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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 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 express ...
, 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 (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 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 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 syste ...
) 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 life cycles. At its core, systems engineering utilizes systems thinki ...
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 :''This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset models. For mathematical definition, please see Stochas ...
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
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 m ...
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 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 m ...
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 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 m ...
. 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
991 Year 991 ( 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 Truce of God, between Æthelred the Unready and Richard I of ...
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 People * Austin Osman Spare (1886–1956), English artist and occultist * Richard ...
s and repairs, Fawzi and Hawkes
990 Year 990 ( CMXC) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Europe * Al-Mansur, ''de facto'' ruler of Al-Andalus, conquers the Castle of Montemor-o-Velho (mode ...
for 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
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 Emp ...
for imperfect maintenance models. A very comprehensive recent book is by Trivedi and Bobbio
017 Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese ...


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 ...
implemented the Generating Availability Data System 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 *
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. F ...
* RAMS


References


Sources

* * K. Trivedi and A. Bobbio, ''Reliability and Availability Engineering: Modeling, Analysis and Applications'', Cambridge University Press, 2017.


External links


Reliability and Availability Basics





How to track and improve Technical Availability?
{{Authority control Telecommunication theory