Abstract
This chapter gives four age replacement models for an operating unit when it works successively for jobs with random working cycles: (1) The unit is replaced at a total operating time T; (2) the unit is replaced at a total operating time T or at a random working cycle Y, whichever occurs first; (3) the unit is replaced at a total operating time T or at a random working cycle Y, whichever occurs last; and (4) the unit is replaced at the first completion of some working cycles over a planned time T. As a particular case of (2)–(4), random replacement, where the unit is replaced only at a random working cycle Y, is considered. Optimal policies for each model are discussed analytically, and Polices (2)–(4) are compared with (1) from the viewpoint of cost rate to find that Policy (1) is the best when preventive replacement costs are the same. However, random replacement and Policy (4) should be better than standard policy when a lower random replacement cost is supposed.
Manuscript chapter submitted to Quality and Reliability Management and Its Applications, H. Pham (Ed.), Springer.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barlow, R. E., & Proschan, F. (1965). Mathematical theory of reliability. New York: Wiley.
Chen, M., Mizutani, S., & Nakagawa, T. (2010a). Random and age replacement policies. International Journal of Reliability, Quality and Safety Engineering, 17, 27–39.
Chen, M., Nakamura, S., & Nakagawa, T. (2010b). Replacement and preventive maintenance models with random working times. IEICE Transaction on Fundamentals, E93-A, 500--507.
Duchesne, T., & Lawless, J. (2000). Alternative time scales and failure time models. Lifetime Data Analysis, 6, 157–179.
Haerder, T., & Reuter, A. (1983). Principles of transaction-oriented database recovery. ACM Computing Surveys, 15, 287–317.
Kobbacy, K. A. H., & Murthy, D. N. P. (2008). Complex system maintenance handbook. London: Springer.
Lewis, P. M., Bernstein, A. J., & Kifer, M. (2002). Databases and transaction processing: An application-oriented approach. Boston: Addison Wesley.
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. (2008). Advanced reliability models and maintenance policies. London: Springer.
Nakagawa, T. (2011). Stochastic process with applications to reliability theory. London: Springer.
Nakagawa, T., & Zhao, X. (2012). Optimization problems of a parallel system with a random number of units. IEEE Transactions on Reliability, 61, 543–548.
Nakagawa, T., Zhao, X., & Yun, W. (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.
Pinedo, M. (2002). Scheduling theory, algorithms and systems. Englewood Cliffs, NJ: Prentice Hall.
Stadje, W. (2003). Renewal analysis of a replacement process. Operations Research Letters, 31, 1–6.
Sugiura, T., Mizutani, S., & Nakagawa, T. (2004). Optimal random replacement policies. In H. Pham & S. Yamada (Eds.), Proceedings of the Tenth ISSAT International Conference on Reliability and Quality in Design (pp. 99–103). Nevada: Las Vegas.
Wang, H., & Pham, H. (2007). Reliability and optimal maintenance. London: Springer.
Zhao, X., & Nakagawa, T. (2011). Optimal age replacement and inspection policies with random failure and replacement times. In H. Pham (Ed.), Proceedings of the 17th ISSAT International Conference on Reliability and Quality in Design (pp. 200–204). B.C.: Vancouver.
Zhao, X., Nakayama, K., & Nakamura, S. (2011). Cumulative damage models with replacement last. In T. Kim, et al. (Eds.), Communications in computer and information science (vol. 257, pp. 338–345). Berlin: Springer.
Zhao, X., & Nakagawa, T. (2012a). A summary of newly proposed age replacement policies. In H. Pham (Ed.), Proceedings of the 18th ISSAT International Conference on Reliability and Quality in Design (pp. 106–110). Boston: Massachusetts.
Zhao, X., & Nakagawa, T. (2012b). Optimization problems of replacement first or last in reliability theory. European Journal of Operational Research, 223, 141–149.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag London
About this chapter
Cite this chapter
Zhao, X., Nakagawa, T. (2016). Age Replacement Models with Random Works. In: Pham, H. (eds) Quality and Reliability Management and Its Applications. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6778-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-6778-5_8
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-6776-1
Online ISBN: 978-1-4471-6778-5
eBook Packages: EngineeringEngineering (R0)