35.1 Introduction

When allowing repair of a failed system, it is not meaningful to speak of the system reliability. The difficulty lies in the fact that system reliability does not allow consideration of system repairs. Consequently, since it should be to our advantage to repair failed systems as rapidly as possible, especially if their operation is critical to some desired objective, we need some additional measure of system performance that considers the effects of repair. For such a measure, availability has been proposed as a fundamental quantity of interest. It is a more appropriate measure than reliability for measuring the effectiveness of maintained systems because it includes reliability as well as maintainability. Lie et al. [1] surveyed and systematically classified the literature relevant to availability.

Three different widely used availability measures are: point availability, interval availability, and steady-state availability. Their definitions can be seen in various literature [2 4]. Those measures well represent a fraction of time that a system is in an operational state. In addition to these traditional availabilities, there are several other kinds of availabilities such as:

• mission availability, work mission availability, and joint availability [5];

• computation availability [6];

• equivalent availability [7].

These special measures have been proposed to suitably represent availabilities for specific application systems.

Another special availability measure, called random-request availability, has been proposed by Lee [8]. A repairable system is considered, which requires the performance of several tasks arriving randomly during the fixed mission duration. Examples include:

• a...