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Erratum to: Mixture representations of residual lifetimes of used systems

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  30 March 2016

Maria Kamińska-Zabierowska  and
Jorge Navarro
Maria Kamińska-Zabierowska*
Affiliation:
Uniwerystet Wrocławski
Jorge Navarro*
Affiliation:
Universidad de Murcia
*
∗Postal address: Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland. Email address: [email protected]
∗∗Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email address: [email protected]
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Abstract

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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.

Keywords

Coherent systemsignaturestochastic ordering

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 1183 - 1186
Copyright
Copyright © Applied Probability Trust 2015 

References

[1] Navarro, J., Balakrishnan, N. and Samaniego, F. J. (2008). Mixture representations of residual lifetimes of used systems. J. Appl. Prob. 45, 1097–1112.CrossRefGoogle Scholar
[2] 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.CrossRefGoogle Scholar
[3] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar