International Science Index


Stochastic Repair and Replacement with a Single Repair Channel

Abstract:This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.
[1] Abdel-Hameed, M. (1978). Inspection and maintenance policies of devices subjected to deterioration. Advances in Applied Probability 10, 509-512.
[2] Brown M. & Proschan F. (1983). Imperfect repair, Journal of Applied Probability, 20: 85lā€“859.
[3] Beichelt F. (1997). Maintenance policies under stochastic repair cost development. Economic Quality Control 12, 173-181.
[4] Moustafa, M. S. (1998). Transient analysis of reliability with and without repair for K-out-of-N: G systems with M failure modes. Reliability Engineering and System Safety 59, 317-320.
[5] Zhao, M. (1994). Availability for repairable components and series systems. IEEE Transactions on Reliability 43(2), 329-334.
[6] Dimitrov B, Chukova S, Khalil Z. (2004). Warrantee costs: An age-dependent failure/repair model, Naval Research Logistics, 51, 959ā€“976.
[7] Pan, R., Rigdon, S.E. (2009). Bayes inference for general repairable systems, Journal of Quality Technology, 41(1), 82-94.
[8] Pandey, M., Zuo, M. J., Moghaddass R. & Tiwari, M. K. (2013). Selective maintenance for binary systems under imperfect repair, Reliability Engineering and System Safety, 113, 42ā€“51.
[9] El-Damcese, M. A. & Shama M. S. (2015) Reliability and availability analysis of a 2-state repairable system with two-types of failures, Eng. Math. Letters, 2, 1-9.
[10] Nguyen, D. T., Dijoux, Y. & Mitra F. (2017). Analytical properties of an imperfect repair model and application in preventive maintenance scheduling, European Journal of Operational Research, Vol. 256, No. 2, 2017, pp. 439-453.