Scheduling optimal maintenance times for a system based on component reliabilities
This dissertation extends the work done on single component maintenance planning to a multi-component series system. An attempt is made to develop a function which represents the expected cost rate (cost per unit time) of any maintenance plan. Three increasingly complex cases are considered.
The first and simplest case assumes that the component is restored to an “as good as new” condition after a maintenance operation. The second case assumes that an occasional imperfect maintenance Operation may occur. During this period of time, the failure rate of the component is higher. Hence, the likelihood of a failure is greater until the component is properly maintained in a subsequent maintenance operation. The final case assumes that there is some deterioration in the component behavior even after a maintenance operation. Therefore, it is necessary to replace the system at some point in time.
Models for all three cases are developed. Based on these models, cost rate functions are constructed. The cost rate functions reflect the cost rates of maintaining a component at a particular time. In addition, the savings obtained through the simultaneous maintenance of components is also accounted for in the cost rate functions. A series of approximations are made in order to make the cost rate functions mathematically tractable. Finally, an algorithmic procedure for optimizing the cost rate functions for all three cases is given.