system reliability analysis-uofwaterloo
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UN 0701 Engineering Risk and Reliability © M. PandeyUniversity of Waterloo
NSERC-UNENE Industrial Research ChairInstitute for Risk ResearchUniversity of Waterloo
System Reliability Analysis
Mahesh Pandey and Mikko Jyrkama
Fundamentals of Reliability© M. Pandey, University of Waterloo
Outline Introduction
Probabilistic safety analysis (PSA) System reliability analysis
Failure Modes and Effects Analysis (FMEA) Reliability Block Diagrams
Series systems Parallel systems
Fundamentals of Reliability© M. Pandey, University of Waterloo
Introduction
Fundamentals of Reliability© M. Pandey, University of Waterloo
Introduction Most engineering systems consist of many elements or
components Need to consider multiple failure modes and/or multiple
component failures Analysis is fairly complicated Need to consider
1. The contribution of the component failure events to the system’s failure
2. The redundancy of the system3. The post-failure behaviour of a component and the rest of the
system4. The statistical correlation between failure events5. The progressive failure of components
Fundamentals of Reliability© M. Pandey, University of Waterloo
Probabilistic Safety Analysis (PSA) System reliability analysis is an integral part of probabilistic
safety analysis (PSA) in a nuclear power plant The main objective of PSA is to provide a reasonable risk-
based framework for making decisions regarding nuclear power plant design, operation, and siting
The main task is to conduct a reliability analysis for all systems and components in the plant
This requires analysis of all possible failure mechanisms and failure rates for
all systems and components involved quantifying the interaction of the failure mechanisms and their
contribution to overall plant reliability (and safety) PSA also involves other aspects, such as consequence
analysis, uncertainty and sensitivity analyses, etc.
Fundamentals of Reliability© M. Pandey, University of Waterloo
System Reliability Analysis System reliability analysis is conducted in terms of
probabilities The probabilities of events can be modelled as logical
combinations or logical outcomes of other random events Two main methods used include:
Fault tree analysis Event tree analysis
Other qualitative and graphical methods include Failure Modes and Effects Analysis (FMEA) Reliability Block Diagrams (RBD) Functional Logic Diagrams
Fundamentals of Reliability© M. Pandey, University of Waterloo
Failure Modes and Effects Analysis (FMEA)
Fundamentals of Reliability© M. Pandey, University of Waterloo
Failure Modes and Effects Analysis Failure modes and effects analysis (FMEA) is a qualitative
technique for understanding the behaviour of components in an engineered systems
The objective is to determine the influence of component failure on other components, and on the system as a whole
It is often used as a preliminary system reliability analysis to assist the development of a more quantitative event tree/fault tree analysis
FMEA can also be used as a stand-alone procedure for relative ranking of failure modes that screens them according to risk i.e., as a screening tool
Fundamentals of Reliability© M. Pandey, University of Waterloo
FMEA (cont’d)
As a risk evaluation technique, FMEA treats risk in it true sense as the combination of likelihood and consequences
However, strictly speaking, it is not a probabilistic method because it does not generally use quantified probability statements Rather, failure mode occurrences are described using
qualitative statements of likelihood (e.g., rare vs. frequent etc.) Consequences are also ranked qualitatively using levels or
categories e.g., ranging from safe to catastrophic
FMEA uses a rank-ordered scale of likelihood with respect to failure mode occurrence, so that together with the consequence categories, a rank-ordered level of relative risk can be derived for each failure mode
Fundamentals of Reliability© M. Pandey, University of Waterloo
FMEA (cont’d)
FMEA consists of sequentially tabulating each component with all associated possible failure modes impacts on other components and the system consequence ranking failure likelihood detection methods compensating provisions
Failure modes effect and criticality analysis (FMECA) is similar to FMEA except that the criticality of failure is analyzed in greater detail
Fundamentals of Reliability© M. Pandey, University of Waterloo
ExampleExample: Consider the following water heater system used in a residential home. The objective is to conduct a failure modes and effects analysis (FMEA) for the system.
Fundamentals of Reliability© M. Pandey, University of Waterloo
Solution (cont’d)
Define consequence categories as I. Safe – no effect on system II. Marginal – failure will degrade system to some extent but will
not cause major system damage or injury to personnel III. Critical – failure will degrade system performance and/or
cause personnel injury, and if immediate action is not taken, serious injuries or deaths to personnel and/or loss of system will occur
IV. Catastrophic – failure will produce severe system degradation causing loss of system and/or multiple deaths or injuries
The FMEA is shown in the following table
Fundamentals of Reliability© M. Pandey, University of Waterloo
SolutionComponent Failure
ModeEffects on other components
Effects on whole system
Consequence Category
Failure Likelihood
Detection Method
Compensating Provisions
Pressure relief valve
Jammed open
Increased gas flow and thermostat operation
Loss of hot water, more cold water input and gas
I - Safe Reasonably probable
Observe at pressure relief valve
Shut off water supply, reseal or replace relief valve
Jammed closed
None None I - Safe Probable Manual testing
No conseq. unless combined with other failure modes
Gas valve Jammed open
Burner continues to operate, pressure relief valve opens
Water temp. and pressure increase; water turns to steam
III - Critical Reasonably probable
Water at faucet too hot; pressure relief valve open (obs.)
Open hot water faucet to relieve pres., shut off gas; pressure relief valve compensates
Jammed closed
Burner ceases to operate
System fails to produce hot water
I - Safe Remote Observe at faucet (cold water)
Thermostat Fails to react to temp. rise
Burner continues to operate, pressure relief valve opens
Water temp. rises; water turns to steam
III - Critical Remote Water at faucet too hot
Open hot water faucet to relieve pressure; pressure relief valve compensates
Fails to react to temp. drop
Burner fails to function
Water temperature too low
I - Safe Remote Observe at faucet (cold water)
Fundamentals of Reliability© M. Pandey, University of Waterloo
Reliability Block Diagrams
Fundamentals of Reliability© M. Pandey, University of Waterloo
Reliability Block Diagrams Most systems are defined through a combination of both
series and parallel connections of subsystems Reliability block diagrams (RBD) represent a system using
interconnected blocks arranged in combinations of series and/or parallel configurations
They can be used to analyze the reliability of a system quantitatively
Reliability block diagrams can consider active and stand-by states to get estimates of reliability, and availability (or unavailability) of the system
Reliability block diagrams may be difficult to construct for very complex systems
Fundamentals of Reliability© M. Pandey, University of Waterloo
Series Systems Series systems are also referred to as weakest link or chain
systems System failure is caused by the failure of any one component Consider two components in series
Failure is defined as the union of the individual component failures
For small failure probabilities
1 2
where Q denotes the probability of failure
Fundamentals of Reliability© M. Pandey, University of Waterloo
Series Systems (cont’d)
For n components in series, the probability of failure is then
Therefore, for a series system, the system probability of failure is the sum of the individual component probabilities
In case the component probabilities are not small, the system probability of failure can be expressed as
For n components in series
Fundamentals of Reliability© M. Pandey, University of Waterloo
Series Systems (cont’d)
Reliability is the complement of the probability of failure For the two components in series, the system reliability can
be expressed as
Assuming independence
For n components in series
Therefore, for a series system, the reliability of the system is the product of the individual component reliabilities
Fundamentals of Reliability© M. Pandey, University of Waterloo
Parallel Systems Parallel systems are also referred to as redundant The system fails only if all of the components fail Consider two components in parallel
Failure is defined by the intersection of the individual (component) failure events
Assuming independence
1
2
Fundamentals of Reliability© M. Pandey, University of Waterloo
Parallel Systems For n components in parallel, the probability of failure is then
Therefore, for a parallel system, the system probability of failure is the product of the individual component probabilities
The reliability of the parallel system is
For n components in parallel, the system reliability is
Fundamentals of Reliability© M. Pandey, University of Waterloo
Example Problem
Solution: First combine the parallel components 2 and 3 The probability of failure is
The reliability is
Example: Compute the reliability and probability of failure for the following system. Assume the failure probabilities for the components are Q1 = 0.01, Q2 = 0.02 and Q3 = 0.03.
2
31
Fundamentals of Reliability© M. Pandey, University of Waterloo
Solution (cont’d)
Next, combine component 1 and the sub-system (2,3) in series
The probability of failure for the system is then
The system reliability is
Fundamentals of Reliability© M. Pandey, University of Waterloo
Solution (cont’d)
The system probability of failure is equal to
The system reliability is
which is also equal to RSYS = 1 – QSYS
As shown in this example, the system probability of failure and reliability are dominated by the series component 1 i.e. a series system is as good as its weakest link
Fundamentals of Reliability© M. Pandey, University of Waterloo
Things to Consider Reliability block diagrams can also be used to assess
Voting systems (k-out-of-n logic) Standby systems (load sharing or sequential operation)
Simple systems can be assessed by gradually reducing them to equivalent series/parallel configurations
More complex systems would require the use of a more comprehensive approach, such as conditional probabilities or imaginary components
For complex systems, great effort is needed to identify the ways in which the system fails or survives Fault trees can be used to decompose the main failure event
into unions and intersections of sub-events Event trees can be used to identify the possible sequence of
events (also failures)