Skip to main content
SpringerLink
Log in

Results on the past lifetime of (n − k + 1)-out-of-n structures with nonidentical components

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

We consider a (n − k + 1)-out-of-n system with independent and nonidentical components. Under the condition that at time t the system has failed we study the past lifetime of the components of the system. The mean past lifetime of the components is defined and some of its properties are investigated. Stochastic comparisons are also made between the past lifetime of different systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Asadi M (2006) On the mean past lifetime of the components of a parallel system. J Stat Plan Inference 136: 1197–1206

    Article  MathSciNet  MATH  Google Scholar 

  • Asadi M, Bayramoglu I (2006) The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans Reliab 55: 314–318

    Article  Google Scholar 

  • Bairamov I, Arnold CB (2007) On the residual lifelengths of the remaining components in an n − k + 1 out of n system. Stat Prob Lett 78: 945–952

    Article  MathSciNet  Google Scholar 

  • Balakrishnan N (2007) Permanents, order statistics, outliers, and robustness. Revista Matematica Complutense 20(1): 7–107

    MathSciNet  MATH  Google Scholar 

  • Bapat RB, Beg MI (1989) Order statistics for nonidentically distributed variables and permanents. Sankhya: Indian J. Stat 51(Ser. A): 79–93

    MathSciNet  MATH  Google Scholar 

  • Block H, Savits TH, Singh H (1998) The reversed hazard rate function. Probab Eng Inf Sci 12: 69–90

    Article  MathSciNet  MATH  Google Scholar 

  • David HA, Nagaraja HNA (2003) Order statistics. John Wiley & Sons, New York

    Book  MATH  Google Scholar 

  • Gurler S, Bairamov I (2009) Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions. Appl Mathe Model 33: 1116–1125

    Article  MathSciNet  MATH  Google Scholar 

  • Khaledi B-E, Shaked M (2007) Ordering conditional lifetimes of coherent systems. J Stat Plan Inference 137: 1173–1184

    Article  MathSciNet  MATH  Google Scholar 

  • Kochar S, Xu M (2010) On results lifetimes of k-out-of-n systems with nonidentical components. Probab Eng Inf Sci 24: 109–127

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Zhang Z (2008) Some stochastic comparisons of conditional coherent systems. Appl Stoch Models Bus Ind 24: 541–549

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Zhao P (2008) Stochastic comparison on general inactivity time and general residual life of k-out-of-n systems. Commun Statist Simul Comput 37: 1005–1019

    Article  MATH  Google Scholar 

  • Mi J (1996) Minimizing some cost functions related to both burn-in and field use. Oper Res 44: 497–500

    Article  MATH  Google Scholar 

  • Nanda AK, Shaked M (2001) The hazard rate the reversed hazard rate orders, with applications to order statistics. Ann Inst Stat Math 53: 853–864

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J, Balakrishnan N (2010) Study of some measures of dependence between order statistics and systems. J Multivar Anal 101: 52–67

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J, Hernandez PJ (2008) Mean residual life functions of finite mixtures, order statistics and coherent systems. Metrika 67: 277–298

    Article  MathSciNet  Google Scholar 

  • Navarro J, Shaked M (2010) Some properties of the minimum and the maximum of random variables with joint logconcave distributions. Metrika 71(3): 313–317

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J, Balakrishnan N, Samaniego FJ (2008) Mixture representations of residual lifetimes of used systems. Appl Probab 45: 1097–1112

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J, Guillamon A, Ruiz MC (2009) Generalized mixtures in reliability modelling: applications to the construction of bathtub shaped hazard models and the study of systems. Appl Stoch Models Bus Ind 25(3): 323–337

    Article  MathSciNet  MATH  Google Scholar 

  • Sadegh MK (2008) Mean past and mean residual Life of parallel system with nonidentical components. Commun Stat Theor Methods 37: 1137–1145

    Google Scholar 

  • Samaniego FJ, Balakrishnan N, Navarro J (2009) Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Res Logist 56: 577–591

    Article  MathSciNet  MATH  Google Scholar 

  • Shaked M, Shanthikumar JG (2007) Stochastic orders and their applications. Springer, New York

    Google Scholar 

  • Tavangar M, Asadi M (2010) A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level. Metrika 72: 59–73

    Article  MathSciNet  MATH  Google Scholar 

  • Vaughan RJ, Venables WN (1972) Permanent expressions for order statistics densities. J Royal Stat Soc B 34(2): 308–310

    MathSciNet  MATH  Google Scholar 

  • Zhang Z (2010) Ordering conditional general coherent systems with exchangeable components. J Stat Plan Inference 140: 454–460

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Isfahan, Isfahan, 81744, Iran

    E. T. Salehi & M. Asadi

Authors
  1. E. T. Salehi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Asadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Asadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salehi, E.T., Asadi, M. Results on the past lifetime of (n − k + 1)-out-of-n structures with nonidentical components. Metrika 75, 439–454 (2012). https://doi.org/10.1007/s00184-010-0335-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-010-0335-3

Keywords

Search

Navigation