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Reliability applications of the relevation transform

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  • Laurence A. Baxter

Abstract

It is shown that Krakowski's relevation transform generates the nonhomogeneous Poisson process in an analogous fashion to the way in which Stieltjes convolution generates the renewal process. Properties of failure rates and of inter‐failure times are discussed and an application to warranty analysis is described.

Suggested Citation

  • Laurence A. Baxter, 1982. "Reliability applications of the relevation transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 323-330, June.
    • Handle: RePEc:wly:navlog:v:29:y:1982:i:2:p:323-330
    DOI: 10.1002/nav.3800290212
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    Cited by:

    1. Antonio Di Crescenzo & Patrizia Di Gironimo & Suchandan Kayal, 2020. "Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy," Mathematics, MDPI, vol. 8(8), pages 1-18, July.
    2. P. G. Sankaran & M. Dileep Kumar, 2019. "Reliability properties of proportional hazards relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 441-456, May.
    3. Antonio Di Crescenzo & Patrizia Di Gironimo, 2018. "Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model," Mathematics, MDPI, vol. 6(10), pages 1-13, October.
    4. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    5. Shey-Huei Sheu & Hsin-Nan Tsai & Tsung-Shin Hsu & Fu-Kwun Wang, 2015. "Optimal number of minimal repairs before replacement of a deteriorating system with inspections," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1367-1379, June.
    6. Félix Belzunce & Carolina Martínez-Riquelme & José A. Mercader & José M. Ruiz, 2021. "Comparisons of policies based on relevation and replacement by a new one unit in reliability," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 211-227, March.
    7. Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    8. Nuria Torrado & Rosa E. Lillo & Michael P. Wiper, 2012. "Sequential Order Statistics: Ageing and Stochastic Orderings," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 579-596, September.

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