Markovian approach of safety engineering of a machines system

To manage exploitation of a system of machine intended to complete a given work is to guarantee the possibility of having this system in operating condition for one determined duration before preventive repair with a given reliability. It is also to have with the availability of the repair service the quantity of parts necessary for this repair in order to the minimum reduce the time of the forced stopping of the engines. The number of machines (elements) depends especially of the repair quality, the strategy of maintenance and of the repair shop importance. The purpose of the study consists, by using the theory of renewal, the graphs of Markov, and that of the queues while passing from a state to another, to find the dependence between the number of machines to be put in redundancy and the importance of the workshop (stands of repair) and thus to have the sufficient number in order to have an availability guaranteeing the correct operation of the compan