  We present a novel mathematical framework for computing the number of
maintenance cycles in a system with critical and non-critical components, where
"critical" (CR) means that the component's failure is fatal for the system's
operation and renders any more repairs inapplicable, whereas "noncritical" (NC)
means that the component can undergo corrective maintenance (replacement or
minimal repair) whenever it fails, provided that the CR component is still in
operation. Whenever the NC component fails, the CR component can optionally be
preventively replaced. We extend traditional renewal theory (whether classical
or generalized) for various maintenance scenarios for a system composed of one
CR and one NC component in order to compute the average number of renewals of
NC under the restriction ("bound") necessitated by CR. We also develop
approximations in closed form for the proposed "bounded" renewal functions. We
validate our formulas by simulations on a variety of component lifetime
distributions, including actual lifetime distributions of wind turbine
components.
