On the Number of Maintenance Cycles in Systems with Critical and Non-Critical Components

TL;DR

This paper introduces a new mathematical framework to calculate the number of maintenance cycles in systems with critical and non-critical components, extending renewal theory and validating with real-world wind turbine data.

Contribution

It develops extended renewal models for systems with critical and non-critical components, providing closed-form approximations and validation through simulations.

Findings

Derived formulas for bounded renewal functions.

Validated models with wind turbine component data.

Provided practical tools for maintenance planning.

Abstract

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.