# Enhancing Antifragile Performance of Manufacturing Systems through Predictive Maintenance
## 1 Introduction  
Antifragility is a concept introduced and developed by [PERSON] in his book \"_Antifragile: Things That Gain from Disorder_\" [1], not even 10 years ago. Of course, antifragility is opposite to fragility, but it is fundamentally different from the usual antonym for fragility, which is robustness. According to [PERSON], antifragility is more than robustness (the capability to withstand or overcome adverse conditions and, therefore, recover from failure) and more than resilience (the capability to resist failure). By definition [1], antifragility is the feature of a system that increases in resilience or robustness as a result of the harmful effects of stressful actions: malfunctions, shocks, errors, noise, mistakes, disturbances, attacks, faults, or failures. In other words, the idea that stands behind antifragility is that some systems (either natural or artificial) can improve their performance and become better when subjected to various forms of stress. Two years after the appearance of [PERSON]'s book, [PERSON] published a work that somewhat systematizes the means by which an antifragile system can be designed, formulating an equation that has won its celebrity: \"Antifragility = Elasticity + Resilience + Machine Learning\" [2]. Machine learning can be defined as the capacity of a computer to learn from previous data, based on certain algorithms, with the goal of making predictions, classifications, or decisions. Leaving aside the theoretical aspects, which are otherwise very rigorous, the paper proposes a scheme capable of self-optimizing system processing using a machine learning stage which succeeds to enhance the ability of the system to adjust to adverse environmentalconditions, so arguing that an antifragile system is able to learn while using flexible and resilient strategies. What is important in this approach is the idea of the self-optimization of the process in hostile environmental conditions, an idea resumed in another paper [3] that suggests the use of game theory to create a framework for modelling both the system and the environment as competitive opponents seeking to develop optimal behavioral winning strategies. From this seminal point, the works on the design of some antifragile systems have gained expansion and offered various implementation solutions. However, most of the results refer to particular situations, especially in social and economic fields, starting from the simple idea that a substantial gain can be obtained only by assuming significant risks. This approach does not seem to be compatible with the management of industrial processes. Usually, the industry favors efficient, profitable solutions also characterized by the fact that they do not involve significant risks. Ideally, by using the antifragility approach, it would be desirable to obtain a system or process that produces a high reward, while reducing the risk exposure, but these two desires are difficult, if not impossible, to be fulfilled simultaneously. In the aforementioned context, the problem to be solved is to avoid the negative effect of the uncertainties that can appear during the operations, especially due to environmental changes. Modern systems permanently monitor the status of a technological installation in operation and try to detect any anomalies in relation to the normal functioning state. The concept of a \"digital twin\" tries to address the virtual system that functions by mirroring the physical one. Anyway, for the \"health\" status of the system to be maintained, periodic checks are made, the worn parts are changed, and the working parameters are reconfigured to obtain the optimum performance. This operation is called preventive maintenance and ensures the robustness of the system. The limits of preventive maintenance are given by the lack of knowledge about the system's evolution, which is leading to uncertainties. However, if we were able to anticipate shortcomings, then the system would be more than robust; it would be antifragile.