The availability of inspected systems subject to shocks and graceful degradation

This paper studies maintained systems with nonself-announcing ("hidden") failures that deteriorate due to both shocks and graceful degradation. Shocks occur according to a Poisson process, shock magnitudes are i.d.d. random variables, and between shocks, deterioration occurs at a constant rate. Inspections are performed periodically. Using regenerative arguments, an expression is derived for limiting average availability. This expression provides insight into the effect of system life distribution on availability, and suggests opportunities for more effective inspection strategies.