A generalised semi-Markov reliability model.

The thesis reviews the history and literature of reliability theory. The implicit assumptions of the basic reliability model are identified and their potential for generalisation investigated. A generalised model of reliability is constructed, in which components and systems can take any values in an ordered discrete or continuous state-space representing various levels of partial operation. For the discrete state-space case, the enumeration of suitable system structure functions is discussed, and related to the problem posed by Dedekind in 1897 on the cardinality of the free distributive lattice. Some numerical enumerations are evaluated, and several recursive bounds are derived. In the special case of the usual dichotomic reliability model, a new upper bound is shown to be superior to the best explicit and non-asymptotic upper bound previously derived. The relationship of structure functions to event networks is also examined. Some specific results for the state probabilities of components with small numbers of states are derived. Discrete and continuous examples of the generalised model of reliability are investigated, and properties of the model are derived. Various forms of independence between components are shown to be equivalent, but this equivalence does not completely generalise to the property of zero-covariance. Alternative forms of series and parallel connections are compared, together with the effects of replacement. Multiple time scales are incorporated into the formulation. The above generalised reliability model is subsequently specialised and extended so as to study the optimal tuning of partially operating components. Simple drift and catastrophic failure mechanisms are considered. Explicit and graphical solutions are derived, together with several bounds. The optimal retuning of such units is also studied and bounds are again obtained, together with some explicit solutions.