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{{About||the thermodynamic function "availability", in the sense of available useful work|exergy|availability as a form of cognitive bias|availability heuristic}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


In [[telecommunication]]s and [[reliability theory]], the term '''availability''' has the following meanings:
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


* 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. Simply put, availability is the proportion of time a system is in a functioning condition.  This is often described as a '''mission capable rate'''.  Mathematically, this is expressed as 1 minus [[unavailability]].
Registered users will be able to choose between the following three rendering modes:
* The ratio of (a) the total time a [[functional unit]] is capable of being used during a given interval to (b) the length of the interval.


For example, a unit that is capable of being used 100 hours per week (168 hours) would have an availability of 100/168.  However, typical availability values are specified in [[decimal]] (such as 0.9998).  In [[high availability]] applications, a metric known as [[nines (engineering)|nines]], corresponding to the number of nines following the decimal point, is used.  In this system, "five nines" equals 0.99999 (or 99.999%) availability.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


== Introduction ==
<!--'''PNG''' (currently default in production)
Availability of a system is typically measured as a factor of its [[reliability (engineering)|reliability]] - as reliability increases, so does availability.  However, no system can guarantee 100.000% reliability;  and as such, no system can assure 100.000% availability.  Further, [[reliability engineering]] and [[maintainability]] involve processes designed to optimize availability under a set of constraints, such as time and cost-effectiveness. Availability is the goal of most [[system]] users, and reliability engineering and maintainability provide the means to assure that availability performance [[requirements]] are achieved.
:<math forcemathmode="png">E=mc^2</math>


==Representation==
'''source'''
The most simple representation for '''availability''' is as 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
:<math forcemathmode="source">E=mc^2</math> -->


: <math>A = \frac{E[\mathrm{Uptime}]}{E[\mathrm{Uptime}]+E[\mathrm{Downtime}]}</math>
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


If we define the status function <math>X(t)</math> as
==Demos==


: <math>X(t)=
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
  \begin{cases}
  1, & \mbox{sys functions at time } t\\
  0, &  \mbox{otherwise}
  \end{cases}
</math>


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


: <math>
* accessibility:
    A(t)=\Pr[X(t)=1]=E[X(t)].</math>
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


Average availability must be defined on an interval of the real line. If we consider an arbitrary constant <math>c>0</math>, then average availability is represented as
==Test pages ==


: <math>
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
    A_c = \frac{1}{c}\int_0^c A(t)\,dt.
*[[Displaystyle]]
</math>
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


Limiting (or steady-state) availability is represented by{{Citation needed|date=August 2010}}
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
: <math>
==Bug reporting==
    A = \lim_{c \rightarrow \infty} A_c.
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
</math>
 
Limiting average availability is also defined on an interval <math>(0,c]</math> as,
 
: <math>
    A_{\infty}=\lim_{c \rightarrow \infty} A_c = \lim_{c \rightarrow \infty}\frac{1}{c}\int_0^c A(t)\,dt,\quad c > 0.
</math>
 
===Example===
If we are using equipment which has [[mean time to failure]] (MTTF) of 81.5 years and [[mean time to repair]] (MTTR) of 1 hour:
 
MTTF in hours = 81.5*365*24=713940
 
Availability= MTTF/(MTTF+MTTR) = 713940/713941 =99.999859%
 
Unavailability = 0.000141%
 
Outage due to equipment in hours per year
 
U=0.01235 hours per year.
<!-- article does not discuss 1+0
That was the case if we are using 1+0 link.. if we are using 1+1 we would use below formula to calculate availability
 
A= Under root  of MTBFa/MTBFa+20ms * MTBFb/MTBFb+20ms
-->
 
==Literature==
'''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." While 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 availilability 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 [[spare part|spare]]s 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.
 
==See also==
* [[High availability]]
* [[List of system quality attributes]]
* [[Spurious trip level]]
* [[Condition-based maintenance]]
* [[Fault reporting]]
 
==References==
{{FS1037C MS188}}
 
==External links==
* [http://www.eventhelix.com/RealtimeMantra/FaultHandling/reliability_availability_basics.htm Reliability and Availability Basics]
* [http://www.eventhelix.com/RealtimeMantra/FaultHandling/system_reliability_availability.htm System Reliability and Availability]
 
[[Category:Applied probability]]
[[Category:Telecommunication theory]]
 
[[ar:التواجدية]]
[[cs:Dostupnost]]
[[de:Verfügbarkeit]]
[[es:Factor de disponibilidad]]
[[eo:Havebleco]]
[[fr:Disponibilité]]
[[it:Disponibilità]]
[[hu:Rendelkezésre állás]]
[[nl:Beschikbaarheid]]
[[ja:可用性]]
[[pl:Dostępność (informatyka)]]
[[ru:Доступность информации]]
[[fi:Saatavuus]]
[[sv:Driftsäkerhet]]
[[uk:Доступність інформаційна]]
[[zh:可用性]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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