The income approach to the problems of optimizing the repair policy

Abstract

The article is devoted to the application of approaches and methods used in the valuation of assets to the problems of reliability theory – the assignment of service life and the timing of preventive repairs to degrading item that are subject to failures. In the works on reliability, changes in the characteristics of the item after repair are described by Kijima models and their modifications, in which the state of item is characterized by a virtual / effective age. A similar indicator has been widely used in appraisal activity since the middle of the last century. Meanwhile, it turns out that indicators of this type do not allow us to adequately describe the state of degraded repairable items. It is proposed to describe their condition by two indicators – the age (operating time) at the beginning of the current inter-repair cycle and the same in this cycle. In combination with Kijima's ideas, this allows us to offer a more adequate model of changing the item’s characteristics after repair. To assign service life and terms of preventive maintenance of items, a well-grounded criterion of optimality is required.It is shown that the usually accepted criterion of the minimum expected maintenance and repair costs per unit of time does not meet the interests of enterprises participating in the market. We propose to use the so-called income approach to valuation, focused on maximizing the market value of the enterprise (in the simplest case, this approach leads to the criterion of the expected discounted costs per unit of work performed by the item). This makes it possible to assess the market value of the work performed by the item necessary for calculations, and the corresponding assessment method can be attributed to the cost approach.We construct and analyze the corresponding mathematical models, provide an algorithm for solving them and a numerical example demonstrating the irrationality of commonly used repair policies.