Definitions

Availability is closely related to reliability, and is defined in ITU-T Recommendation E.800 as follows:

"The ability of an item to be in a state to perfrom a required function at a given instant of time or at any instant of time within a given time interval, assuming that the external resources, if required, are provided."

An important difference between reliability and availability is that reliability refers to failure-free operation during an interval, while availability refers to failure-free operation at a given instant of time, usually the time when a device or system is first accessed to provide a required function or service.

Different Meanings of Availability:

1. The ratio of the total time a functional unit is capable of being used during a given interval to the length of the interval.
2. The degree to which a system, subsystem, or equipment is operable and in a committable state at the start of a mission, when the mission is called for at an unknown, i.e., a random, time.
3. The amount of time that a system is available during those time periods when it is expected to be available. Availability is often measured as a percentage of an elapsed year.
4. In a telephone circuit, availability is the ratio between the time during which the circuit is operational and elapsed time.

Formal Definitions of Availability:

1. Instantaneous Availability
   
   We define the instantaneous Availability or point availability A(t) of a component (or a system) as the probability that the component is properly functioning at time t. Note that in the absence of a repair or a replacement, availability A(t) is simple equal to the reliability R(t) of the component.
   
   The component may be functioning at time t by reason of two mutually exclusive cases: either the component has not failed from beginning (no renewals in the period (0,t] with the associated probability R(t), or the last renewal (repair) ocurred at time x, 0 < x < t with renewal density m(x) and the component has continued to function since that time. The probability associated with the second case is
   
   
   
   Thus
   
   
   
   Note that the instantaneous availability is always greater than or equal to the reliability.
   
   
2. Limiting Availability
   
   We define the limiting or steady-state availability (or simply availability) A as the limiting value of A(t) as t approaches infinity. Here we point out another distinction between the notions of reliability and availability. The limiting reliability is given by
   
   
   
   Whereas the limiting Availability
   
   
   
   is usually nonzero.
   
   The limiting availability A is given by
   
   
   
   where 1/ is the mean time to failure (MTTF) and 1/ is the mean time to repair (MTTR). This shows that the limiting availability depends only on the mean time to failure and mean time to repair, and not on the nature of the distributions of failure times and repair times.
   
   From the system unavailability, the downtime during an observation interval of duration T is given by (1-A)*T. For example, 99.95% availability equates to 4.38 hours of downtime in a year (0.0005 * 365 * 24 = 4.38).
   
   The above steady-state availability expression is valid for a system without any redundancy. For systems with redundancy, the steady-state availability can be written as
   
   
   
   where _eq and _eq are the equivalent failure rate and repair rate for the system.
   
   
3. Interval Availability
   
   We define the interval (or average) availability as the expected fraction of time the system is up in a given interval (0,t]. The interval availability is given by
   
   
   
   The relation between the above three availabilies are as follows:
   
   
   
   

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Last updated on 4 October 2001