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Aspects of positive ageing

Published online by Cambridge University Press:  14 July 2016

Jayant V. Deshpande ,
Subhash C. Kochar  and
Harshinder Singh
Jayant V. Deshpande*
Affiliation:
University of Poona
Subhash C. Kochar*
Affiliation:
Panjab University
Harshinder Singh*
Affiliation:
Panjab University
*
∗Postal address: Department of Statistics, University of Poona, Ganeshkhind, Pune 411 007, India.
∗∗Postal address: Department of Statistics, Panjab University, Chandigarh 160014, India.
∗∗Postal address: Department of Statistics, Panjab University, Chandigarh 160014, India.
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Abstract

The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distributions of residual lifetimes, failure rates, equilibrium distributions, etc. In this paper we further analyse this concept and relate it to stochastic dominance of first and higher orders. In the process we gain many insights and are able to define several new kinds of ageing criteria which supplement those existing in the literature.

Keywords

RELIABILITY THEORYSURVIVAL ANALYSISFAILURE RATEMEAN RESIDUAL LIFEEQUILIBRIUM DISTRIBUTIONIFRIFRANBUDMRLNBUEHNBUE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 748 - 758
Copyright
Copyright © Applied Probability Trust 1986 

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References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt Rinehart and Winston, New York.Google Scholar
Brown, M. and Ge, G. (1984) Exponential approximations for two classes of ageing distributions. Ann. Prob. 12, 869–875.Google Scholar
Bryson, M. C. and Siddioui, M. M. (1969) Some criteria for aging. J. Amer. Statist. Assoc. 64, 1472–1483.CrossRefGoogle Scholar
Deshpande, J. V. and Singh, S. P. (1984) Ordering of probability distributions in the context of economics. Proc. Ann. Conf. Indian Soc. Theory Probability and Applications (1981 session).Google Scholar
Fishburn, P. C. (1977) Mean-risk analysis with risk associated with below-target returns, Amer. Econom. Rev. 67, 116–126.Google Scholar
Hanoch, G. and Levy, H. (1969) The efficiency analysis of choices involving risk. Rev. Econom. Stud. 36, 335–346.CrossRefGoogle Scholar
Singh, Harshinder and Deshpande, J. V. (1985) On some new aging properties. Scand. J. Statist. Google Scholar
Klefsjö, B. (1983) A useful aging property based on the Laplace transform. J. Appl. Prob. 20, 615–626.Google Scholar
Klefsjö, B. (1984) Reliability interpretations of some concepts from economics. Naval Res. Logist. Quart. 31, 301–308.Google Scholar
Loh, W. Y. (1984) Bounds on ARE's for restricted classes of distributions defined via tail orderings. Ann. Statist. 12, 685–701.Google Scholar
Rolski, T. (1975) Mean residual life. Internat. Statist. Inst. 46, 266–270.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Stein, W. E., Dattero, R. and Pfaffenberger, R. C. (1984) Inequalities involving the lifetime of series and parallel systems. Naval Res. Logist. Quart. 31, 647–651.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Tesfatsion, L. (1976) Stochastic dominance and the maximization of expected utility. Rev. Econom. Stud. 43, 301–314.Google Scholar
Whitmore, G. A. (1970) Third order stochastic dominance, Amer. Econom. Rev. 50, 457–459.Google Scholar