Abstract
When a unit is running successive works with cycle times, it would be uneconomical or impractical to do maintenances during any working cycle. This paper firstly reviews two replacement models proposed in literatures as follows: (1) replacement is done over a planned time \(T\) at the completion of the working cycle, which is called over-time replacement, and (2) replacement is done over damage level \(Z\) at the completion of the forthcoming working cycle, which is called over-level replacement. From the viewpoint of replacement cost savings, we secondly focus on comparisons of over-time replacement and its standard age-based policy, over-level replacement and its standard condition-based policy. Furthermore, modified over-time and over-level replacement costs are obtained to specify critical points at which these new replacements, rather than their standard polices, would save more replacement costs. Discussions in this paper are given analytically and computed numerically.
Similar content being viewed by others
References
Ahmad, R., & Kamaruddin, S. (2012). An overview of time-based and condition-based maintenance in industrial application. Computers and Industrial Engineering, 63, 135–149.
Barlow, R. E., & Proschan, F. (1965). Mathematical Theory of Reliability. New York: Wiley.
Chien, Y. H., & Sheu, S. H. (2006). Extended optimal age-replacement policy with minimal repair of a system subject to shocks. European Journal of Operational Research, 174, 169–181.
Chen, J., & Li, Z. (2008). An extended extreme shock maintenance model for a deteriorating system. Reliability Engineering and System Safety, 93, 1123–1129.
Chen, M., Mizutani, S., & Nakagawa, T. (2010). Random and age replacement policies. International Journal of Reliability, Quality and Safety Engineering, 17, 27–39.
Chien, Y. H., Chang, C. C., & Sheu, S. H. (2010). Optimal age-replacement model with agedependent type of failure and random lead time based on a cumulative repair-cost limit policy. Annals of Operations Research, 181, 723–744.
Chang, C. C., Sheu, S. H., & Chien, Y. H. (2011). Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks. Annals of Operations Research, 186, 317–329.
Chien, Y. H., Sheu, S. H., & Zhang, Z. G. (2012). Optimal maintenance policy for a system subject to damage in a discrete time process. Reliability Engineering and System Safety, 103, 1–10.
Finkelstein, M., & Marais, F. (2010). On terminating poisson processes in some shock models. Reliability Engineering and System Safety, 95, 874–879.
Gray, J., & Reuter, A. (1992). Transaction processing: Concepts and techniques. Los Altos, CA: Morgan Kaufmann.
Haerder, T., & Reuter, A. (1983). Principles of transaction-oriented database recovery. ACM Computing Surveys, 15, 287–317.
Ito, K., & Nakagawa, T. (2006). Maintenance of a cumulative damage model and its application to gas turbine engine of co-generation system. In H. Pham (Ed.), Reliability modeling, analysis and optimization, series on quality, reliability and engineering statistics (pp. 429–438). Singapore: World Scientific.
Kobbacy, K. A. H., & Murthy, D. N. P. (2008). Complex system maintenance handbook. London: Springer.
Lewis, M. L., Bernstein, B., & Kifer, M. (2002). Databases and transaction processing: An application-oriented approach. Reading, MA: Addison Wesley.
Liu, X., Li, J., Al-Khalifa, K. N., Hamouda, A. M. S., Coit, E., & Elsayed, D. (2013). Condition-based maintenance for continuously monitored degrading systems with multiple failure modes. IIE Transactions, 45, 422–435.
Manzini, R., Regattieri, A., Pham, H., & Ferrari, E. (2010). Maintenance for industrial systems. London: Springer.
Nakagawa, T. (2005). Maintenance theory of reliability. London: Springer.
Nakagawa, T. (2007). Shock and damage models in reliability theory. London: Springer.
Nakagawa, T. (2011). Stochastic process with applications to reliability theory. London: Springer.
Nakagawa, T., Zhao, X., & Yun, W. Y. (2011). Optimal age replacement and inspection policies with random failure and replacement times. International Journal of Reliability, Quality and Safety Engineering, 18, 405–416.
Osaki, S. (2002). Stochastic models in reliability and maintenance. Berlin: Springer.
Pham, H. (2003). Handbook of reliability engineering. London: Springer.
Qian, C., Pan, Y., & Nakagawa, T. (2002). Optimal policies for a database system with two backup schemes. RAIRO-Operations Research, 36, 227–235.
Wang, H., & Pham, H. (2006). Reliability and optimal maintenance. London: Springer.
Zhao, X., Nakamura, S., & Nakagawa, T. (2011). Two generational garbage collection models with major collection time. IEICE Transactions on Fundamentals, E94–A, 1558–1566.
Zhao, X., & Nakagawa, T. (2012). Optimization problems of replacement first or last in reliability theory. European Journal of Operational Research, 223, 141–149.
Zhao, X., Qian, C., & Nakagawa, T. (2013a). Optimal policies for cumulative damage models with maintenance last and first. Reliability Engineering and System Safety, 110, 50–59.
Zhao, X., Nakamura, S., & Nakagawa, T. (2013b). Optimal maintenance policies for cumulative damage models with random working times. Journal of Quality in Maintenance Engineering, 19, 25–37.
Acknowledgments
This work is supported by Qatar National Research Fund under Grant No. NPRP 4-631-2-233.
Author information
Authors and Affiliations
Corresponding author
Additional information
Revised work of the 19th ISSAT submitted to Special Volume of Reliability Management and Computing of the Annals of Operations Research.
Rights and permissions
About this article
Cite this article
Zhao, X., Nakagawa, T. Over-time and over-level replacement policies with random working cycles. Ann Oper Res 244, 103–116 (2016). https://doi.org/10.1007/s10479-015-1871-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-015-1871-z