@article{ref1,
title="Some replacement-times distributions in two-component systems",
journal="Reliability engineering",
year="1984",
author="Kotz, Samuel and Johnson, Norman L.",
volume="7",
number="3",
pages="151-157",
abstract="We consider a system consisting of two modules, one of which cannot be easily inspected, while the other is monitored continuously. A fault developing in the first module is called 'unrevealed' (U), while the one in the second module (which is assumed to be detected immediately) is called 'revealed' (R). It is supposed that repairs are initiated as soon as an R is observed, but not otherwise. Phillips1,2 assumed that both modules are always replaced. In this paper we allow for replacement of the first module, only if a U fault is found on special inspection. Expressions are derived for the joint distribution of time to first repair and time between first and second repairs. Special cases are considered in which fairly simple results are obtained by general arguments without recourse to analysis. Detailed formulas are developed for a particular parametric model. Relationships with relevation theory are indicated.<p />",
language="",
issn="0143-8174",
doi="10.1016/0143-8174(84)90013-1",
url="http://dx.doi.org/10.1016/0143-8174(84)90013-1"
}