Department of Media Informatics, Aichi University of Technology, Aichi, Japan.
Department of Business Administration, Aichi Institute of Technology, Aichi, Japan.
We propose an extended maintenance overtime policy for the cumulative damage model where an operating unit suffers some damage due to shocks. It is assumed that the total damage is additive, and the unit fails when the total damage has exceeded a prespecified damage level. It is supposed that we start to observe occurrence of shocks after time T, and the unit is replaced at Nth (N=1,2,…) shock over time T or at failure, whichever occurs first. That is, we propose a new policy by extending maintenance overtime policy. One example is a rental of system such as industrial equipment with some reservations. For such systems, they should be maintained or replaced at a prespecified number of uses over a scheduled time. For such a model, we obtain the mean time to replacement and the expected costs rate. Further, we discuss about optimal number N^* and time T^* which minimizes the expected cost rate when shocks occur in a Poisson process. Finally, numerical examples are given, and suitable discussions are made.
Keywords- Overtime policy, Replacement policy, Shock model, Cumulative damage.
Mizutani, S., & Nakagawa, T. (2018). Maintenance Overtime Policy with Cumulative Damage. International Journal of Mathematical, Engineering and Management Sciences, 3(2), 123-135. https://dx.doi.org/10.33889/IJMEMS.2018.3.2-010.
Conflict of Interest
Barlow, R. E., & Proschan, F. (1965). Mathematical theory of reliability. John Wiley & Sons, New York.
Bogdanoff, J. L., & Kozin, F. (1985). Probabilistic models of cumulative damage. John Wiley & Sons, New York.
Cha, J. H., & Finkelstein, M. (2013). On history-dependent shock models. Operations Research Letters, 41(3), 232-237.
Chen, M., Mizutani, S., & Nakagawa, T. (2010a). Random and age replacement policies. International Journal of Reliability Quality and Safety Engineering, 17(1), 27-39.
Chen, M., Nakamura, S., & Nakagawa, T. (2010b). Replacement and preventive maintenance models with random working times. IEICE Transactions on Fundamentals, E93-A(2), 500-507.
Eryilmaz, S. (2016). Discrete time shock models in a Markovian environment, IEEE Transactions on Reliability, 65(1), 141-146.
Nakagawa, T. (2005). Maintenance theory of reliability. Springer-Verlag, London.
Nakagawa, T. (2007). Shock and damage models in reliability theory. Springer-Verlag, London.
Nakagawa, T. (2014). Random maintenance policies. Springer-Verlag, London.
Nakagawa, T., & Zhao, X. (2015). Maintenance overtime policies in reliability theory. Spring-Verlag, London.
Stallmeyer, J. E., & Walker, W. H. (1968). Cumulative damage theories and application. Journal of the Structual Division, 94(12), 2739-2750.
Zarezadeh, S., Ashrafi, S., & Asadi, M. (2016). A shock model based approach to network reliability, IEEE Transactions on Reliability, 65(2), 992-1000.
Zhao, X., & Nakagawa, T. (2013). Optimal periodic and random inspection with first, last, and overtime policies. International Journal of Systems Science, 46(9), 1648-1660.
Zhao, X., Qian, C., & Nakamura, S., (2014). Age and periodic replacement with overtime policies. International Journal of Reliability, Quality and Safety Engineering, 21(4), 1450016.