A Study Of System Reliability Design And Optimization Based On Interval Analysis

Reliability is an important performance measure for an industrial system, especially when it is of safety-critical concerns. The concept of system reliability has drawn much attention since it emerged with a technological meaning at the beginning of last century. Most results reported in existing literature on the optimization of system reliability have been based on the assumption that the probabilistic properties or parameters of time-to-failure involved are deterministic. However, due to observation difficulties, resource limits and system complexities, uncertainties are unavoidable in the modeling of real industrial systems. For many engineering problems, it is overly difficult or costly to collect sufficient data about the uncertainties, especially at the very beginning of the design process. Additionally, as the pace of technological upgrading and increasing becomes faster and faster and the competition on industrial products becomes more and more intense, system designers cannot spare too much time to collect sufficient data and information. This is why uncertainties unavoidably occur. In many cases, the probability distribution of measurement uncertainty is known, but there are some other situations when only the lower and upper bounds of uncertainty are known. Up to now, research on interval uncertainty problems for system reliability optimization and maintenance is relatively less and new.This dissertation presents a study of interval analysis for system reliability optimization and maintenance. It contributes to the modeling and optimization of system reliability and maintenance with due consideration being given to interval uncertainties. The study is confined to the three parts of works described below.The first part of this dissertation discusses the utilization of interval analysis for solving reliability optimization problems. Partly known reliabilities of components or imprecise parameters related to the lifetimes of the components are presented as uncertain-but-bounded values. Three types of standby redundancy are considered in the system reliability optimization problems:active standby (also referred as hot-standby), cold-standby and warm-standby. Interval analysis theory is then applied to handle the uncertain issues involved. The aim of works presented in this part is to enable one to solve system reliability optimization problems even though there are unavoidable interval uncertainties. In order to compare any two interval numbers, we define a new pair of order relations for intervals based on the level of decision maker’s preference.Traditionally, multi-state systems have been characterized by varying performance rates that captured usually exact numbers. However, in some real life situations, the performance values could be dynamic and vary within a certain range. Therefore, we use interval values to represent and deal with performance rates that cannot be represented easily as exact numbers. The second part of this dissertation proposes a new model of a linear multi-state system with interval-valued states. A universal generation function technique for interval values is used to evaluate system reliability. Importance indices for component reliabilities of multi-state systems are also discussed and extended for the new developed model of multi-state systems with interval-valued performance rates.The presence of degradation is a common situation arising in many practical systems. To extend the system’s life and reduce catastrophic breakdown risks, maintenance policies are often adopted. The third part of this dissertation discusses system performance degradation of a cold-standby system along with the maintenance problems of multi-state system with interval-valued states. We develop a model for the reliability and availability of multi-state degraded systems when the system states are represented as interval-valued numbers. We also consider the case of minimal repairs and imperfect preventive maintenance. The system is modeled as a continuous time Markov process. Based on the Markov model, the availability and the reliability of a multi-state degraded system can be evaluated. Moreover, we carry out a study of the redundancy allocation problem for cold-standby systems with degrading components.