Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T03:12:39.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on the relative ageing of two life distributions

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Debasis Sengupta  and
Jayant V. Deshpande
Debasis Sengupta*
Affiliation:
Indian Statistical Institute
Jayant V. Deshpande*
Affiliation:
University of Poona
*
∗Postal address: Computer Science Unit, 203 Barrackpore Trunk Road, Calcutta 700 035, India.
∗∗Postal address: Department of Statistics, University of Poona, Pune 411 007, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.

Keywords

CROSSING HAZARD RATESINCREASING HAZARDS RATIOIFRIFRANBURELIABILITY OF BOUNDSSTABILITY OF DISTRIBUTIONS

MSC classification

Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 991 - 1003
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Reinhart and Winston, New York.Google Scholar
Begg, C. B., Mcglave, P. B., Bennet, J. M., Cassileth, P. A. and Oken, M. M. (1984) A critical comparison of allogeneic bone marrow transplantation and conventional chemotherapy as treatment for acute non-lymphomytic leukemia. J. Clin. Oncol. 2, 369–378.CrossRefGoogle ScholarPubMed
Champlin, R., Mitsuyasu, R., Elashoff, R. and Gale, R. P. (1983) Recent advances in bonemarrow transplantation. In UCLA Symposia on Molecular and Cellular Biology , ed. Gale, R. P., 7, pp. 141–158. Alan R. Liss, New York.Google Scholar
Deshpande, J. V., Singh, H., Bagai, I. and Jain, K. (1990) Some partial orders describing positive aging. Stoch. Models 6, 471–481.CrossRefGoogle Scholar
Kalashnikov, V. V. and Rachev, S. T. (1986) Characterization of queueing models and their stability. In Probability Theory and Mathematical Statistics , ed. Prohorov, Yu. K. et al., 2, pp. 37–53. VNU Science Press, Amsterdam.Google Scholar
Pocock, S. J., Gore, S. M. and Kerr, G. R. (1982) Long-term survival analysis: the curability of breast cancer. Statist. Medicine 1, 93–104.CrossRefGoogle ScholarPubMed
Rachev, S. T. (1991) Probability Metrics and the Stability of Stochastic Models. Wiley, New York.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Sengupta, D. (1994) Another look at the moment bounds on reliability. J. Appl. Prob. 31, 777–787.CrossRefGoogle Scholar
Stoyan, P. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Tops⊘e, F. (1967) Preservation of weak convergence under mappings. Ann. Math. Statist. 38, 1661–1665.CrossRefGoogle Scholar
Zolotarev, V. M. (1976) Metric distances in spaces of random variables and their distributions. Math. USSR Sb. 30, 373–401.CrossRefGoogle Scholar