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.

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