AS IEC 61165 pdf download – Application of Markov techniques
1 scope
This International Standard provides guidance on the application of Markov techniques tomodel and analyze a system and estimate reliability, availability,maintainability and safetymeasures.
This standard is applicable to all industries where systems, which exhibit state-dependentbehaviour, have to be analyzed. The Markov techniques covered by this standard assumeconstant time-independent’state transition rates.’Such techniques are often calledhomogeneous Markov techniques.
2Normative references
The following referenced documents are indispensable for the application of this document.For dated references,only the edition cited applies. For undated references, the latest editionof the referenced document (including any amendments) applies.
References to international standards that are struck through in this clause are replaced byreferences to Australian or Australian/New Zealand Standards that are listed immediatelythereafter and identified by shading.Any Australian or Australian/New Zealand Standard thatis identical to the International Standard it replaces is identified as such.
IEC 60050(191):1990,International Electrotechnical Vocabulary (IEV) – Chapter 191:Dependability and quality of service
IEC 60300-3-1:Dependability management – Part 3-1:Application guide – Analysis techniquesfor dependability: Guide on methodology
AS IEC 60300.3.1,Dependability management—Application guide—Analysis techniques fordependability-Guide on methodology
IEC 61508-4:1998,Functional safety of electrical/electronic/programmable electronic safety-related systems – Part 4: Definitions and abbreviations
3Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050(191):1990and the following apply.
NOTE To facllitate the application of this standard for safety evaluations, the terminology from lEC 61508 is usedwhere appropriate.
3.1
system
set of interrelated or interacting elements[Iso 9o0o，3.2.1]
NOTE 1 In the context of dependability,a system will have a defined purpose expressed in terms of intendedfunctions,stated conditions of operationiuse,and defined boundaries.
NOTE 2 The structure of a system may be hierarchical.
3.2
element
component or set of components, which function as a single entity
NOTE An element can usually assume only two states: up or down (see 3.4 and 3.5)， For convenience the termelement state will be used to denote the state of an element.
3.3
system statext)
particular combination of element states
NOTE X(t) is the state of the system at time t. There are other factors that may have an effect on the system state(e. g. mode of operation,.
3.4
up state
system (or element) state in which the system (or element) is capable of performing therequired function
NOTE A system can have several distinguishable up states (e.g. fully operational states and degraded states)
3.5
down state
system (or element) state in which the system (or element) is not capable of performing therequired function
NOTE A system can have severall distinguishable down states.
3.6
hazard
potential source of physical injury or damage to the health of people or property[IEC61508-4，3.1.2,modified]
3.7
dangerous failure
failure which has the potential to put the safety-related system in a hazardous state or fail-to-function state
[1EC61508-4，3.6.7 ,modified]
NOTE 1 Whether or not the potential is realised may depend on the architecture of the system.NOTE 2 The term unsafe failure or hazardous failure is also commonly used in this context.
3.8
safe failure
failure which does not have the potential to put the safety-related system in a hazardous stateor fail-to-function state
[lEC 61508, modified]
3.9
transition
change from one state to another state
NOTE Transition takes place usually as a result of failure or restoration. A transition may also be caused by otherevents such as human errors,external events,reconfiguration of software,etc
3.10
transition probabilityPrj(t)
conditional probability of transition from state i to state j in a given time interval (s, s+t) giventhat the system is in state i at the beginning of the time interval
NOTE 1 Formally P;(s,s+t)= P(X(s+t)= j |X(s) = i).When the Markov process is time-homogeneous, then P,(s.s+fy does not depend on s and is designated as P(t)-
NOTE2 For an irreducible Markov process (i.e. if every state can be reached from every other state) it holds thatPfo )=P, where P, is the asymptotic and stationary or steady-state probability of state j.
3.11
transition rateaij
limit, if it exists, of the ratio of the conditional probability that a transition takes place fromstate i to state j within a given time interval (t, t+ at) and the length of the interval t, when Attends to zero, given that the system is in state i at time t
NOTE py or c are also used in this context.
3.12
initial state
system state at time t = o
NOTE Generally, a system starts its operation at t = 0 from an up state in which all elements of the system arefunctioning and transits towards the final system state,which is a down state, via other system up states havingprogressively fewer functioning elements.
3.13
absorbing state
state which once entered,cannot be left (i. e.no transitions out of the state are possible)
AS IEC 61165 pdf download – Application of Markov techniques
