Availability

# Availability

Discussion

Encyclopedia
In telecommunication
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...

s and reliability theory
Reliability theory
Reliability theory describes the probability of a system completing its expected function during an interval of time. It is the basis of reliability engineering, which is an area of study focused on optimizing the reliability, or probability of successful functioning, of systems, such as airplanes,...

, the term availability has the following meanings:
• The degree to which a system
System
System is a set of interacting or interdependent components forming an integrated whole....

, 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
Unavailability
Unavailability can be defined as the probability that an item will not operate correctly at a given time and under specified conditions. It opposes availability....

.
• 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
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

(such as 0.9998). In high availability
High availability
High availability is a system design approach and associated service implementation that ensures a prearranged level of operational performance will be met during a contractual measurement period....

applications, a metric known as nines
Nines (engineering)
The colloquial term nines is used in engineering to indicate reliability or purity . It is preceded by a number indicating the degree of such reliability or purity. For example, 0.999 pure silver would be 3 nines pure...

, corresponding to the number of nines following the decimal point, is used. In this system, "five nines" equals 0.99999 (or 99.999%) availability.

## Availability in Layman's Terms

Availability of a system over its life-cycle is typically measured as a factor of its reliability
Reliability
In general, reliability is the ability of a person or system to perform and maintain its functions in routine circumstances, as well as hostile or unexpected circumstances.Reliability may refer to:...

- 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
Reliability engineering
Reliability engineering is an engineering field, that deals with the study, evaluation, and life-cycle management of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is often measured as a probability of...

and maintainability
Maintainability
In engineering, maintainability is the ease with which a product can be maintained in order to:* isolate defects or their cause* correct defects or their cause* meet new requirements* make future maintenance easier, or* cope with a changed environment...

involve processes designed to optimize availability under a set of constraints, such as time and cost-effectiveness. Availability is the goal of most system
System
System is a set of interacting or interdependent components forming an integrated whole....

users, and reliability engineering and maintainability provide the means to assure that availability performance requirements are achieved.

## Representation

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

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,

### Example

If we are using equipment which has mean time to failure
Mean time to failure
No artical exists on Wiki, please create one.In short Mean Time to Failure is the time taken for a part or system to fail for the first time.A very brief formula for the Mean Time To Failure of an event which occurs with probability P is: 1 / P....

(MTTF) of 81.5 years and mean time to repair
Mean time to repair
Mean time to repair is a basic measure of the maintainability of repairable items. It represents the average time required to repair a failed component or device. Expressed mathematically, it is the total corrective maintenance time divided by the total number of corrective maintenance actions...

(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.

## Literature

Availability is well established in the literature of stochastic modeling and optimal maintenance
Optimal maintenance
Optimal maintenance is the discipline within operations research concerned with maintaining a system in a manner that maximizes profit or minimizes cost. Cost functions depending on the reliability and maintainability characteristics of the system of interest determine the parameters to minimize...

. 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
Downtime
The term downtime is used to refer to periods when a system is unavailable.Downtime or outage duration refers to a period of time that a system fails to provide or perform its primary function...

. 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
Spare part
Spare Parts may also refer to:* Spare Parts , by Status Quo* Spare Parts is a Doctor Who audio drama.* Spare Parts , by Servotron* "Spare Parts" , by Bruce Springsteen* "Spare Parts"...

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.