Availability

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)

${\displaystyle A={\frac {E[\mathrm {uptime} ]}{E[\mathrm {uptime} ]+E[\mathrm {downtime} ]}}={\frac {E[\mathrm {uptime} ]}{C}}}$

Another equation for availability (A) is a ratio of the Mean Time To Failure (MTTF) and Mean Time Between Failure (MTBF), or

${\displaystyle A={\frac {MTTF}{MTTF+MTTR}}={\frac {MTTF}{MTBF}}}$

If we define the status function ${\displaystyle X(t)}$ as

${\displaystyle X(t)={\begin{cases}1,&{\text{sys functions at time }}t\\0,&{\text{maintenance}}\end{cases}}}$

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

${\displaystyle A(t)=\Pr[X(t)=1]=E[X(t)].\,}$

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

${\displaystyle A_{c}={\frac {1}{c}}\int _{0}^{c}A(t)\,dt.}$

Limiting (or steady-state) availability is represented by[1]

${\displaystyle A=\lim _{c\rightarrow \infty }A_{c}.}$

Limiting average availability is also defined on an interval ${\displaystyle [0,c]}$ as,

${\displaystyle A_{\infty }=\lim _{c\rightarrow \infty }A_{c}=\lim _{c\rightarrow \infty }{\frac {1}{c}}\int _{0}^{c}A(t)\,dt,\quad c>0.}$

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).

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." 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.

Availability measures are classified by either the time interval of interest or the mechanisms for the system downtime. If the time interval of interest is the primary concern, we consider instantaneous, limiting, average, and limiting average availability. The aforementioned definitions are developed in Barlow and Proschan [1975], Lie, Hwang, and Tillman [1977], and Nachlas [1998]. The second primary classification for availability is contingent on the various mechanisms for downtime such as the inherent availability, achieved availability, and operational availability. (Blanchard [1998], Lie, Hwang, and Tillman [1977]). Mi [1998] gives some comparison results of availability considering inherent availability.

Availability considered in maintenance modeling can be found in Barlow and Proschan [1975] for replacement models, Fawzi and Hawkes [1991] for an R-out-of-N system with spares and repairs, Fawzi and Hawkes [1990] for a series system with replacement and repair, Iyer [1992] for imperfect repair models, Murdock [1995] for age replacement preventive maintenance models, Nachlas [1998, 1989] for preventive maintenance models, and Wang and Pham [1996] for imperfect maintenance models. A very comprehensive recent book is by Trivedi and Bobbio [2017].

Availability is used extensively in power plant engineering. For example, the North American Electric Reliability Corporation implemented the Generating Availability Data System in 1982.[5]

• Reliability engineering
• Safety engineering
• List of system quality attributes
• Spurious trip level
• Condition-based maintenance
• Fault reporting
• High availability
• RAMS

•  This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).
• K. Trivedi and A. Bobbio, Reliability and Availability Engineering: Modeling, Analysis and Applications, Cambridge University Press, 2017.

• Reliability and Availability Basics
• System Reliability and Availability
• Availability and the Different Ways to Calculate It
• How to track and improve Technical Availability?