The limiting failure rate for a convolution of life distributions

Henry W. Block, Naftali A. Langberg, Thomas H. Savits

Research output: Contribution to journalArticlepeer-review


In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more life distributions. In a previous paper on mixtures, Block, Mi and Savits (1993) showed that the failure rate behaves like the limiting behavior of the strongest component. We show a similar result here for convolutions. We also show by example that unlike a mixture population, the ultimate direction of monotonicity does not necessarily follow that of the strongest component.

Original languageEnglish
Pages (from-to)894-898
Number of pages5
JournalJournal of Applied Probability
Issue number3
StatePublished - Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 Applied Probability Trust.


  • Convolution
  • Decreasing failure rate
  • Failure rate function
  • Increasing failure rate
  • Reliability

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty


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