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Some results on the proportional reversed hazards model. (English) Zbl 0967.60016
Summary: The proportional reversed hazards model consists in describing random failure times by a family \(\{[F(x)]^\theta,\;\theta>0\}\) of distribution functions, where \(F(x)\) is a baseline distribution function. We show various results on this model related to some topics in reliability theory, including ageing notions of random lifetimes, comparisons based on stochastic orders, and relative ageing of distributions.

60E15 Inequalities; stochastic orderings
90B25 Reliability, availability, maintenance, inspection in operations research
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[1] Block, H.W.; Savits, T.H.; Singh, H., The reversed hazard rate function, Probab. eng. inf. sci., 12, 69-90, (1998) · Zbl 0972.90018
[2] Brown, M.; Proschan, F., Imperfect repair, J. appl. probab., 20, 851-859, (1983) · Zbl 0526.60080
[3] Di Crescenzo, A., Ricciardi, L.M., 1998. On a discrimination problem for a class of stochastic processes with ordered first-passage times. Preprint no. 41, Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”. · Zbl 0973.62006
[4] Gupta, R.C.; Gupta, R.D.; Gupta, P.L., Modeling failure time data by lehman alternatives, Comm. statist. theory methods, 27, 887-904, (1998) · Zbl 0900.62534
[5] Lehman, E.L., The power of rank tests, Ann. math. statist., 24, 28-43, (1953)
[6] Marshall, A.W.; Olkin, I., Inequalities: theory of majorization and its applications, (1979), Academic Press New York · Zbl 0437.26007
[7] Rowell, G.; Siegrist, K., Relative aging of distributions, Probab. eng. inf. sci., 12, 469-478, (1998) · Zbl 1014.60014
[8] Sengupta, D.; Deshpande, J.V., Some results on the relative ageing of two life distributions, J. appl. probab., 31, 991-1003, (1994) · Zbl 0812.60079
[9] Shaked, M.; Shanthikumar, J.G., Stochastic orders and their applications, (1994), Academic Press San Diego · Zbl 0806.62009
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