Optimizing the timeframe of scheduled repairs using valuation techniques

Aim. The paper examines technical systems (machinery and equipment), whose condition deteriorates in the course of operation, yet can be improved through repairs (overhaul). The items are subject to random failures. After another failure, an item can be repaired or disposed of. A new or repaired item is to be assigned the date of the next scheduled repairs. Regarding a failed item, the decision is to be taken as to unscheduled repairs or disposal. We are solving the problem of optimization of such repair policy. At the same time, it proves to be important to take into consideration the effect of repairs, first, on the choice of appropriate indicators of item condition that define its primary operational characteristics, and second, on a sufficiently adequate description of the dynamics of items’ performance indicators. Methods. Assigning the timeframe of scheduled repairs normally involves the construction of economic and mathematical optimization models that are the subject matter of a vast number of publications. They use various optimality criteria, i.e., probability of no failure over a given period of time, average repair costs per service life or per unit of time, etc. However, criteria of this kind do not take into account the performance dynamics of degrading items and do not fully meet the business interests of the item owners. The criterion of maximum expected total discounted benefits is more adequate in such cases. It is adopted in the theory of investment projects efficiency estimation and the cost estimation theory and is, ultimately, focused on maximizing a company’s value. The model’s formulas associate the item’s benefit stream with its primary characteristics (hazard of failure, operating costs, performance), which, in turn, depend on the item’s condition. The condition of non-repairable items is usually characterized by their age (operating time). Yet the characteristics of repairable items change significantly after repairs, and, in recent years, their dynamics have been described by various models using Kijima’s virtual age indicator (a similar indicator of effective age has long been used in the valuation of buildings, machinery and equipment). That allows associating the characteristics of items in the first and subsequent inter-repair cycles. However, analysis shows that this indicator does not allow taking into consideration the incurable physical deterioration of repaired items. The paper suggests a different approach to describing the condition of such objects that does not have the above shortcoming. Conclusions. The author constructed and analysed an economic and mathematical model for repair policy optimisation that is focused on maximizing the market value of the company that owns the item. It is suggested describing the condition of an item with two indicators, i.e., the age at the beginning of the current inter-repair cycle and time of operation within the current cycle. It proves to be possible to simplify the dependence of an item’s characteristics on its condition by using the general idea of Kijima models, but more adequately taking into consideration the incurable physical deterioration of such item. The author conducted experimental calculations that show a reduction of the duration of planned repairs as machinery ages at the beginning of an inter-repair cycle. Some well-known repair policies were critically evaluated.

1. International Valuation Standards (IVS) (2019). Effective 31 January 2020. International Valuation Standards Council.

2. Fedotova M.A., Koroliov I.V., Kovaliov A.P., et al. Fedotova M.A, editor. [Evaluation of machines and equipment: Textbook. Second edition, updated and revised]. Moscow: INFRA-M; 2018. (in Russ.)

3. Aven T. Optimal replacement under a minimal repair strategy. Advances in Applied Probability 1983;15(1):198-211. DOI: 10.2307/1426990.

4. Bergman B. Optimal Replacement under a general failure model. Advances in Applied Probability 2;10(2):431-451.

5. Christer A.H., Waller M.W. Tax-Adjusted Replacement Models. Journal of the Operational Research Society 1987; 38(11):993-1006. DOI: 10.1057/jors.1987.170.

6. Jiang R. Performance evaluation of seven optimization models of age replacement policy. Reliability Engineering & System Safety 2018;180(C):302-311. DOI: 10.1016/j.ress.2018.07.030.

7. Van Horenbeek A., Pintelon L., Muchiri P. Maintenance optimization models and criteria. International Journal of System Assurance Engineering and Management 2010;1(3):189-200. DOI: 10.1007/s13198-011-0045-//.

8. [Guidelines for efficiency assessment of investment projects. Second edition. Approved by the Ministry of Economy of the RF, Ministry of Finance of the RF, Gosstroy of the RF, 21.06.1999, no. VK477]. Moscow: Ekonomika; 2000. (in Russ.)

9. Vilensky P.L., Livshits V.N., Smolyak S.A. [Efficiency assessment of investment projects: theory and practice. Study guide. Fifth edition]. Moscow: PoliPrintServis; 2015. (in Russ.)

10. Mikerin G.I., Smolyak S.A. [Efficiency assessment of investment projects and property valuation: convergence opportunities]. Moscow: CEMI RAS Publishing; 2010. (in Russ.)

11. Smolyak S.A. [Preventive repairs of machines in a Kijima-type model]. Vestnik CEMI RAS 2018;1(2). Available at: https://cemi.jes.su/s111111110000091-3-1/. DOI: 10.33276/S0000091-3-1. (in Russ.)

12. Smolyak S.A. [Valuation of machines and equipment (secrets of discounted cash flow)]. Moscow: Optsion; 2016. (in Russ.)

13. Livshits V.N., Smolyak S.A. [Service life of fixed assets in an optimal plan]. In: Proceedings of the First Conference for Optimal Economy Planning and Management. Section 1, Issue 1. Moscow: CEMI RAS; 1971. P. 352-357. (in Russ.)

14. Kijima M. Some results for repairable systems with general repair. Journal of Applied Probability 1989;26:89-102.

15. Welch R.B. Depreciation of buildings for assessment purposes. Chicago: International Association of Assessing Officers; 1943.

16. Chumakov I.A., Chepurko V.A., Antonov A.V. [On some properties of Kijima incomplete recovery models]. Dependability 2015;3(54):10-15.

17. Smolyak S.A. Overhaul policy optimization and equipment valuation concerning its reliability. Journal of the New Economic Association 2014;2(22):102-131. (in Russ.)

18. Smolyak S.A. Optimization of the Number and Frequency of Repairs. Economics of Contemporary Russia 2019;2:84-103. DOI: 10.33293/1609-1442-2019-2(85)-84-103. (In Russ.)

19. Lin Ye (Lam Yeh). Geometric processes and replacement problem. Acta Mathematicae Applicatae Sinica 1988,4:366-377. DOI: 10.1007/BF02007241.