###### Abstract  
The optimization of predictive maintenance relies mainly on the reduction of costs and risks, which can be of various types. The evaluation of risks cannot be realized independently of the psychology state and cognitive knowledge of the decision maker. In this article, we demonstrate this through the proposal of a methodology that tackles both optimization of maintenance and estimation of failure risks at the same time. The methodology takes as input the remaining useful life of the system at instant t and determines the optimal inspection step and the threshold of remaining useful life for predictive maintenance. The originality of the methodology consists of using a theory inspired by behavioral economics called prospect theory. Prospect theory allows modeling the outcome of a decision making by considering several aspects related to the decision maker, mainly loss aversion and a tendency to overestimate events with low probability of occurrence but with high economic losses. A case study was then developed where both cases were considered: with prospect theory and without prospect theory. A sensitivity analysis of the results under variation of some input parameters was carried out in a final step to confirm the consistency of the results and show the interest of prospect theory. predictive maintenance; optimization; risks; prospect theory; remaining useful life  
Risk Assessment. _Appl. Sci._**2022**, 12, 11748. [[https://doi.org/10.3390/app122211748](https://doi.org/10.3390/app122211748)]([https://doi.org/10.3390/app122211748](https://doi.org/10.3390/app122211748))  
Academic Editor: [PERSON]  
Received: 13 October 2022  
Accepted: 15 November 2022  
Published: 18 November 2022  
**Published: 18 November 2022**  
avoiding equipment failure, thus reducing failure cost, and providing an optimal use of the equipment, leading to reducing maintenance costs, at the same time. It is usually performed _\"following a forecast derived from repeated analysis and evaluation of significant parameters describing the degree of degradation of the system\"_[1]. A widespread measure of the health state of the system is the remaining useful life \"RUL\". The \"RUL\" is defined as _\"the expected length of time left for the system before it falls down\"_[4; 5; 6]. Thanks to PdM, in industry, we are now capable of assessing the RUL of the system as one among other measures used to predict the failure time of the system, and repair/replace the system before it fails. A main challenge facing the industry at present is finding the optimal time to perform PdM. The optimization criteria can be mainly cost minimization or reliability maximization. These different purposes are often considered separately, and may very well be conflictual. In this paper, we focus on a common criterion, which is cost minimization, by also considering the risks that can emerge following a maintenance decision. These risks can be human, financial, or environmental [7; 8]. While it is simple to evaluate economically financial risks, the evaluation of human and environmental risks turns out to be a challenging task. The human decision making is an inherent task to PdM. The human decision making is very complex and includes several aspects related to the cognitive and emotional process of humans. For example, facing a situation of risk, people make decisions relative to the eventual gains or eventual losses regarding a specific situation (reference point) and not in absolute terms. We call this reference dependence [9; 10; 11]. Prospect theory, a theory of the psychology of choice, developed by [PERSON] and [PERSON] in 1979, allows taking into account the complexity of cognitive knowledge and human emotion in decision making under risk [9; 11]. It considers the concept of loss aversion as an asymmetric form of risk aversion and the fact that people reactions differ whether they are in front of eventual losses or in front of eventual gains.