Availability of periodically inspected systems subject to Markovian degradation

Abstract

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

Availability of periodically inspected systems with Markovian wear and shocks

“…The main result for the limiting average availability (Theorem 5) is contained in Kiessler et al [6]; however, we review this result within the framework of our model, which differs from that of [6] in a few important ways. In our model, a failure occurs when the cumulative degradation (due to wear and shocks) reaches or exceeds a deterministic threshold.…”

“…Fortunately, numerical inversion algorithms abound for this task, and the truncation point γ is well defined by the parameters τ and r 1 . By contrast, the results of [6] require evaluation of an infinite Fourier series to compute p i,k and the conditional expectations.…”

“…Subsequently, Klutke and Yang [7] derived an availability result for a system subject to constant degradation, shocks, and a deterministic inspection policy. In a model similar to the one presented in [5] and in this paper, Kiessler et al [6] studied the limiting average availability of a system for which the wear rate depends on a continuous-time Markov chain. Their model considers an independent, identically distributed sequence of nominal lifetimes that determine the failure criterion, rather than the deterministic threshold value we consider.…”

“…Their model considers an independent, identically distributed sequence of nominal lifetimes that determine the failure criterion, rather than the deterministic threshold value we consider. However, unlike our model, that of [6] does not explicitly provide reliability measures and does not include the degradation due to random shocks. This paper extends the results of [5] and [6] by providing both reliability and availability measures for a system subject to Markovian wear and degradation due to random shocks.…”

“…However, unlike our model, that of [6] does not explicitly provide reliability measures and does not include the degradation due to random shocks. This paper extends the results of [5] and [6] by providing both reliability and availability measures for a system subject to Markovian wear and degradation due to random shocks. Additionally, we demonstrate that the results may be implemented numerically in a straightforward manner by employing standard Laplace transform inversion algorithms.…”