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On some comparisons of lifetimes for reliability analysis

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  • Finkelstein, Maxim

Abstract

Ordering of non-negative random variables (lifetimes) has been intensively studied in the literature. When comparing lifetimes in different applications such as reliability and risk analysis, it is often of interest to analyze also the distances between these lifetimes. In this paper, we define and discuss the stress–strength ordering and distance on the basis of the well-known stress–strength model that describes, e.g., the probability that the strength of a structure is larger than the external stress. We also compare this probability with the distance based on the difference between the means of random variables of interest and discuss several examples. The results can be useful, e.g., for analyzing reliability and safety requirements at the design stage for various engineering objects.

Suggested Citation

  • Finkelstein, Maxim, 2013. "On some comparisons of lifetimes for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 300-304.
    • Handle: RePEc:eee:reensy:v:119:y:2013:i:c:p:300-304
    DOI: 10.1016/j.ress.2013.06.043
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    References listed on IDEAS

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    1. M. S. Finkelstein, 2003. "On some measures and distances for positive random variables," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(2), pages 133-146, April.
    2. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    3. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    4. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, December.
    5. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    6. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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    Cited by:

    1. Das, Rabindra Nath & Kim, Jinseog & Park, Jeong-Soo, 2015. "Robust D-optimal designs under correlated error, applicable invariantly for some lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 92-100.
    2. Ji Hwan Cha & Maxim Finkelstein, 2018. "On stochastic comparisons for population age and remaining lifetime," Statistical Papers, Springer, vol. 59(1), pages 199-213, March.

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