Depreciation of machinery and equipment during the complex Poisson process of their degradation

Machines undergoing degradation are widely studied in reliability theory. However, the constructed models of the degradation process cannot be applied to assess the market value of used equipment. We solve this problem using a new mathematical model of the degradation process. In this model, the condition of the machine is characterized by the intensity of variable benefits (the market value of the work performed in a small unit of time minus the variable part of the operating costs). The degradation of the machine is described by a complex Poisson process. During operation, the machine is subjected to hidden failures that occur with constant intensity. After failure, the operating characteristics of the machine are subjected to a deteriorating jump. In our model, it is assumed that in this case the intensity of the variable benefits is multiplied by a random decreasing coefficient having a power distribution. We specify the limit conditions of the machine in which it should be disposed of. We construct the dependence of the market value of the machine on its condition. It can be used if it is possible to measure the benefits of the machine, and the market value of the new machine and the scrap value of the machines are known. Much more often, the appraiser knows only about the age of used machine. In this case, he can use information about the average service life of the machines and the coefficient of variation of this service life. This information allows him to set the values of the main parameters of the model. However, machines of the same age may be in different states, and therefore it is only possible to offer formulas for estimating their average market value. The constructed model also makes it possible to take into account the impact of inflation by properly adjusting the discount rate.