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العنوان
The Use of Progressive Stress
Accelerated Life Testing under Weibull
Extension Distribution /
المؤلف
Elham AbdelMalik AbdelRahman AbdelMalik,
هيئة الاعداد
باحث / Elham AbdelMalik AbdelRahman AbdelMalik
مشرف / Abdalla A. Abdel-Ghaly
مشرف / Hanan M. Aly
مناقش / Abdalla A. Abdel-Ghaly
الموضوع
Statistics
تاريخ النشر
2022.
عدد الصفحات
137 p. :
اللغة
الإنجليزية
الدرجة
الدكتوراه
التخصص
الإحصاء والاحتمالات
تاريخ الإجازة
11/7/2022
مكان الإجازة
جامعة القاهرة - كلية اقتصاد و علوم سياسية - Statistics
الفهرس
Only 14 pages are availabe for public view

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from 167

Abstract

In this thesis, the problems of estimating the unknown parameters and
prediction of future observations are considered when the lifetime units follow
an extended Weibul (EW) distribution under ramp stress accelerated life
testing (RS-ALT) in the presence of adaptive type-II progressive censoring
(A-II-PC) samples. Thus, this thesis is divided into two main parts. In part
one, both classical and Bayesian approaches are adopted to obtain point and
interval estimators for the parameters and the acceleration factors. Under
classical approach, three algorithms called scoring, expectation-maximization
(EM), and stochastic expectation-maximization (SEM) algorithms are
applied and the associated asymptotic and bootstrap condence intervals
(CIs) are derived. While an extension of Hamiltonian Monte Carlo (HMC)
method, called No-U-Turn Sampler (NUTS) is implemented through Stan
software to obtain Bayesian point and interval estimates.
In part two, one-sample and two-sample prediction problems are discussed
from Bayesian and classical viewpoints. Under the latter, point prediction
estimators are obtained using the best unbiased predictor (BUP) and
conditional median predictor (CMP) while interval prediction estimators
are constructed using a pivotal quantity. Concerning Bayesian method, two
dierent methods based on NUTS applied by Stan are used to compute point
and interval prediction estimates.
To assess the performance of the suggested methods in this thesis, a Monte
Carlo simulation study is conducted and revealed that all the proposed
methods display good and close performance either under point or interval
estimation and prediction. However, Bayesian approach shows superiority
over classical approach under parameter estimation. While, the latter
slightly outperforms the former in case of predicting the future observations
under one-sample and two-sample problems. To illustrate the applicability
of the methods provided in this thesis in reality, a real data example is
presented and discussed. In this example, a new goodness of t test proposed by Gaigall (2019) in case of multi-samples is applied and proved a good t for the EW distribution in representing RS-ALT data.