Optimization of the availability of multi-states systems under uncertainty.

Summary Dependability (SoF) has become a necessity in the industrial world during the 20th century. SoF is a field of activity that proposes ways to increase system attributes in a reasonable time and at a lower cost. In systems engineering, SoTL is defined as the property that allows system users to place justified confidence in the service it provides and is a measure of a system's availability, reliability and maintainability, and the performance of maintenance support, and, in some cases, other characteristics such as durability, safety and security. The concept on which our work is based is textbf availability. A(t) availability is the ability of a system to be operational at a specific time. The cost of a high availability system is very expensive. The designer must make a trade-off between availability and economic costs. Users may reject unsafe, unreliable or unsecure systems. Therefore, any user (or industry) will ask this question before having a product: "What is the optimal product on the market?" To answer this question, we must combine the following two points: - The best availability of the system: the user wants a product that lasts as long as possible. - The best cost of the system: the user wants a product that does not cost him a fortune. The calculation of availability is mainly based on the knowledge of failure rates and repairs of the system components. The availability analysis allows to calculate the capacity of a system to provide a required level of performance according to the level of degradation. Several methods have been used to calculate the availability of a system, including the Universal Generator Function (UGF), the inclusion-exclusion technique, Markov models, etc. These methods use different probabilistic techniques to evaluate this criterion, but these proposed approaches remain effective only for very specific cases, for example the cases of binary systems. A binary system is a system where two cases are possible: perfect operation and total failure. While multi-state systems (MSS) considerably restrict the application of most of these methods. In real life, systems correspond to EMS. In such scenarios, systems and their components may operate at different performance levels between the perfect operating state and the total failure state. However, the availability assessment of EMSs is more difficult than in the binary case, as different combinations of component failure modes must be considered. Throughout this thesis, we are looking for a method that helps us to calculate and optimize the availability of EMS taking into account the cost factor.