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Properties of proportional mean residual life model. (English) Zbl 1089.62120

Summary: The proportional mean remaining life (PMRL) model has been introduced in the literature by H. Zahedi [J. Stat. Plann. Inference 29, 221–228 (1991)] for modelling and analysing failure time data. In this paper, some properties of the PMRL model related to reliability analysis are investigated. Closure properties of a few aging classes and those of partial orders under the proportional mean residual life model are discussed.

MSC:

62N99 Survival analysis and censored data
62E10 Characterization and structure theory of statistical distributions
60E15 Inequalities; stochastic orderings
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[1] Barlow, R.E., Proschan, F., 1981. Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring. · Zbl 0379.62080
[2] Bryson, M.C.; Siddiqui, M.M., Some criteria for aging, J. amer. statist. assoc., 64, 1472-1483, (1969)
[3] Cox, D.R., Regression models and life tables (with discussion), J. roy. statist. soc. B, 34, 187-202, (1972) · Zbl 0243.62041
[4] Di Crescenzo, A., Some results on the proportional reversed hazards model, Statist. probab. lett., 50, 313-321, (2000) · Zbl 0967.60016
[5] Guess, F.; Proschan, F., Mean residual life: theory and applications, (), 215-224
[6] Gupta, R.C.; Gupta, R.D.; Gupta, P.L., Modelling failure time data by lehmann alternatives, Comm. statist. theory methods, 27, 887-904, (1998) · Zbl 0900.62534
[7] Kapan, S., Mazzuchi, T.A., 2004. Interrelationship of burn-in criteria. YA/EM 2004-Y öneylem Arastirmasi/Endüstri Mühendisligˇi-XXIV Ulusal Kongresi, Haziran, 2004, Gaziantep-Adana, pp. 15-18.
[8] Kupka, J.; Loo, S., The hazard and vitality measures of aging, J. appl. probab., 26, 532-542, (1989) · Zbl 0681.60091
[9] Lehmann, E.L., The power of rank test, Ann. math. statist., 24, 23-43, (1953) · Zbl 0050.14702
[10] Marshall, A.W.; Olkin, I., Inequalities: theory of majorization and its applications, (1979), Academic Press New York · Zbl 0437.26007
[11] Muth, E.J., Reliability models with positive memory derived from the Mean residual life function, (), 401-435
[12] Shaked, M.; Shanthikumar, J.G., Stochastic orders and their applications, (1994), Academic Press San Diego · Zbl 0806.62009
[13] Zahedi, H., Proportional Mean residual life model, J. statist. plann. inference, 29, 221-228, (1991)
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