Citation

Sheikh AK, Ahmad M. Reliab. Eng. 1987; 18(2): 73-99.

Copyright

(Copyright © 1987, Elsevier Publishing)

DOI

10.1016/0143-8174(87)90024-2

PMID

unavailable

Abstract

Several types of damage processes lead to the failure of mechanical devices. Some examples of these damage processes are: wear, fatigue, creep and corrosion. In this paper we consider a generalized damage process defined by the random function D(t); D(t) = AtB; t ϵ T, where A,B and T are random variables, and D(t) = damage incurred at time t.

If the life of the device is terminated when the damage exceeds a limiting value Dl (i.e. D(t) ≥ Dl), then it will be shown that, under certain assumptions regarding random variables A and B, the reliability model of the device is R(t)=Φloge t−Clα1(loge t)2 + βl where Φ(z)=12π∫−∞z exp [−12ξ2]dξ and Cl, αl, βl are the functions of Dl and the mean and variance of the random variables A and B.

In this paper various statistical characteristics of the above-mentioned model are discussed. The generalized nature of the proposed model is emphasized, and it is shown that the lognormal model is a special case of the proposed model. The method of estimation of the parameters of the reliability model from a set of realizations (sample functions) of the damage process is also illustrated.