Methodology for imprecise availability computing and optimization

One of the undeniable steps in the safe design of systems is the problem of choosing the best system configuration in the most effective way so as to maximize the overall system availability and to minimize the overall system cost. The main objective of our paper is to propose a methodology of optimization of the availability of multi-states systems with multi-states components in presence of both aleatory and uncertainties. The problem is formulated as follows: let us consider several configurations of a system, each configuration consisting of components with several states of working and imprecise failure and repair rates provided in form of intervals. The objective is to find the best configuration regarding the system availabilities and costs. We first compute the imprecise steady availability of each configuration by using an original method based on Markov approaches combined with interval contraction techniques. We also compute the overall cost of each configuration. When having the availability and the cost of all the configurations, the idea is to define an objective function in terms of cost, lower and upper bounds of availability, and imprecision (length of availability interval). Then, this function is computed so that we have the best configuration according to our criterion. To illustrate our proposed methodology, we will propose a use-case describing a system formed of n components, and each component has different degraded states from perfect functioning to total failure. Each configuration of the system will have a different structure (parallel, series, series-parallel, complex,...), with different choices of component characteristics (imprecise failure and repair rates). Then, according to different criteria as high availability, low cost, or low availability imprecision, we will propose the best system configuration.