On the problem of optimal control of operating backup machines

We consider machines used in the production process of an enterprise, the failure of which leads to a stoppage of this process and losses. The technical condition and operating characteristics of machines deteriorate with an increase in their operating time. We construct a model for determining the optimal service life of such machines, which assumes that a failed machine is disposed and immediately replaced with a new machine of the same brand. However, the replacement process usually requires random, sometimes quite a long time. Then it is advisable to use a backup machine, and the subject of consideration is a complex of interchangeable main (working) and backup machines of the same brand. In this case, losses from stopping the production of the enterprise arise only after the failure of both machines of the complex, when orders for the delivery of replacement new machines is not yet been fulfilled. Methods of reliability theory and general principles of valuation theory allow us to construct a model for solving the problem of optimal control of the specified complex in discrete time. It turns out that decisions on decommissioning of one machine of the complex, on its designation as the main or backup machine should be made depending on the existence and condition of the second machine. The calculations carried out allow us to assume that of the two machines in the complex, the machine with the lower operating time should be designated as the main one, however, it is not possible to prove the validity of this hypothesis.

machine, failure, replacement, backup machine, service life, market value, anticipation of benefits principle, sliding mode