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A characterization and sufficient conditions for the total time on test transform order

Author

Listed:
  • Félix Belzunce
  • Carolina Martínez-Riquelme
  • José Ruiz

Abstract

The total time on test transform has been used in reliability to compare two random lifetimes. Despite that it has been used widely in this context, it is not very clear in which sense the random variables are being compared. In this paper we provide a characterization which reveals the true nature of this comparison. Given that this comparison is of particular interest when the stochastic order does not hold, we also provide sufficient conditions for the comparisons of the total time on test transforms, when the stochastic order does not hold. Applications to the comparison of several parametric families of distributions are provided. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Félix Belzunce & Carolina Martínez-Riquelme & José Ruiz, 2014. "A characterization and sufficient conditions for the total time on test transform order," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 72-85, March.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:1:p:72-85
    DOI: 10.1007/s11749-013-0342-6
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    References listed on IDEAS

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    1. Miguel Sordo & Héctor Ramos, 2007. "Characterization of stochastic orders by L-functionals," Statistical Papers, Springer, vol. 48(2), pages 249-263, April.
    2. Belzunce, F., 1999. "On a characterization of right spread order by the increasing convex order," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 103-110, November.
    3. Neath, Andrew A. & Samaniego, Francisco J., 1992. "On the total time on test transform of an IFRA distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 289-291, July.
    4. Li, Xiaohu & Shaked, Moshe, 2004. "The observed total time on test and the observed excess wealth," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 247-258, July.
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