Analysis of Discrete Fix Up Limit Time of Two Systems Prediction

Document Type : Original Research Article


School of Continuing Education, Bayero University Kano, Nigeria.


This paper studies a discrete fix-up limit policy for two systems. Because sometimes, a failed system cannot be completely fixed at the optimal fix-up limit time due to some logistic issues. This paper provides a chance to complete fixing up a failed system within a discrete fix-up limit time LT (L=1,2,3…) for a fixed T. The explicit expression of the expected long-term cost per unit time is derived for the two systems based on the assumptions of the systems. Finally, a numerical example is given to illustrate the theoretical results of the proposed model.


Main Subjects

[1]     Al-Chalabi, H., “Development of an economic  replacement time model for mining equipment : a case study”, Life Cycle Reliab Saf Eng,, 2022.
[2]     Aven, T. and Castro, I. T., “A minimal repair replacement model with two types of failure and a safety constraint”, European Journal of Operational Research, 188, 506-515, doi:10.1016/j.ejor.2007.04.038, 2008.
[3]     Bai J. and Hoang P., “Repair limit risk free warranty  policies with imperfect repair”, IEEE Transactions on Systems, Man and Cybernetics – Part A: Systems and Humans, 35(6), 2005.
[4]     Beichelt, F., Nkadimeng, R. M.and Yadavalli, S. S., “Maintenance policies based on time-dependent repair cost limits”, South African Journal of Science,102, 2006.
[5]     Bi, X., Wu, J., Sun, C. and Ji, K. “Resilience-based repair strategy for gas network system and water network system in urban city”, Sustainability,, 2022.
[6]     Chang, C. C., Sheu, S. H. and Chen, Y. L., “Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy”, Computers and Industrial  Engineering, 59, 603-610, 2010.
[7]     Chen, Y. L. and Chang, C. C., “Optimum imperfect maintenance policy with cumulative damage model for a used system subject to number dependent shocks”, Int  J  Sys Sci, 2(1): pp25-34,, 2015.
[8]     Kapur, P. K., Garg, R. B. and Butani, N. L., “Some replacement policies with minimal repairsand cost limit”, Int J Sys Sci,, 2007.
[9]     Laia, M. T., Chena, C. H. and Harigunab, T., “A bivariate optimal replacement with cumulative repair cost limit for a two-unit system under shock damage interaction”, Brazilian Journal of Probability and Statistics, 31(2), DOI:10.1214/16- BJPS317, 2017.
[10]  Lewaherilla, N., Pasaribu, U. S., Husniah, H. and Supriantna, A. K.,“A preventive maintenance  and minimal repair costs model with interest rate”, American Institute of Physics,, 2016.
[11]  Maihula, A. S, Yusuf, I. and Bala, S. I., “Reliability and performance analysis of series -parallel system usingGumbel-Hougaard family copula”, JCCE,, 2021.
[12]  Mirjalili, S. M. and Kazempoor, J., “Life extension for a coherent system through cold standby and minimal repair policies for their independent components”, IJRRS, 3(2): pp 51-54,, 2020.
[13]  Nakagawa, T., “Maintenance theory of reliability”, Springer-Verlag, London Limited, 2005.
[14]  Niwas, R. and Garg, H., An approach for analyzing the reliability and profit of an industrial system based on the cost free warranty policy. J BrazSocMech SciEng ,, 2018.
[15]  Rebaiaia, M. L. and Ait-kadi, D., “Maintenance policies with minimal repair and replacement on failures: analysis and comparison”,Int J Prod Res,, 2020.
[16]  Safaei, F., Ahmadi, J. and Balakrishnan N., “A repair and replacement policy for systems based on probability and mean of profits”, Reliab Eng Syst Saf ,DOI: 10.1016/j.ress.2018.11.012,  2018.
[17]  Safaei, F., Chatelet, E., and Ahmadi, J.,“Optimal age replacement policy for parallel and series systems with dependent components”, Reliab Eng Syst Saf, DOI: 10.1016/j.ress.2020.106798, 2020. 
[18]  Sanoubar, S., Maillart, L. M, and Prokopyev O. A., “Age replacement policies under age dependent replacement costs, operations and engineering and analytics”, IISE Transactions,,  2020.
[19]  Sanusi, A. and Yusuf, I., “Reliability assessment and profit analysis of distributed data center network topology”, Life Cycle ReliabSafEng,  022-00186-3, 2020.
[20]  Sheu, S. H., Liu, T. H. and Zhang, Z. G., “Extended optimal preventive replacement policies with random working cycle”, Reliab Eng Syst Saf, DOI: 10.1016/j.ress.2019.03.036, 2019.
[21]  Sudheesd, K. K., Asha, G. and Krishna, K. M. J., “On the mean time to failure of an age-replacement model in discrete time”, COMMUN STAT-THEOR M,, 2019.
[22]  Wang, J., Ye, J. and Xie, P, “New repairable system model with two types repair based on extended geometric process”, J Syst Eng Electron, 30(3): pp 613 – 623, 2019.
[23]  Wu, W., Song, J., Jiang, K. and Li, H., “Optimal replacement policy based on the effective  age of  the system for a deteriorating repairable system with multiple vacations”, J Qual Maint Eng,, 2021.
[24]  Waziri,  T. A. “On discounted discrete scheduled replacement model”, AOTP,, 2021.
[25]  Waziri, T. A. and Yusuf, I., “On discrete scheduled replacement model of series-parallel System”, RTA,, 2021.
[26]  Xie, L., Lundteigen, M. A. and Liu, Y., “Reliability and barrier assessment of series-parallel systems subject to cascading failures”,  J Risk Reliab,, 2020.