Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T17:03:43.810Z Has data issue: false hasContentIssue false
  • English
  • Français

ON DEGRADATION-BASED REMAINING LIFETIME

Published online by Cambridge University Press:  16 March 2021

Maxim Finkelstein Open the ORCID record for Maxim Finkelstein [Opens in a new window]  and
Ji Hwan Cha Open the ORCID record for Ji Hwan Cha [Opens in a new window]
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics, University of the Free State, Bloemfontein, South Africa
Ji Hwan Cha
Affiliation:
Department of Statistics, Ewha Womans University, Seoul 120-750, Republic of Korea E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The new reliability notion describing the remaining lifetime is introduced for items with monotonically increasing degradation. We consider the remaining lifetime of an item (to be called, the predicted remaining lifetime) after its degradation reaches the predetermined level. The prediction is executed at inception of an item into operation. For the nonhomogeneous stochastic processes of degradation, this characteristic depends on the random first passage time of a degradation process. Some properties of the predicted remaining lifetime and the corresponding stochastic comparisons are discussed for items from homogeneous and heterogeneous populations, and a generalization to the case of the n-component coherent system is outlined. The problem of regime switching is described, and the new notion of the corresponding virtual age after the switching is proposed.

Keywords

first passage timegamma processstochastic comparisonsvirtual age
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 812 - 823
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinerhart & Winston.Google Scholar
Cai, N. & Zheng, Y. (2012). Preservation of generalized ageing class on the residual life at random time. Journal of Statistical Planning and Inference 142: 148–154.CrossRefGoogle Scholar
Cha, J.H. & Finkelstein, M. (2018). On stochastic comparisons for population age and remaining lifetime. Statistical Papers 59: 199–213.CrossRefGoogle Scholar
Cha, J.H. & Finkelstein, M. (2018). Point processes for reliability analysis: shocks and repairable systems. London: Springer.CrossRefGoogle Scholar
Finkelstein, M. (2008). Failure rate modelling for reliability and risk. London: Springer.Google Scholar
Finkelstein, M. & Cha, J.H. (2013). Stochastic modelling for reliability: shocks, burn-in and heterogeneous population. London: Springer.CrossRefGoogle Scholar
Finkelstein, M. & Vaupel, J.W. (2015). On random age and remaining lifetime for populations of items. Applied stochastic Models in Business and Industry 31: 681–689.CrossRefGoogle Scholar
Hazra, N.K., Finkelstein, M., & Cha, J.H. (2018). Stochastic ordering for populations of manufactured items. TEST 27: 173–196.CrossRefGoogle Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability 26: 89–102.CrossRefGoogle Scholar
Li, X. & Fang, R. (2018). Stochastic properties of two general versions of the residual lifetime at random times. Applied Stochastic Models in Business and Industry 34: 528–543.CrossRefGoogle Scholar
Li, X. & Lu, J. (2003). Stochastic comparisons on residual life and inactivity time of series and parallel systems. Probability in the Engineering and Informational Sciences 17: 267–275.CrossRefGoogle Scholar
Li, X. & Zuo, M.J. (2004). Stochastic comparison of residual life and inactivity time at a random time. Stochastic Models 20: 229–235.CrossRefGoogle Scholar
Meeker, W.Q. & Escobar, L.A. (1998). Statistical methods for reliability data. New York: John Wiley.Google Scholar
Misra, N., Gupta, N., & Dhariyal, I.D. (2008). Stochastic properties of residual life and inactivity time at a random time. Stochastic Models 24: 89–102.CrossRefGoogle Scholar
Nanda, A.K. & Kundu, A. (2009). On generalized stochastic orders of dispersion-type. Calcutta Statistical Association Bulletin 16: 241–244.Google Scholar
Nelson, W. (1982). Applied life data analysis. New York: Wiley.CrossRefGoogle Scholar
Nelson, W. (1990). Accelerated testing, statistical models, test plans and data analysis. New York: Wiley.Google Scholar
van Noortwijk, J.M. (2009). A survey of the application of gamma processes in maintenance. Reliability Engineering & System Safety 94: 2–21.CrossRefGoogle Scholar
Yue, D. & Cao, J. (2000). Some results on the residual life at random time. Acta Mathematicae Applicatae Sinica 16: 436–443.Google Scholar