# Enhancing Antifragile Performance of Manufacturing Systems through Predictive Maintenance
## 5 Dealing with Uncertainties in Antifragile Manufacturing Systems
Of course, this approach is mainly reflected in the transposition of uncertainty based on the degree of confidence in the predictive maintenance algorithms. One of the major challenges in PdM is validation of the prognostic methods, which require the comparison of estimated failure times with the observed failures. In fact, this is the main element that creates the difference between PdM and PvM. The performance of a forecast model can only be tested when a failure occurs. PvM policies, as they greatly reduce the number of failures observed, significantly complicate the validation of the prognostic method. Solutions for checking the status of a system at predefined fixed intervals become insufficient in the case of increasingly complex manufacturing processes. In the case of PdM, which permanently provides additional information about the level of system degradation or the occurrence of behavioral anomalies, information about the possibility of a failure is already available before the actual failure occurs. The limitations of the probabilistic approaches are mainly due to three causes: (i) model uncertainty (there is no perfect model; the accuracy of the model depends on the volume of knowledge and the level of detail); (ii) data uncertainty (the use of expert data, accuracy, and relevance in the data acquisition); and (iii) the changing context (events cannot be known with certainty because of their continuous change). We have already mentioned in Section 3 that an ASIS has in principle nonconflicting optimization objectives and, as such, can successfully solve multiobjective optimization (MOPs) problems. On the other hand, we discussed only well-defined objectives, unaltered by uncertainties. The problem is complicated if the control techniques aim to identify optimal solutions in an uncertain environment. In MOPs, uncertainties are due either to disturbances in the variables involved in the decision-making processes or unpredictable changes in the environmental parameters. In this context, we want to develop methods that determine the most robust solutions, i.e., the least sensitive to disturbances. However,in this situation, we reach again the situation in which we have to accept a compromise between achieving optimal performance and robustness, respectively. An interesting solution, which we decided to adopt, is to combine a PdM procedure with the method presented in [23], whose objective is to minimize the weighted amount of quality robustness (QR) and robustness of the solution, which in our paper we call functional robustness (FR). The antifragile MOP solution we discuss below starts from the design of a model that integrates a PdM procedure with the dynamic phases of the production plan and aims for the optimization of two objectives--maximizing the QR and FR parameters. The main instrument that ensures balance in the process of simultaneous optimization of the production scheduling and maintenance policy is a time buffer that must be inserted to deal with uncertainties that may cause damages or failures, which, from a mathematical point of view, represents a stochastic optimization procedure with discrete and continuous variables. In summary, the steps of the optimization procedure in the simple case of a single machine system are:  
1. Establishing a set of tasks (jobs) with a prefixed processing time, with all jobs available at the initial moment. 2. Establishing, based on the exploitation indicators processed in the previous stages, the law of distribution of the probability of failure. 3. Establishing the weighting coefficient which reflects the increase in the probability of defect due to the increase in the operating life of the machine (aging). 4. Establishing the time of the production horizon in which we must carry out the maintenance procedure, after which the machine is restored to the same operating conditions that it had at the initial time, i.e., it becomes a machine \"like a new one\". (We must remember that during the execution of the maintenance, work jobs cannot be performed on the machine.)