# Fleet Resilience: Evaluating Maintenance Strategies in Critical Equipment
## 1 Introduction  
Resilience can be defined as the ability of a system to withstand the challenges and threats imposed by the environment. The term resilience originates in the field of ecology [1], but has been expanded to a number of other fields, such as sociology, infrastructure, industry, among others [1]. In industry, the concept of resilience raises as a means to measure the ability of a physical asset, or system of physical assets, to react quickly to disruptive events and to recover its operational condition and operational readiness. However, there is no unanimous measure for such a concept, nor a single way of measuring it. Several authors have suggested resilience metrics in different industry sectors, civil, gas supply [2], electric distribution networks [3], water infrastructure [4], wind farms [5], etc. [PERSON] et al. [6, 7] discuss the use of the concept of resilience across several application areas. In engineering systems, and according to the American Society of Mechanicals Engineers (ASME) [8], resilience is the ability to withstand disruptive events, both internal and external, without interruption in operation, and if it occurs, to recover completely and quickly. The definition of the resilience concept and its measurement combines both quantitative and qualitative aspects [9]. A brief review of the literature shows that there is a number of alternative definitions of resilience. Among the terms used to represent resilience are robustness, survivability, reliability, and availability. [PERSON] et al. [10] proposed three inter-related terms: Reliability, as the degree of susceptibility to failure; Resilience, as the speed with which the system recovers from a failure; Vulnerability, as the degree of severityof failures and their consequences. [PERSON] et al. [11] define vulnerability as the \"non-resilience\" characteristic. According to [PERSON] et al. [12] resilience overlaps with adaptability, robustness, redundancy, flexibility, survivability, recoverability, speed, resourcefulness and reparability. On the other hand, resilience is frequently considered as the speed of recovery from a shock. However, the speed of recovery does not consider the magnitude of the damage caused by the shock [4]. According to [13], resilience should capture the recovery process as the rate between recovered functionality and lost functionality. [PERSON] [14] proposes a metric called the \"quality of resilience\" in which she summarizes the aspects of frequency and extent of interruptions. [PERSON] et al. [15] propose four basic properties that explain, through the 4 Rs framework, the concept of resilience: robustness, redundancy, rapidity and resourcefulness. Robustness is interpreted as the ability to \"avoid\" events that cause a decline in system functionality. Redundancy is based on the existence in the system of alternative resources and elements, to \"cope with\" such a loss of functionality. Rapidity is the ability to act quickly and expeditiously upon the condition that caused the loss of functionality. Finally, resourcefulness represents the condition that a system possesses to trigger the process of recovering the level of functionality. Some authors emphasize that the degree of recovery does not imply a perfect restoration of the system's functionality but considers that the system has returned to a level or state in which it can be considered functional. This situation is recurrent in complex engineering systems that, even in the presence of local failures, the functionality of the system is not completely shut down, but it may occur in a gradual performance degradation process. On the other hand, other authors emphasize that it is necessary that the system recovers the level of functionality that it had before the shock, or at least, a value similar to this one [16; 17]. This reflects two slightly different ways of understanding resilience. One considers resilience as the property of a system to remain close to a stable balance, in regard to its functionality.