Some Replacement - Times Distributions in Two-Component Systems

摘要

Considered herein is 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 model 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. This paper allows 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.