Anatomy of the failure rate : A mathematical dissection

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Nozer D. Singpurwalla

Detail(s)

Original languageEnglish
Pages (from-to)164-171
Journal / PublicationApplied Stochastic Models in Business and Industry
Volume27
Issue number2
Publication statusPublished - Mar 2011
Externally publishedYes

Abstract

The failure rate function is one of the most commonly used notion in reliability engineering and in survival analysis. The purpose of this expository paper is to point out some mathematical issues connected with this notion, a consequence of which is that under certain circumstances the famous exponentiation formula overestimates the probability of survival. To demonstrate this we point out a scenario that results in Volterra's product integrals, instead of the usual Lebesgue integral for which the exponentiation formula is exact. Copyright © 2011 John Wiley & Sons, Ltd.

Research Area(s)

  • absolutely continuous distribution function, cumulative hazard, exponentiation formula, Lebesgue-Stiltjes integral, multiplication formula, product integrals, right-hand derivative

Citation Format(s)

Anatomy of the failure rate : A mathematical dissection. / Singpurwalla, Nozer D.

In: Applied Stochastic Models in Business and Industry, Vol. 27, No. 2, 03.2011, p. 164-171.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review