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

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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.

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Acknowledgements

The authors want to acknowledge the comments by an anonymous referee, an anonymous Associate Editor and the Editor of Test which have improved significantly the presentation of this paper. The authors acknowledge support received from the Ministerio de Ciencia e Innovación under grant MTM2009-08311-FEDER, Ministerio de Economía y Competitividad under grant MTM2 012-34023-FEDER and Fundación Séneca (CARM 08811/PI/08). Carolina Martínez-Riquelme acknowledges support received from the Ministerio de Ciencia e Innovación under grant BES2010-036561.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain

    Félix Belzunce, Carolina Martínez-Riquelme & José M. Ruiz

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  1. Félix Belzunce
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  2. Carolina Martínez-Riquelme
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  3. José M. Ruiz
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Correspondence to Félix Belzunce.

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Belzunce, F., Martínez-Riquelme, C. & Ruiz, J.M. A characterization and sufficient conditions for the total time on test transform order. TEST 23, 72–85 (2014). https://doi.org/10.1007/s11749-013-0342-6

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  • DOI: https://doi.org/10.1007/s11749-013-0342-6

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