In reliability engineering, the term availability has the following meanings:
Normally high availability systems might be specified as 99.98%, 99.999% or 99.9996%.
Availability of a system is typically calculated as a function of its reliability, maintainability and its redundancy. As reliability increases and as redundancy increases, so does availability. As maintenance downtime decreases availability increases.
Availability of a system may also be increased by the strategy of focusing on minimizing downtime by increasing testability, diagnostics and maintainability. Improving maintainability during the early design phase is generally easier than reliability. Maintainability estimates (item repair [by replacement] rates) are also generally more accurate. However, because the uncertainties in the reliability estimates are in most cases very large, it is likely to dominate the availability (and the prediction uncertainty) problem, even while maintainability levels are very high. Furthermore, when reliability is not under control, then many and different sorts of issues may arise, for example:
For high levels of system availability, such as the availability of engine thrust in an aircraft, the use of redundancy may be the best option to reduce the system failure rate. Refer to reliability engineering. Reliability needs to be evaluated and improved related to both availability and the cost of ownership due to cost of spare parts, maintenance man-hours, transport costs, storage cost, part obsolete risks etc. Often a trade-off is needed between the two. There might be a maximum ratio between availability and cost of ownership. The maintenance strategy can influence the reliability of a system (e.g. by preventive and/or predictive maintenance), although it can never bring it above the inherent reliability. So, Maintainability and Maintenance strategies influences the availability of a system. In theory this can be almost unlimited if one would be able to always repair any fault in an infinitely short time. This is in practice impossible. Repair-ability is always limited due to testability, manpower and logistic considerations. Reliability is not limited. Reliable items can be made that outlast the life of a machine with almost 100% certainty.
An availability plan should clearly provide a strategy for availability control. Whether only Availability or also Cost of Ownership is more important depends on the use of the system. For example, a system that is a critical link in a production system - e.g. a big oil platform - is normally allowed to have a very high cost of ownership if this translates to even a minor increase in availability, as the unavailability of the platform results in a massive loss of revenue which can easily exceed the high cost of ownership. A proper reliability plan should always address Reliability, Availability, Maintainability and Testability (RAMT) analysis in its total context.
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, or
Another equation for availability(A) is a ratio of the Mean Time Between Failure (MTBF) and Mean Time To Repair (MTTR), or
If we define the status function 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 , then average availability is represented as
Limiting (or steady-state) availability is represented by
Limiting average availability is also defined on an interval as,
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).
Furthermore, these methods are capable to identify the most critical items and failure modes or events that impact availability.
Availability, inherent (Ai)  The probability that an item will operate satisfactorily at a given point in time when used under stated conditions in an ideal support environment. It excludes logistics time, waiting or administrative downtime, and preventive maintenance downtime. It includes corrective maintenance downtime. Inherent availability is generally derived from analysis of an engineering design:
It is based on quantities under control of the designer.
Availability, achieved (Aa)  The probability that an item will operate satisfactorily at a given point in time when used under stated conditions in an ideal support environment (i.e., that personnel, tools, spares, etc. are instantaneously available). It excludes logistics time and waiting or administrative downtime. It includes active preventive and corrective maintenance downtime.
Availability, operational (Ao)  The probability that an item will operate satisfactorily at a given point in time when used in an actual or realistic operating and support environment. It includes logistics time, ready time, and waiting or administrative downtime, and both preventive and corrective maintenance downtime. This value is equal to the mean time between failure (MTBF) divided by the mean time between failure plus the mean downtime (MDT). This measure extends the definition of availability to elements controlled by the logisticians and mission planners such as quantity and proximity of spares, tools and manpower to the hardware item.
Refer to Systems engineering for more details
Outage due to equipment in hours per year = 1/rate = 1/MTTF = 0.01235 hours per year.
Availability is well established in the literature of stochastic modeling and optimal maintenance. Barlow and Proschan  define availability of a repairable system as "the probability that the system is operating at a specified time t." Blanchard  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  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 , Lie, Hwang, and Tillman , and Nachlas . 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 , Lie, Hwang, and Tillman ). Mi  gives some comparison results of availability considering inherent availability.
Availability considered in maintenance modeling can be found in Barlow and Proschan  for replacement models, Fawzi and Hawkes  for an R-out-of-N system with spares and repairs, Fawzi and Hawkes  for a series system with replacement and repair, Iyer  for imperfect repair models, Murdock  for age replacement preventive maintenance models, Nachlas [1998, 1989] for preventive maintenance models, and Wang and Pham  for imperfect maintenance models. A very comprehensive recent book is by Trivedi and Bobbio .
This article incorporates public domain material from the General Services Administration document: "Federal Standard 1037C". (in support of MIL-STD-188) K. Trivedi and A. Bobbio, Reliability and Availability Engineering: Modeling, Analysis and Applications, Cambridge University Press, 2017.