In reliability engineering, 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. The probability that an item will operate satisfactorily at a given point in time when used under stated conditions in an ideal support environment. Normally high availability systems might be specified as 99.98%, 99.999% or 99.9996%. The converse, unavailability, is 1 minus the availability.
Representation The simplest representation of availability (A) is a ratio of the expected value of the uptime of a system to the aggregate of the expected values of up and down time (that results in the "total amount of time" C of the observation window)
A = E [ u p t i m e ] E [ u p t i m e ] + E [ d o w n t i m e ] = E [ u p t i m e ] C {\displaystyle A={\frac {E[\mathrm {uptime} ]}{E[\mathrm {uptime} ]+E[\mathrm {downtime} ]}}={\frac {E[\mathrm {uptime} ]}{C}}}
Another equation for availability (A) is a ratio of the Mean Time To Failure (MTTF) and Mean Time Between Failure (MTBF), or
A = M T T F M T T F + M T T R = M T T F M T B F {\displaystyle A={\frac {MTTF}{MTTF+MTTR}}={\frac {MTTF}{MTBF}}}
If we define the status function X ( t ) {\displaystyle X(t)} as
X ( t ) = { 1 , sys functions at time t 0 , maintenance {\displaystyle X(t)={\begin{cases}1,&{\text{sys functions at time }}t\\0,&{\text{maintenance}}\end{cases}}}
therefore, the availability A(t) at time t > 0 is represented by
A ( t ) = Pr [ X ( t ) = 1 ] = E [ X ( t ) ] . {\displaystyle A(t)=\Pr[X(t)=1]=E[X(t)].\,}
Average availability must be defined on an interval of the real line. If we consider an arbitrary constant c > 0 {\displaystyle c>0} , then average availability is represented as
A c = 1 c ∫ 0 c A ( t ) d t . {\displaystyle A_{c}={\frac {1}{c}}\int _{0}^{c}A(t)\,dt.}
Limiting (or steady-state) availability is represented by
A = lim c → ∞ A c . {\displaystyle A=\lim _{c\rightarrow \infty }A_{c}.}
Limiting average availability is also defined on an interval [ 0 , c ] {\displaystyle [0,c]} as,
A ∞ = lim c → ∞ A c = lim c → ∞ 1 c ∫ 0 c A ( t ) d t , c > 0. {\displaystyle A_{\infty }=\lim _{c\rightarrow \infty }A_{c}=\lim _{c\rightarrow \infty }{\frac {1}{c}}\int _{0}^{c}A(t)\,dt,\quad c>0.}
Availability is the probability that an item will be in an operable and committable state at the start of a mission when the mission is called for at a random time, and is generally defined as uptime divided by total time (uptime plus downtime).
Series vs Parallel components
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