Valuation of machines with a randomly decreasing service life

We consider machines that are subject to a Poisson failure stream and whose operational characteristics deteriorate during operation. The market value of the new machine and its assigned service life are known. In case of machine failure, its remaining service life is abruptly shortened by a random value distributed according to a power law. A new model has been built that links the dynamics of the market value of the machine with its remaining service life. This is not enough for a practical valuation, since appraisers often only know their age about cars. However, the machines of the same age may be in different condition, and here appraisers have to rely on the dependence of the average cost of machines on age. We have obtained formulas for constructing similar dependencies, according to which experimental calculations have been carried out. It is shown that such dependencies change little when the discount rate and the assigned service life change, although they differ with different coefficients of service life variation.

machinery, degradation, failure, service life, market value, group-specific inflation