Much of the recent work on modeling repairable systems involves Poisson processes with nonconstant intensity functions, viz, nonhomogeneous Poisson processes. Since times between failures are not identically distributed when the process is nonhomogeneous, it is not clear what concept should take the place of the mean time between failures in assessing the reliability of a repairable system. A number of alternate concepts can be found in the literature. We investigate the relationship between two of the most frequently considered alternatives: the reciprocal of the intensity function, and the mean waiting time from t until the next failure. Theorem 1 states a necessary and sufficient condition for the mean time until the next failure to be asymptotically proportional to the reciprocal of the intensity function. Some examples, including the familiar log-linear and power-intensity processes satisfy this condition. A monotonicity property is also established between these two concepts which could be used to obtain conservative statistical confidence limits for the mean time until the next failure, based on results which are already available for the intensity function of the power-intensity process. However, further study of concepts such as the rate of convergence would be needed in order to determine the degree of approximation of the nominal confidence level to the actual level. Until more is known about the mean time from t until the next failure, it would be advisable to use the reciprocal of the intensity function, which has been studied more extensively, as the basis of reliability assessment for a repairable system. Copyright © 1986 by the Institute of Electrical and Electronics Engineers, Inc.


Geosciences and Geological and Petroleum Engineering

Second Department

Mathematics and Statistics

Keywords and Phrases

Log-linear process; Mean time between failures; Nonhomogeneous Poisson; Power-intensity process; process

International Standard Serial Number (ISSN)

1558-1721; 0018-9529

Document Type

Article - Journal

Document Version


File Type





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Publication Date

01 Jan 1986