###### Abstract
For example:  
* In front of a risky choice with possible gains, individuals are risk-averse, opting for solutions with a lower expected utility but with a higher certainty. * In front of a risky choice with possible losses, individuals are risk-seeking, opting for solutions with a lower expected utility as long as it has the potential to avoid losses. * Individuals overestimate low probabilities and underestimate medium probabilities. In financial terms, this means that investors heavily weight extreme events whose probability of occurrence is very low, such as market crashes, for example. This may induce a higher risk premium than expected utility theory models. On the other hand, speaking of gains, this distortion of probabilities explains why individuals participate in games of chance, even unfavorable ones, when there is a high number of winnings. Expected utility theory supposes that people will choose the outcome that provides the maximum utility, given the probability of outcomes, where utility is used to assign a value or a worth to an outcome. The use of a proper utility function (usually a continuous and an increasing function, able to rank each gain or loss of an outcome) is essential in this case [11]. Prospect theory takes another turn from this classic model of the expected utility theory, which only considers options with the maximum utility [12]. It emphasizes the fact that individuals frame situation regarding their personal experience and knowledge of that situation. They tend to overweight certain outcomes rather than probable ones, and their behavior varies according to whether they are facing positive gains or negative gains (losses). Prospect theory provides answers to what appears in the theory of expected utility as an anomaly or a puzzle. In fact, prospect theory considers the fact that people may decide not on the basis of maximizing a utility but they may place other considerations in priority such as seeking loss avoidance in the zone of losses, instead of seeking a maximum utility. The motivation for handling risk behavior in this way is that it allows accommodating heuristics and biases already shown by several works [13]. In this framework, gains and losses are evaluated quite differently as risk behavior works differently in gains and losses. For example, individuals both choose insurance and play lottery. Second, as observed empirically, low probability events are systematically amplified by people [14]. To accommodate what is empirically documented, Prospect Theory is based on three key components, which are the following:  
* Consequences defined in terms of deviation from the reference point. * A value function that is concave for gains and convex for losses, with a slope steeper for losses than for gains. * A non-linear transformation of the probability scale, overestimating events of low probability and underestimating events that are more probable. Several applications of prospect theory have been proposed in recent decades, notably in the fields of political sciences, medical choice, finance, insurance, industrial organization, and environmental choices. According to our understanding, only two papers deal with maintenance and Prospect Theory [15,16]. However, none of them addresses the specific purpose of predictive maintenance and the environmental, finance and human risk evaluations. This paper proposes a PdM optimization approach following the criterion of cost minimization. This approach not only takes into consideration direct maintenance costs but also maintenance risks. We give a mathematical model to evaluate economically risks mainly human and environmental risks. We integrate, in a second step, prospect theory into the model of maintenance risks to represent the cognitive and emotional process of human decision making. Finally, we give an example of case study that illustrates our optimization approach and compare the numerical results between two cases: not considering prospect theory in the first case, and integrating it in the optimization process in the second case.