Source: J. Appl. Probab. Volume 47, Number 2
(2010), 394-406.
We analyze the notion of `reliability prediction' by studying in detail a key
property that is tacitly assumed to make reliability prediction possible. The
analysis leads in turn to a special type of point process for which the
connection of future to past can be explicitly displayed. In this type of
process, the semi-renewal process, all finite-dimensional distributions
are completely determined by the distribution of the time to the first event in
the process. The theory provides a heretofore unappreciated unification of the
two most commonly used reliability prediction models for maintained systems,
namely, the renewal and revival processes. We show that familiar results from
renewal theory extend and generalize to semi-renewal processes.
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