Economic Design and Maintenance of a Circular k-Out-of-n: G Balanced System With Load-Sharing Units

This article proposes a system design optimization for a circular k-out-of-n: G balanced system with equal load-sharing units. The system consists of n identical units whose failure times are assumed to follow an exponential distribution, and it is subject to an equally shared load among the working units. The load-sharing relationship between the amount of load and the failure rates of the working units is assumed to follow a power rule. If the system is not balanced, it can be balanced by forcing some operating units into standby or returning the standby units into operation. We arrange the system failure paths and use them in the exact reliability evaluation for systems with a small number of units (rotors). Due to the longer computation time, we use a Monte Carlo simulation to approximate the reliability of systems with a large number of units (rotors). We apply two maintenance policies, corrective maintenance, and condition-based preventive maintenance, to understand the effects of system balance conditions, load-sharing rule parameters, system configuration k, and various cost parameters on the optimal maintenance settings, using numerical examples.

I. Introduction

Unmanned aerial vehicles, or drones, are categorized by fixed wings or rotary wings. The flight of drones with rotary wings depends on the operation of the rotors that are spatially distributed along multiple intersected axes and represented by the structure of the circular k-out-of-n: G balanced system. If some rotors fail during flight, the other rotors must work harder to maintain velocity, and we infer that the drone's weight will affect operational efficiency. Thus, a load-sharing dependency occurs because the operating rotors share the load equally.