Wednesday, June 5, 2013

Basic concepts and references on aging and reliability, Barlow & Proschan 1996

IFR: increasing failure rate
DFR: decreasing failure rate

The failure rate function $r(t)$ is defined as: $r(t) = f(t) / S(t) = f(t) / (1- F(t))$ in Barlow & Proschan96 on page 10. Function $f(t)$ should be the pdf of death,  and $F(t)$ is the failure distribution (page 2), and $S(t)$ should be viability.

Barlow&Proschan96 quote $r(t)$ as "force of mortality" by Steffernson 1930. The reference is missing in the book's reference list), "hazard rate", "intensity function".  I found a JSTOR examination of actuarial science in 1910 with a question of comparing 'force of mortality' and 'rate of mortality'.  So, this concept should goes back much earlier.


Parzen, E, 1962, stochastic process, holden-Day, San Francisco


Gumbel 1958, Statistics of extremes. Columbia Univ Press.
Discussed exponential distribution and limiting distribution.

Lawrence Leemis, Reliability-Probabilistic models and statistical methods, second edition, 2009.
Its explanation on series and parallel structure functions are really clear.


Gavrilov 1991


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