Numerical values associated with the calculation of availability are often awkward, consisting of a series of 9s before reaching any significant numerical information (e.g. 0.9999999654). For this reason, it is more convenient to use the complement measure of availability, namely, unavailability. Expressed mathematically, unavailability is 1 minus the availability. Therefore, a system with availability 0.9999999654 is more concisely described as having an unavailability of 3.46E-8.
Unavailability may be expressed mathematically as the ratio,
- U = MTTR/(MTTR+MTTF)
where MTTR is the mean time to repair, and MTTF is the mean time to failure. Alternatively, this can be written as
- U = λ'/(λ'+μ')
where λ' is the critical failure rate (λ without the tick is the total failure rate) and μ' is the critical repair rate (rate at which critical failures are repaired).
In telecommunication, an unavailability is an expression of the degree to which a system, subsystem, or equipment is not operable and not in a committable state at the start of a mission, when the mission is called for at an unknown, i.e. random, time. The conditions determining operability and committability must be specified.
- Dunn, William R (2002). Practical Design of Safety-Critical Computer Systems. Reliability Press. ISBN 0-9717527-0-2.