# Fleet Resilience: Evaluating Maintenance Strategies in Critical Equipment
## 2 Resilience Metrics  
As certain confusion exists between different terms and definitions of the resilience concept, there is a wide range of metrics that seek to assess and quantify the resilience of a system. The challenge of finding the right resilience metric, considering important properties such as performance and time-related properties and the necessary simplicity of implementation is still open. In 2016, [PERSON] and [PERSON] [32] presented a comprehensive review of the engineering resilience literature, suggesting the need to develop a generally applicable engineering resilience analysis framework. A quantitative analysis of the resilience concept should initially acknowledge that this approach has been little used in the engineering context. [PERSON] et al. [13] suggest a resilience metric to compare the recovery strategies from cyber infrastructure systems failures. Through simulation, they obtain information about possible cascading failures by providing a stochastic reliability model to obtain the resilience assessment. This model is illustrated through the representation of a smart grid type system. The authors do not identify the variable that identifies the level of functionality, nor the performance of the system. They only refer to it as some quantifiable indicator (F(t)). The paper by [33] proposes a set of factors that are used to quantify the resilience of microgrid systems. The level of resilience measurement is determined by the assessment of the percentage of voltage, the level of yield reduction measured by the percentage of reduction in the served load, the recovery time and the time to reach the power balance state. [PERSON] et al. [34] proposed another metric based on the triangle of resilience. This metric is based on the concept of urban infrastructure quality and is founded on the concepts of robustness, redundancy, speed and resourcefulness. These concepts were partially defined by the authors. [PERSON] and [PERSON] [35] proposed a metric to measure the resilience of mechanical systems. The defined metric can be used for system design through time-dependent reliability analysis. The performance measure is expressed as a quantity of interest (economic value of system performance, or other measures). Some authors associate two well known engineering metrics to resiliency: reliability and availability at the system level. [PERSON] et al. [4] mention two main elements: the frequency of disruptive events and their duration. The first element can easily be related to the concept of mean time between failures (MTBF) and reliability, while the second element is a measure of the maintainability of the system, and can be expressed as mean time to repair (MTTR). [PERSON] et al. [36] associate the concepts of availability and resistance. The former represents the percentage of demand that is satisfied during an interruption, while the latter represents the response to a failure, even if it is not a full failure. The resilience concept can be better represented considering Figure 1 (adapted from [37]). This shows the behavior of a given performance metric (e.g., its functionality). This, over time, may suffer variations due to disruptive events. In one such event, performance suffers a significant decline in its level, to a minimum value. From that moment on, the functional performance begins to increase its value in time, until it reaches an \"acceptable\" level, indicated in Figure 1 as the final functional state. [PERSON] [14] emphasizes that resilience must be seen as a global measure that comes from the structure of the system and takes into account all its parts, their interrelationships and local performances, with the way they impact on the whole. According to [PERSON] et al. [38] there is the need to consider the functionality of a system in a holistic way. Thus, different levels of abstraction are possible and necessary. [PERSON] et al.