In
reliability engineering
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ... , the term availability has the following meanings:
* The degree to which a
system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ... ,
subsystem
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expressed ... 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)=1 E (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
Fault tree analysis (FTA) is a type of failure analysis in which an undesired state of a system is examined. This analysis method is mainly used in safety engineering and reliability engineering to understand how systems can fail, to identify t ... 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 (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:
# 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
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system ... MTBF/(MTBF+ mean time to repair
Mean time to repair (MTTR) 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 for ... 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
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the ''arithme ... (MTTF)/(MTTF + the mean time to repair
Mean time to repair (MTTR) 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 for ... 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
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system ... ) 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
Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their enterprise life cycle, life cycles. At its core, systems engineering util ... for more details
Basic example
If we are using equipment which has a mean time to failure
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the ''arithme ... (MTTF) of 81.5 years and mean time to repair
Mean time to repair (MTTR) 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 for ... (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 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, availability and maintainability characteristics o ... . Barlow and Proschan 975
Year 975 (Roman numerals, CMLXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Byzantine Empire
* Arab–Byzantine wars#Byzantine resurgence, 863–11th century, A ... define availability of a repairable system as "the probability that the system is operating at a specified time t." Blanchard 998
Year 998 ( CMXCVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* Spring – Otto III retakes Rome and restores power in the papal city. Crescenti ... 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 977
Year 977 ( CMLXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar.
Events
By place Europe
* May – Boris II, dethroned emperor (''tsar'') of Bulgaria, and his brother Roman ma ... 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
The term downtime is used to refer to periods when a system is unavailable.
The unavailability is the proportion of a time-span that a system is unavailable or offline.
This is usually a result of the system failing to function because of an un ... . 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
Year 975 (Roman numerals, CMLXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Byzantine Empire
* Arab–Byzantine wars#Byzantine resurgence, 863–11th century, A ... Lie, Hwang, and Tillman 977
Year 977 ( CMLXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar.
Events
By place Europe
* May – Boris II, dethroned emperor (''tsar'') of Bulgaria, and his brother Roman ma ... and Nachlas 998
Year 998 ( CMXCVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* Spring – Otto III retakes Rome and restores power in the papal city. Crescenti ... 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
Year 998 ( CMXCVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* Spring – Otto III retakes Rome and restores power in the papal city. Crescenti ... Lie, Hwang, and Tillman 977
Year 977 ( CMLXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar.
Events
By place Europe
* May – Boris II, dethroned emperor (''tsar'') of Bulgaria, and his brother Roman ma ... . Mi 998
Year 998 ( CMXCVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* Spring – Otto III retakes Rome and restores power in the papal city. Crescenti ... gives some comparison results of availability considering inherent availability.
Availability considered in maintenance modeling can be found in Barlow and Proschan 975
Year 975 (Roman numerals, CMLXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Byzantine Empire
* Arab–Byzantine wars#Byzantine resurgence, 863–11th century, A ... for replacement models, Fawzi and Hawkes 991
Year 991 (Roman numerals, CMXCI) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar.
Events
* March 1: In Rouen, Pope John XV ratifies the first Peace and Truce of God, Truce of God, between ... for an R-out-of-N system with spare
Spare or Spares may refer to:
Common meanings
* Spare (bowling), a term for knocking down all the pins using two bowling balls
* short for spare part
** Spare tire
A spare tire (or stepney in some countries) is an additional tire (or tyre - s ... s and repairs, Fawzi and Hawkes 990 for a series system with replacement and repair, Iyer 992
Year 992 ( CMXCII) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Worldwide
* Winter – A superflare from the sun causes an Aurora Borealis, with visibility as fa ... for imperfect repair models, Murdock 995
Year 995 (Roman numerals, CMXCV) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar.
Events
By place
Japan
* 17 May - Fujiwara no Michitaka (imperial regent) dies.
* 3 June: Fujiwara no ... for age replacement preventive maintenance models, Nachlas 998, 1989 for preventive maintenance models, and Wang and Pham 996
Year 996 ( CMXCVI) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar.
Events
By place
Japan
* February - Chotoku Incident: Fujiwara no Korechika and Takaie shoot an arrow at Retired Em ... for 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
The North American Electric Reliability Corporation (NERC) is a nonprofit corporation based in Atlanta, Georgia, and formed on March 28, 2006, as the successor to the North American Electric Reliability Council (also known as NERC). The original N ... implemented the Generating Availability Data System The Generating Availability Data System (GADS) is a database produced by the North American Electric Reliability Corporation (NERC). It includes annual summary reports comprising the statistics for power stations in the United States and Canada.
G ... in 1982.
See also
* Reliability engineering
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ...
* Safety engineering
Safety engineering is an engineering discipline which assures that engineered systems provide acceptable levels of safety. It is strongly related to industrial engineering/systems engineering, and the subset system safety engineering. Safety en ...
* List of system quality attributes
Within systems engineering, quality attributes are realized non-functional requirements used to evaluate the performance of a system. These are sometimes named architecture characteristics, or "ilities" after the suffix many of the words share. ...
* Spurious trip level Spurious trip level (STL) is defined as a discrete level for specifying the spurious trip requirements of safety functions to be allocated to safety systems. An STL of 1 means that this safety function has the highest level of spurious trips. The hi ...
* Condition-based maintenance
The technical meaning of maintenance involves functional checks, servicing, repairing or replacing of necessary devices, equipment, machinery, building infrastructure, and supporting utilities in industrial, business, and residential installa ...
* Fault reporting
Fault reporting is a maintenance concept that increases operational availability and that reduces operating cost through three mechanisms.
* Reduce labor-intensive diagnostic evaluation
* Eliminate diagnostic testing down-time
* Provide notificati ...
* High availability
High availability (HA) is a characteristic of a system which aims to ensure an agreed level of operational performance, usually uptime, for a higher than normal period.
Modernization has resulted in an increased reliance on these systems. Fo ...
*
HOME
Content is Copyleft Website design, code, and AI is Copyrighted (c) 2014-2017 by Stephen Payne
Consider donating to Wikimedia
As an Amazon Associate I earn from qualifying purchases