Keele Research Repository

The thesis considers several connected problems in the study of reliability of systems with unreliable components. Initially it reviews the dichotomic case introducing a new characterization which clarifies the importance of the k-out-of-n structures. This characterization is applied to two problems, failure to operate and to idle and stress-strength modelling. Whilst most previous work has concerned itself with coherent structures, being thought of as reasonable systems, the latter section of the chapter considers the case of non coherent structures. The following chapter moves from the dichotomic models to multilevel models, considering possible extensions and producing a hierarchy within the possible definitions. Chapter 3 considers the stochastic properties of such systems, again attension is paid to the k-out-of-n structures and non-coherent models. The final two chapters consider component performance. In chapter 4 the system is assumed to be hierarchical, so that a component is part of a subsystem, and it is assumed the whole subsystem may be replaced. The effect on the component is examined. The final chapter considers optimal age replacement of a component considering 3 possible alternative criteria.