Operation of two parallel devices with regard to the time of their replacement

I. V. Atlasov

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2016), pp. 49-79

Résumé

This problem was the result of a generalization of the problem from the book "The course of the theory of probability" by B.V. Gnedenko. He examined work of the system consisting of two interchangeable devices. These devices work in the next order: the first device works first, then it falls out and while being repaired it is replaced by the second device. After that the second device falls out and is being repaired also. If the time of operation of the first device is less than time for repair for the second device, the operation continues with the first device. If not, then we consider that the system finished its work and overall time of work equals to the time of work of the first and second devices. If the time of operation of the second device is greater than time for repair of the first device then operation continues with the first device et cetera. The characteristic function of time of work of the system is built as a result. Using this characteristic function the expected value of time of work of the system is found and methods to increase it are offered. In the present work we consider a system consisting of two elements operating simultaneously. The work of the system is interrupted when we carry out repair of both elements. We construct a characteristic function for continuous time of work of the system. Recommendations for increasing its expected value are considered.

Détail

Keywords: period of work, characteristic function.