Skip to main content
SpringerLink
Log in

A new perspective to stress–strength models

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

The stress–strength models have been widely used for reliability design of systems. In these models the reliability is defined as the probability that the strength is larger than the stress. The analysis is then based on the binary reliability theory since there are two possible states for the system. In this paper, we study the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. In other words, the stress–strength reliability is studied under multi-state system modeling. System state probabilities are evaluated and estimated under various assumptions on the system. The multicomponent form is also studied and some results are provided for large 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

  • An Z.-W., Huang H.-Z., Liu Y. (2008) A discrete stress–strength interference model based on universal generating function. Reliability Engineering & System Safety, 93(1485–1490): 93 1485–1490

    Google Scholar 

  • Barlow R.E., Wu A.S. (1978) Coherent systems with multi-state components. Mathematics of Operation Research, 3: 275–281

    Article  MATH  MathSciNet  Google Scholar 

  • Bhattacharyya G.K., Johnson R.A. (1974) Estimation of reliability in a multicomponent stress–strength model. Journal of the American Statistical Association, 69: 966–970

    Article  MATH  MathSciNet  Google Scholar 

  • Block H.W., Savits T.H. (1982) A decomposition for multi-state monotone systems. Journal of Applied Probability, 19: 391–402

    Article  MATH  MathSciNet  Google Scholar 

  • Eryılmaz S. (2008a) Consecutive k-out-of-n: G system in stress–strength setup. Communications in Statistics: Simulation and Computation, 37: 579–589

    Article  MATH  Google Scholar 

  • Eryılmaz, S. (2008b). Multivariate stress–strength reliability model and its evaluation for coherent structures. Journal of Multivariate Analysis. doi:10.1016/j.jmva.2008.01.015

  • Ewing D.J., Neilson J.M.M., Travis P. (1984) New method for assessing cardiac parasympathetic activity using 24 hour elctrocardiograms. British Heart Journal, 52: 396–402

    Article  Google Scholar 

  • Johnson R.A. (1988) Stress–strength models for reliability. In: Krishnaiah P.R., Rao C.R.(eds) In handbook of statistics Vol 7. Elsevier, North-Holland, pp 27–54

    Google Scholar 

  • Kotz S., Lumelskii Y., Pensky M. (2003) The stress-stength model and its generalizations. World Scientific, Singapore

    Book  Google Scholar 

  • Krishnamoorthy K., Mukherjee S., Guo H.Z. (2007) Inference on reliability in two-parameter exponential stress–strength model. Metrika, 65: 261–273

    Article  MathSciNet  Google Scholar 

  • Kuo W., Zuo M.J. (2003) Optimal reliability modeling, principles and applications. Wiley, New York

    Google Scholar 

  • Lisnianski A., Levitin G. (2003) Multi-state system reliability: Assessment, optimization and applications. World Scientific, Singapore

    MATH  Google Scholar 

  • Mokhlis N.A. (2005) Reliability of a stress–strength model with Burr type III distributions. Communications in Statistics: Theory and Methods, 34: 1643–1657

    Article  MATH  MathSciNet  Google Scholar 

  • Ross S.M. (1979) Multivalued state component systems. The Annals of Probability, 7: 379–383

    Article  MATH  MathSciNet  Google Scholar 

  • Turkkan N., Gia T.P. (2007) System stress–strength reliability: The multivariate case. IEEE Transactions on Reliability, 56: 115–124

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Izmir University of Economics, Balcova, Izmir, Turkey

    Serkan Eryılmaz

Authors
  1. Serkan Eryılmaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Serkan Eryılmaz.

About this article

Cite this article

Eryılmaz, S. A new perspective to stress–strength models. Ann Inst Stat Math 63, 101–115 (2011). https://doi.org/10.1007/s10463-008-0211-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10463-008-0211-3

Keywords

Search

Navigation