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PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS

Year 2017, Volume: 10 Issue: 2, 45 - 51, 31.07.2017

Abstract

An important reliability index is the residual lifetime (RL). The RL may be used for designing engineering systems, maintenance policy programs as well as for comparison and prediction of system lifetimes. In this paper, dynamic r-out-of-n systems are considered as an subclass of engineering coherent systems. Given the rst s component failure times, the RL of the system is predicted and the mean residual lifetime (MRL) is evaluated. Illustrative examples are also given.

References

  • Aitchison, J. and Dunsmore, I. R. (1975).Statistical prediction analysis. Cambrige university press, UK.
  • Baratnia, M. and Doostparast, M. (2016). Modelling lifetime of sequential r-out-of-n systems with independent and heterogeneous components. Commun. Stat. B-Simul, DOI: 10.1080/03610918.2016.1236956.
  • Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, New York.
  • Billinton, R. and Allan, R. N. (1992). Reliability Evaluation of Engineering Systems: Concepts and Techniques, 2nd edition. Springer, New York.
  • Burkschat, M. and Navarro, J. (2011). Ageing properties of sequential order statistics. Probab. Engrg.Inform. Sci, 25, 1-19.
  • Cramer, E. and Kamps, U. (1996). Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates. Ann. Inst. Statist. Math, 48, 535-549.
  • Cramer, E. and Kamps, U. (2001). Sequential k-out-of-n systems. Handbook of Statistics 20: Advances in Reliability (N. Balakrishnan and C.R. Rao, eds.). Elsevier, Netherlands, 301-372.
  • Cramer, E. and Kamps. U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika, 58,293-310.
  • David, H. A. and Nagaraja, H. N. (2003). Order Statistics, Third edition. Wiley, New Jersey.
  • Gurler, S. (2012). On residual lifetimes in sequential (n 􀀀 k + 1)-out-of-n systems. Stat. Papers, 53, 23-31.
  • Kamps, U. (1995). A concept of generalized order statistics. J. Statist. Plann. Infer, 48, 1-23.
  • Khuri, A. I. (2003). Advanced Calculus with Applications in Statistics: Second Edition Revised and Expanded. Wiley, Florida.
  • Madadi, M., Khalilpoor, P., and Jamalizadeh, A. (2015). Regression mean residual life of a system with three dependent components with normal lifetimes. Statist. Probab. Lett, 100, 182-191.
  • Navarro, J. and Eryilmaz, S. (2007). Mean residual lifetimes of consecutive k-out-of-n systems. J. Appl. Probab, 44, 82-98.
  • Raqab, M. Z. and Nagaraja, H. N. (1995). On some predictors of future order statistics. Metron, 53, 185-204.
  • Raqab, M. Z. (2010). Evaluations of the mean residual lifetime of an m-out-of-n system. Statist. Probab. Lett, 80, 333-342.
  • Salehi, E. T., Asadi, M. and Erylmaz, S. (2012). On the mean residual lifetime of consecutive k-out-of-n systems. Test, 21, 93-115.
Year 2017, Volume: 10 Issue: 2, 45 - 51, 31.07.2017

Abstract

References

  • Aitchison, J. and Dunsmore, I. R. (1975).Statistical prediction analysis. Cambrige university press, UK.
  • Baratnia, M. and Doostparast, M. (2016). Modelling lifetime of sequential r-out-of-n systems with independent and heterogeneous components. Commun. Stat. B-Simul, DOI: 10.1080/03610918.2016.1236956.
  • Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, New York.
  • Billinton, R. and Allan, R. N. (1992). Reliability Evaluation of Engineering Systems: Concepts and Techniques, 2nd edition. Springer, New York.
  • Burkschat, M. and Navarro, J. (2011). Ageing properties of sequential order statistics. Probab. Engrg.Inform. Sci, 25, 1-19.
  • Cramer, E. and Kamps, U. (1996). Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates. Ann. Inst. Statist. Math, 48, 535-549.
  • Cramer, E. and Kamps, U. (2001). Sequential k-out-of-n systems. Handbook of Statistics 20: Advances in Reliability (N. Balakrishnan and C.R. Rao, eds.). Elsevier, Netherlands, 301-372.
  • Cramer, E. and Kamps. U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika, 58,293-310.
  • David, H. A. and Nagaraja, H. N. (2003). Order Statistics, Third edition. Wiley, New Jersey.
  • Gurler, S. (2012). On residual lifetimes in sequential (n 􀀀 k + 1)-out-of-n systems. Stat. Papers, 53, 23-31.
  • Kamps, U. (1995). A concept of generalized order statistics. J. Statist. Plann. Infer, 48, 1-23.
  • Khuri, A. I. (2003). Advanced Calculus with Applications in Statistics: Second Edition Revised and Expanded. Wiley, Florida.
  • Madadi, M., Khalilpoor, P., and Jamalizadeh, A. (2015). Regression mean residual life of a system with three dependent components with normal lifetimes. Statist. Probab. Lett, 100, 182-191.
  • Navarro, J. and Eryilmaz, S. (2007). Mean residual lifetimes of consecutive k-out-of-n systems. J. Appl. Probab, 44, 82-98.
  • Raqab, M. Z. and Nagaraja, H. N. (1995). On some predictors of future order statistics. Metron, 53, 185-204.
  • Raqab, M. Z. (2010). Evaluations of the mean residual lifetime of an m-out-of-n system. Statist. Probab. Lett, 80, 333-342.
  • Salehi, E. T., Asadi, M. and Erylmaz, S. (2012). On the mean residual lifetime of consecutive k-out-of-n systems. Test, 21, 93-115.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mohammad Baratnia This is me

Mahdi Doostparast This is me

Publication Date July 31, 2017
Acceptance Date December 5, 2016
Published in Issue Year 2017 Volume: 10 Issue: 2

Cite

APA Baratnia, M., & Doostparast, M. (2017). PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS. Istatistik Journal of The Turkish Statistical Association, 10(2), 45-51.
AMA Baratnia M, Doostparast M. PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS. IJTSA. July 2017;10(2):45-51.
Chicago Baratnia, Mohammad, and Mahdi Doostparast. “PREDICTING RESIDUAL LIFETIMES OF DYNAMIC R-Out-of-N SYSTEMS”. Istatistik Journal of The Turkish Statistical Association 10, no. 2 (July 2017): 45-51.
EndNote Baratnia M, Doostparast M (July 1, 2017) PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS. Istatistik Journal of The Turkish Statistical Association 10 2 45–51.
IEEE M. Baratnia and M. Doostparast, “PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS”, IJTSA, vol. 10, no. 2, pp. 45–51, 2017.
ISNAD Baratnia, Mohammad - Doostparast, Mahdi. “PREDICTING RESIDUAL LIFETIMES OF DYNAMIC R-Out-of-N SYSTEMS”. Istatistik Journal of The Turkish Statistical Association 10/2 (July 2017), 45-51.
JAMA Baratnia M, Doostparast M. PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS. IJTSA. 2017;10:45–51.
MLA Baratnia, Mohammad and Mahdi Doostparast. “PREDICTING RESIDUAL LIFETIMES OF DYNAMIC R-Out-of-N SYSTEMS”. Istatistik Journal of The Turkish Statistical Association, vol. 10, no. 2, 2017, pp. 45-51.
Vancouver Baratnia M, Doostparast M. PREDICTING RESIDUAL LIFETIMES OF DYNAMIC r-out-of-n SYSTEMS. IJTSA. 2017;10(2):45-51.