Availability of Periodically Inspected Systems with Markovian Wear and Shocks
We analyze 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. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.
Journal of Applied Probability
Kharoufeh, J. P., Finkelstein, D. E., & Mixon, D. G. (2006). Availability of periodically inspected systems with Markovian wear and shocks. Journal of Applied Probability, 43(2), 303–317. https://doi.org/10.1239/jap/1152413724