Abstract
The most common scale in reliability analysis is the chronological time scale. There can be another option for systems operating in a random environment described by a shock process.
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References
Boland PJ (1982) Periodic replacement when minimal repair costs vary with time. Naval Res Log 29:541–546
Bracquemond C, Gaudoin O, Roy D, Xie M (2001) On some notions of discrete aging. System and Bayesian reliability: essays in Honor of Professor Richard E. Barlow. World Scientific Publishing Company, Singapore
Brown M, Proschan F (1983) Imperfect repair. J Appl Probab 20:851–859
Cha JH, Finkelstein M (2011) On new classes of extreme shock models and some generalizations. J Appl Probab 48:258–270
Cha JH, Finkelstein M (2016) On some properties of shock processes in a ‘natural’ scale. Reliab Eng Syst Saf 145:104–110
Finkelstein M, Gertsbakh I (2015a) On ‘time-free’ preventive maintenance of systems with structures described by signatures. Appl Stoch Models Bus Ind 31:836–845
Finkelstein M, Gertsbakh I (2015b) On preventive maintenance of systems subject to shocks. J Risk Reliab 230:220–227
Finkelstein M, Levitin G (2017a) Optimal mission duration for partially repairable systems operating in a random environment. Methodol Comput Appl Probab. https://doi.org/10.1007/s11009-017-9571-6
Finkelstein M, Levitin G (2017b) Optimal mission duration for systems subject to shocks and internal failures. J Risk Reliab (In Print)
Gertsbakh I, Shpungin Y (2011) Network reliability and resilience. Springer, Berlin
Lai CD, Xie M (2006) Stochastic aging and dependence for reliability. Springer, New York
Levitin G, Xing L, Dai Y (2017) Mission abort policy in heterogeneous non-repairable 1-out-of-N warm standby systems. IEEE Trans Reliab (In print)
Myers A (2009) Probability of loss assessment of critical k-out-of-n:G systems having a mission abort policy. IEEE Trans Reliab 58:694–701
Samaniego FJ (2007) System signatures and their applications in engineering reliability. Springer, New York
Shaked M, Shanthikumar JG, Valdez-Tores JB (1995) Discrete hazard rate function. Comput Oper Res 22:391–402
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Cha, J.H., Finkelstein, M. (2018). Shocks as the Discrete Scale. In: Point Processes for Reliability Analysis. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-73540-5_12
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DOI: https://doi.org/10.1007/978-3-319-73540-5_12
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