# Availability

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In telecommunications and reliability theory, the term availability has the following meanings:

• The degree to which a system, subsystem, or equipment is in a specified operable and committable state at the start of a mission, when the mission is called for at an unknown, i.e., a random, time. Simply put, availability is the proportion of time a system is in a functioning condition. This is often described as a mission capable rate. Mathematically, this is expressed as 1 minus unavailability.
• The ratio of (a) the total time a functional unit is capable of being used during a given interval to (b) the length of the interval.

For example, a unit that is capable of being used 100 hours per week (168 hours) would have an availability of 100/168. However, typical availability values are specified in decimal (such as 0.9998). In high availability applications, a metric known as nines, corresponding to the number of nines following the decimal point, is used. In this system, "five nines" equals 0.99999 (or 99.999%) availability.

## Contents

### Representation

The most simple representation for availability is as a ratio of the expected value of the uptime of a system to the aggregate of the expected values of up and down time, or

If we define the status function X(t) as

therefore, the availability A(t) at time t>0 is represented by

Average availability must be defined on an interval of the real line. If we consider an arbitrary constant c > 0, then average availability is represented as

Limiting (or steady-state) availability is represented by[citation needed]

Limiting average availability is also defined on an interval (0,c] as,

### Example

If we are using equipment which has mean time between failure (MTBF) of 81.5 years and mean time to recovery (MTTR) of 1 hour:

MTBF in hours = 81.5*365*24=713940

Availability= MTBF/(MTBF+MTTR) = 713940/713941 =99.999859%

Unavailability = 0.000141%

Outage due to equipment in hours per year

U=0.01235 hours per year.

### Literature

Availability is well established in the literature of stochastic modeling and optimal maintenance. Barlow and Proschan [1975] define availability of a repairable system as "the probability that the system is operating at a specified time t." While Blanchard [1998] gives a qualitative definition of availability as "a measure of the degree of a system which is in the operable and committable state at the start of mission when the mission is called for at an unknown random point in time." This definition comes from the MIL-STD-721. Lie, Hwang, and Tillman [1977] developed a complete survey along with a systematic classification of availability.