تقدير دوال موثوقية القوة-الإجهاد لتوزيع معكوس رايلي الأسي
Estimation of Stress-Strength Reliability Functions for Exponentiated Inverse Rayleigh Distribution
- الباحث
- محمد أمين عقبة محمد نوري الأغا
- المشرف
- ريا سالم محمد علي الرسام
- الجامعة
- جامعة الموصل
- الكلية / القسم
- كلية علوم الحاسوب والرياضيات / الإحصاء والمعلوماتية
- الشهادة
- ماجستير
- السنة
- 2023
- لغة الرسالة
- عربي
- الكلمات المفتاحية
- موثوقية القوة والإجهاد ; توزيع معكوس رايلي الأسي ; تقدير المعلمات ; المحاكاة
Abstract
In this thesis, a mathematical formula was found for the stress- strength reliability function when the component strength (X) is subject to stress (T) ; as well as a mathematical formula for the stress-strength reliability function when the components' strength (X) lie in between two stresses (T ) and (Z) for the complete data, where each of X, T, Z follows the Exponentiated inverse Rayleigh distribution with an equal (common) and known scale parameter (λ); and different unknown shape parameters , and then these formulas were estimated using point estimation methods, which are the maximum likelihood estimation (MLE) and the Bayesian method under a symmetric loss function (Quadratic loss function) and an asymmetric loss function (Weighted square error loss function) when the prior distributions are nun-informative and also when The prior distributions are informative, and the interval estimation of the stress-strength reliability function formulas was also found in the case of large samples by relying on the maximum likelihood estimators of the reliability function. On the experimental side, random samples of sizes (n,m) for and of sizes (n,m,w) for were generated using the (R Studio) program, and the experiment was repeated 1000 times. Then the estimators of the maximum likelihood and the Bayesian method were found, and a comparison was made between these estimates using the mean squares errors criteria . also a real data has been applied for which represent two data sets of coating weights which used for coating the roofing iron sheets taken from ALAF industry; and the estimated stress-strength reliability has been calculated for these data It was found that the probability of rusting on the upper and lower surfaces of the coated iron sheets with aluminum-zinc mixture is 50% compared to the uncoated iron sheets.
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