الفهرس 
ACKNOWLEDGEMENTS
CHAPTER 1 :Basic Concepts and Previous StudiesOnly 14 pages are availabe for public view
 |  | from | 112 |  |  |
| | | from | 112 | | |
Abstract
In the statistical literature R = P(Y<X) is known as the stress-strength parameter and it has received significant attention in the last few decades. The parameter R is referred to as the reliability parameter. This problem arises in the classical stress- strength reliability where one is interested in assessing the proportion of the times the random strength X of a component exceeds the random stress Y to which the component is subjected. This problem also arises in situations where X and Y represent lifetimes of two devices and one wants to estimate the probability that one fails before the other. As can be seen from the cited literature, the developments in this field covered a variety of data types including complete data, censored data as well as data with explanatory variables. However, there are many situations in which only observations more extreme than the current extreme value are recorded. If the observation is greater than all the preceding observations it is called an ”upper” record. This thesis is divided into two parts. The first part consists of two chapters dealing with the estimation problem of the stress strength reliability model for Rayleigh distribution (RD). The second part (one chapter) dealing with the problems of one-sample and two- sample predictions using various type of data from RD.
In the first Chapter: Basic concepts, some important definitions and notations
are given. A literature review and some real applications concerning the Rayleigh distribution are reviewed. The Bayesian and non-Bayesian approaches with some related topics are described in details. The description of the problem is presented.
Chapter 2 is concerned with the problem of estimation the stress strength
reliability model R1 = P(Y<X) of Rayleigh distribution when both X and Y are k- upper record values. For this purpose, we propose the ML, Bootstrap and Bayes methods. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX) loss function. Numericall examples using simulated k- upper record data are illustrated and the results of different methods are compared with each others. Finally, Monte Carlo simulation studies have been conducted in order to compare the performance of different methods of estimation.
Chapter 3 is concerned with the problem of estimation the stress strength reliability model R2 = P(Y<X) of Rayleigh distribution when X and Y are of types k-upper record values and ordinary order statistics respectively. We propose the ML, Bootstrap and Bayes methods. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX) loss function. Numericall examples using simulated k-upper record values and ordinary order statistics are illustrated and the results of different methods are compared with each others. Monte Carlo simulation studies have been conducted in order to compare the performance of different methods of estimation.
In Chapter 4 (i) based on a set of k-upper record values from the Rayleigh distribution, the problem of predicting the future k-upper record values (one-sample prediction) is addressed, either point or interval predictions are discussed. The
v
Bayesian prediction interval and the point prediction under symmetric and
asymmetric loss functions for future k-upper record values from the RD are
discussed.
(ii) Prediction bounds for future order statistics from RD based on past sample of k-
upper record values (two-sample prediction) are obtained. The Bayesian prediction interval and the point prediction under symmetric and asymmetric loss functions for future order statistics from the RD are discussed.
(iii) Prediction bounds for future k-upper record values from RD based on past
sample of order statistics (two-sample prediction) are obtained. The Bayesian prediction interval and the point prediction under symmetric and asymmetric loss functions for future k-upper record values from the RD are discussed.
Finally, practical examples using real data set were used for illustration, and Monte
Carlo simulation studies have been carried out for comparison purpose.