Journal of Applied Probability

Erratum to: Mixture representations of residual lifetimes of used systems

Maria Kamińska-Zabierowska and Jorge Navarro

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Abstract

We have found a mistake in the proofs of Navarro (2008, Theorem 2.3(b) and 2.3(c)) due to misapplication of properties of hazard rate and likelihood ratio orders. In this paper we show with an example that the stated results do not hold. This example is interesting since it proves some unexpected properties for these orderings under the formation of coherent systems. The result stated in Navarro (2008, Theorem 2.3(a)) for the usual stochastic order is correct.

Article information

Source
J. Appl. Probab., Volume 52, Number 4 (2015), 1183-1186.

Dates
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1450802761

Digital Object Identifier
doi:10.1239/jap/1450802761

Mathematical Reviews number (MathSciNet)
MR3439180

Zentralblatt MATH identifier
06554320

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Keywords
Coherent system signature stochastic ordering

Citation

Kamińska-Zabierowska, Maria; Navarro, Jorge. Erratum to: Mixture representations of residual lifetimes of used systems. J. Appl. Probab. 52 (2015), no. 4, 1183--1186. doi:10.1239/jap/1450802761. https://projecteuclid.org/euclid.jap/1450802761


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References

  • Navarro, J., Balakrishnan, N. and Samaniego, F. J. (2008). Mixture representations of residual lifetimes of used systems. J. Appl. Prob. 45, 1097–1112.
  • Navarro, J., del Águila, Y., Sordo, M. A. and Suárez-Llorens, A. (2013). Stochastic ordering properties for systems with dependent identically distributed components. Appl. Stoch. Models Business Industry. 29, 264–278.
  • Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.