Available Storage Technologies, Their Capacity And Discharge Time

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%.

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 amont of time" ''C'' of the observation window)

: $A = \frac = \frac$

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

: $A = \frac = \frac$

If we define the status function $X(t)$ as

: $X(t)= \begin 1, & \text t\\ 0, & \text \end$

therefore, the availability ''A''(''t'') at time ''t'' > 0 is represented by

: A(t)=\Pr (t)=1E (t) \,

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

: $A_c = \frac \int_0^c A(t)\,dt.$

Limiting (or steady-state) availability is represented by
: $A = \lim_ A_c.$

Limiting average availability is also defined on an interval ,c/math> as,

: $A_\infty =\lim_ A_c = \lim_\frac \int_0^c A(t)\,dt,\quad c > 0.$

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).

Methods and techniques to model availability

Reliability Block Diagrams or Fault Tree Analysis are developed to calculate availability of a system or a functional failure condition within a system including many factors like:

* Reliability models
* Maintainability models
* Maintenance concepts
* Redundancy
* Common cause failure
* Diagnostics
* Level of repair
* Repair status
* Dormant failures
* Test coverage
* Active operational times / missions / sub system states
* Logistical aspects like; spare part (stocking) levels at different depots, transport times, repair times at different repair lines, manpower availability and more.
* Uncertainty in parameters

Furthermore, these methods are capable to identify the most critical items and failure modes or events that impact availability.

Definitions within systems engineering

Availability, inherent (A_i)
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:
# The impact of a repairable-element (refurbishing/remanufacture isn't repair, but rather replacement) on the availability of the system, in which it operates, equals mean time between failures MTBF/(MTBF+ mean time to repair MTTR).
# The impact of a one-off/non-repairable element (could be refurbished/remanufactured) on the availability of the system, in which it operates, equals the mean time to failure (MTTF)/(MTTF + the mean time to repair MTTR).

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

Basic example

If we are using equipment which has a mean time to failure (MTTF) of 81.5 years and mean time to repair (MTTR) of 1 hour:

: MTTF in hours = (This is a reliability parameter and often has a high level of uncertainty!)

: Inherent availability (Ai)

: Inherent unavailability

Outage due to equipment in hours per year = 1/rate = 1/MTTF = 0.01235 hours per year.

Literature

Availability is well established in the literature of stochastic modeling and optimal maintenance. Barlow and Proschan 975define availability of a repairable system as "the probability that the system is operating at a specified time t." Blanchard 998gives 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 977developed 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 975 Lie, Hwang, and Tillman 977 and Nachlas 998 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 998 Lie, Hwang, and Tillman 977. Mi 998gives some comparison results of availability considering inherent availability.

Availability considered in maintenance modeling can be found in Barlow and Proschan 975for replacement models, Fawzi and Hawkes 991for an R-out-of-N system with spares and repairs, Fawzi and Hawkes 990for a series system with replacement and repair, Iyer 992for imperfect repair models, Murdock 995for age replacement preventive maintenance models, Nachlas 998, 1989for preventive maintenance models, and Wang and Pham 996for imperfect maintenance models. A very comprehensive recent book is by Trivedi and Bobbio 017

Applications

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

See also

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

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