The deterioration observed in many industrial systems may be modelled in two phases. In the first phase, a period during which the system operates fault free ends with entry into a worn state. In the second phase, the system spends time in the worn state prior to failure. Should the system be found to be in the worn state upon inspection, failure can be pre-empted by preventive maintenance. The first goal of analysis is the design of cost effective policies for the inspection, repair, and renewal of such systems. The thesis extends previous work by offering a choice between a (cheap) repair and a (more expensive) renewal of the system, should it be found to be in the worn state upon inspection. The decision-maker may also renew the system at any time without inspection. Simple, cost effective heuristic policies are proposed, whose design avoids the computational complexities of a full dynamic programming (DP) solution. The second goal of analysis is to determine when deployment of an error-prone sensor may be beneficial to the operation of such systems. It is supposed that a system is monitored continuously by such a sensor, which returns a positive result should entry into the worn state be detected. The sensor may produce errors of both kinds, false-positive and false-negative. Extending the earlier work of the thesis, simple, cost effective heuristics are developed for use with the sensor. In se- -i 11 lected cases, numerical investigation identifies operational characteristics for which use ofa sensor is (i) cost indifferent, (ii) beneficial, and (iii) not beneficial. The question of how sensor quality impacts upon heuristic design is also investigated. To the author's knowledge, the model proposed in this section of the thesis is new to the literature.