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Abstract
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A system consists of two modules, both of which must operate for the system to operate. One of the modules is inaccessible to inspection, while the second is continuously monitored. When a revealed fault occurs in the second module the system is replaced by a new system. So if no preventive maintenance plan is used then the system will fail to operate when an unrevealed fault occurs in the first module until a revealed fault occurs in the second module and the system is replaced.
A preventive maintenance plan can be used to periodically replace the system with a new system, and so improve the availability of the systems. The optimum inspection intervals can be chosen using either the criterion of maintaining the system availability above a given level or the criterion of minimising the cost of the expected number of unmet demands on the system and the cost of the plan.
Results are obtained for a model of the system when replacement is instantaneous. Firstly, these are given when the modules fail independently and the failure times have negative exponential distributions. Secondly, these are given when the modules' failures are dependent. In this case it can be shown that if the failure times to unrevealed faults (in the first module) have a negative exponential distribution and this distribution is independent of the distribution of times between unrevealed faults (in the first module) and revealed faults (in the second module) then the results are independent of the distribution of failure times to revealed faults (in the second module). The optimum inspection intervals are given for these models. |