1. Optimum preventive maintenance policies maximizing the mean time to the first system failure for a two-unit standby redundant system
- Author
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S. Osaki and T. Nakagawa
- Subjects
Control and Optimization ,System failure ,Applied Mathematics ,Cumulative distribution function ,Theory of computation ,Management Science and Operations Research ,Systems modeling ,Inspection time ,Preventive maintenance ,Unit (housing) ,Mathematics ,Reliability engineering - Abstract
A two-unit standby redundant system with repair and preventive maintenance is considered under the following assumptions: (I) the inspection of an operative unit is made only if the other unit is in standby; and (II) an operative unit, which forfeited inspection due to assumption (I), undergoes inspection just upon repair completion of the failed unit (or inspection completion). We derive the Laplace-Stieltjes transform of the cumulative distribution function of the time to the first system failure and the mean time to the first system failure. Further, we obtain the necessary and sufficient conditions for an optimum preventive maintenance policy to exist with respect to the mean time to the first system failure. More importantly, under certain conditions, we find the analytical form of an optimum inspection time maximizing the mean time to the first system failure. A numerical example is presented.
- Published
- 1974
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