modified logarithmic Bayes estimator (MLB) and modified precautionary Bayes estimator (MPB)) respectively.Second : - Experimental study by designing number of simulation experiments using various values of parameters and sample sizes, and with repetition of (10000) times for the comparison among the estimators and by using the mean square error (MSE) to reach efficient estimators with minimum variance. And a collection of real negative and positive values have been tried for the constant which is used in proposed loss functions to reach the best value may used in the comparison, and then a comparison between the six preference estimators is done to show which estimator is the most accurate to be used for estimation the reliability function of Weibull failure model, and best results have been obtained from those simulation experiments.The results of these experiments showed that the modified precautionary Bayes estimator (MPB) is the best for the reliability function of Weibull failure model than the other estimators which have been used in this thesis, and the second best method is the modified logarithmic Bayes estimator (MLB), and after that the precautionary Bayes estimator (PB) and then the modified quadratic Bayes estimator (MQB), also all proposed estimators are better than the logarithmic Bayesestimator (LB) and the quadratic Bayes estimator (QB) which results not to be shown in preferences.Also the results of these experiments show that every proposed estimator is better than its known counterpart.Third : - Application study by taking the best Bayesian estimator in the simulation experiments which is the proposed modified precautionary Bayes estimator (MPB) and applied practically on two experimental real data from WeatherFord company for oil well digging in the Bazergan area of Misan governorate which are represented by the time to failure of the operation of the drilling fluid pumps.From all above, the most important conclusions and recommendations have been offered from the results of this thesis as a specific contribution in the reliability field.
