Some notes on unobserved parameters (frailties) in reliability modeling

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Unobserved random quantities (frailties) often appear in various reliability problems especially when dealing with the failure rates of items from heterogeneous populations. As the failure rate is a conditional characteristic, the distributions of these random quantities, similar to Bayesian approaches, are updated in accordance with the corresponding survival information. At some instances, apart from a statistical meaning, frailties can have also useful interpretations describing the underlying lifetime model. We discuss and clarify these issues in reliability context and present and analyze several meaningful examples. We consider the proportional hazards model with a random factor; the stress-strength model, where the unobserved strength of a system can be viewed as frailty; a parallel system with a random number of components and, finally, the first passage time problem for the Wiener process with random parameters.

Original languageEnglish
Pages (from-to)99-103
Number of pages5
JournalReliability Engineering and System Safety
StatePublished - Mar 2014

Bibliographical note

Funding Information:
The authors wish to thank two reviewers for helpful comments which have improved the presentation of this paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the first author was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0093827 ). The work of the second author was supported by the NRF ( National Research Foundation of South Africa ) Grant FA 2006040700002 .


  • Frailty
  • Heterogeneous populations
  • Inverse-Gaussian distribution
  • Stress-strength model
  • Wiener process with drift


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