الفهرس 
DEFINITIONS AND BASIC CONCEPTSOnly 14 pages are availabe for public view
Abstract
The importance and usefulness of a system depend on its performance. The reliability of a system or a component is defined as the ability of performing its required task. There are many types of systems in reliability evaluation. Some of these types are parallel systems, series systems, k-out-of-n systems, and consecutive k-out-of-n systems. Recently, there has been a considerable interest in the linear consecutive k-out-of-n: F systems, due to their importance in engineering fields and industry. A linear consecutive k-out-of-n: F system is a system consisting of n components arrenged in a line, and the system fails on the failure of at least k consecutive components. There are many practical applications of this type of systems, for example, the oil pipeline and gas systems. In an oil pipeline system, the system consists of n pump stations, each station is powerful enough to send oil as far as to the next k stations. If at least k consecutive pump stations fail, then the oil flow stops, and the system fails. Also, relayed linear consecutive k-out-of-n: F systems are of practical importance. There are two types of relayed linear consecutive k-out-of-n: F systems: unipolar-relayed and bipolar-relayed linear consecutive k-out-of-n: F systems. A unipolar-relayed linear consecutive k-out-of-n: F system is a linear consecutive k-out-of-n: F system, but with the necessity of having the first component working, in order of having no system failure. The bipolar-relayed linear consecutive k-out-of-n: F system is similar but with the necessity of the first and the last components working for system non-failure. A telecommunication system is an example of the relayed linear consecutive k-out-of-n: F systems. This system consisting of a sequence of intermediate stations to transfer some objects, be it a message or a signal from a source to a sink. Since the system works only if the source (sink) works, regardless of the value of k. Such a system is a relayed linear consecutive k-out-of-n: F system, unipolar if only the source is included, and bipolar if both source and sink are part of the system.
The term “stress-strength reliability”, is simply described as an assessment of the reliability of a component in terms of random variables X representing the stress imposed on the component, and Y representing the strength of the component to overcome the stress. If the stress exceeds the strength (X>Y), the component would fail. The stress- strength reliability is then defined as the probability of not failing, and is denoted by R=P(Y>X). Generally, the stress-strength model has been applicated in many areas of life, especially engineering, industry, economics, and medicine.
The objective of this thesis is to study the reliability of regular and relayed linear consecutive k-out-of-n: F systems with a stress-strength setup, when the systems may have one or more change points. A change point in a system means that the reliabilities of the components of the system change after this point. The change may be due to change in stress imposed on components, change in strengths of components, or change in both stress and strength. Practically systems with change points are found in our day life. For example, pipelines transporting gas between two places may be modelled as regular or relayed linear consecutive k-out-of-n: F system having one or more change points. As the system may pass across different environmental factors (for example sea or land). Also, the chiller systems. In such systems, the system components are under different pressure levels.
The thesis is composed of five chapters.
Chapter (Ι), presents basic concepts, definitions, types of systems, and distributions used throughout the thesis. The chapter contains also a brief survey on work done in the literature related to the topic of interest.
Chapter (ΙΙ), introduces a one change point model of regular and relayed linear consecutive k-out-of-n: F systems. Explicit formulas for the reliability of regular and relayed linear consecutive k-out-of-n: F systems are obtained conditioning on the state of the component at the change point, (working or failed). The reliability is obtained for any value of k,1≤k≤n. The reliability of some special types of systems are deduced as special cases from the formulas obtained. A numerical illustration is presented showing the effect of the position of the change point, and the value of k, on the reliability of the system.
Chapter (ΙΙΙ), introduces a model of regular and relayed linear consecutive k-out-of-n: F systems, with m change points. The reliabilities of the systems are obtained using the longest failure “zero’s” run statistic, for 2k≥n. A numerical illustration is presented at the end of the chapter to highlight the theoretical results obtained.
Chapters (ΙV) and (V), are devoted for studying the stress-strength reliability of the models discussed in Chapters (ΙΙ) and (ΙΙΙ), respectively. The change point(s) are assumed to be due to three possibilities: change in stress, change in strength, and change in both stress and strength. The stress-strength reliability formulas of the regular and the relayed linear consecutive k-out-of-n: F systems are derived for any continuous distributions of stresses and strengths. As an application, two cases are studied, Case Ι and Case ΙΙ. In Case Ι, the stresses and strengths are assumed to have the same form of distributions, as an example, the exponential form distribution is considered. Exact formulas of the stress-strength reliability are obtained in this case. In Case II, the stresses and strengths are assumed to have different forms of distributions. As an example, negative exponential distribution for stresses and generalized Lindley distribution for strengths, are applied. Numerical illustration is performed for both cases, Case Ι and Case ΙΙ, showing the effect of the distributions parameters on the stress-strength reliability for all models discussed. Estimators of the stress-strength reliability of all models are obtained by means of maximum likelihood estimation for Case Ι, and Expectation-Maximization (EM) algorithm for Case ΙΙ. The performance of the estimators obtained is detected via a simulation study, showing satisfactory results.
Some of the results of Chapters (ΙΙI) and (V) are published in the “Journal of Statistics Applications & Probability”, and some of the results of Chapters (ΙΙ) and (IV) are published in the “Pakistan Journal of Statistics and Operation Research”.