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Availability of periodically inspected systems with Markovian wear and shocks. (English) Zbl 1132.90006
The present paper analyzes a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. The authors explicitly derive the system’s lifetime distribution and mean time to failure, as well as the limiting average availability. The results may be implemented numerically in a straightforward manner by employing standard Laplace-transform inversion algorithms. The Laplace-Stieltjes transform of the unconditional and conditional lifetime distribution functions as well as the unconditional and conditional mean system lifetimes are provided in a closed form. The main results are illustrated in two numerical examples.
MSC:
90B25Reliability, availability, maintenance, inspection, etc. (optimization)
60K37Processes in random environments