Citation

Nieuwhof GWE. Reliab. Eng. 1986; 14(2): 149-161.

Copyright

(Copyright © 1986, Elsevier Publishing)

DOI

10.1016/0143-8174(86)90049-1

PMID

unavailable

Abstract

If we know the failure rate function of a system, λs(t), we can determine its reliability over the considered time interval (t1 → t2) by using the General Equation for Reliability, namely: R5(t1→t2)=exp −∫I1I2 λs(t)dt An analytical interpretation of this equation reveals that any continuous time function, that fits the observed failure rate data of the system, can be used as the failure rate function of the system, λs(t), provided it satisfies the following: Condition I: ∫0∞λs(t) dt = ∞Condition II: λs(t)≤0 (t≤0) If so, we can derive the probability functions of the failure of the system, i.e. the cumulative distribution function (cdf); and the probability density function (pdf). This is different from the traditional standard methods, where the failure data is forced into the 'straightjacket' of a known probability distribution, e.g. Weibull, lognormal, exponential, etc. This is normally done graphically by means of the 'best' straight line fit.

The methodology outlined in this paper makes it possible to derive various new types of probability failure distributions, which are more tuned to the real world. It opens up a large field of research and development in reliability and safety analyses. Five worked-out examples are presented to illustrate the methodology.