TABLE OF CONTENTS The most basic maintenance policy for units is to do some maintenance of failed units which is called corrective maintenance; i.e., when units fail, they may undergo repair or may be scrapped and replaced. After the repair completion, units can operate again. A system with several units forms semi-Markov processes and Markov renewal processes in stochastic processes. Such reliability models are called repairman problems [1], and some useful expressions of reliability measures of many redundant systems were summarized in [2], [3]. Early results of two-unit systems and their maintenance (see Section 6.2) were surveyed in [4]. Furthermore, imperfect repair models that do not always become like new after repair were proposed in [5], [6] (see Chapter 7).
In this chapter, we are concerned only with reliability characteristics of repairable systems such as mean time to system failure, availability, and expected number of system failures. Such reliability measures are obtained by using the techniques of stochastic processes as described in Section 1.3.
In Section 2.1, we consider the most fundamental one-unit system and survey its reliability quantities such as transition probabilities, downtime distribution, and availabilities. Another point of interest is the repair limit policy where the repair of a failed unit is stopped if it is not completed within a planned time T [7]. It is shown that there exists an optimum repair limit time T* that minimizes the expected cost rate when the repair cost is proportional to time.
