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# System Reliability Analysis

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Introduction
Probabilistic safety analysis (PSA)
System reliability analysis
Failure Modes and Effects Analysis (FMEA)
Reliability Block Diagrams
Series systems
Parallel system

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### System Reliability Analysis

1. 1. UN 0701 Engineering Risk and Reliability © M. Pandey University of WaterlooSystem ReliabilityAnalysisMahesh Pandey and Mikko JyrkamaNSERC-UNENE Industrial Research ChairInstitute for Risk ResearchUniversity of Waterloo
2. 2. Outline Introduction  Probabilistic safety analysis (PSA)  System reliability analysis Failure Modes and Effects Analysis (FMEA) Reliability Block Diagrams  Series systems  Parallel systemsFundamentals ofReliability© M. Pandey, University
3. 3. IntroductionFundamentals ofReliability© M. Pandey, University
4. 4. 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 system 3. The post-failure behaviour of a component and the rest of the system 4. The statistical correlation between failure events 5. The progressive failure of componentsFundamentals ofReliability© M. Pandey, University
5. 5. 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 ofReliability© M. Pandey, University
6. 6. 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 DiagramsFundamentals ofReliability© M. Pandey, University
7. 7. Failure Modes and Effects Analysis (FMEA)Fundamentals ofReliability© M. Pandey, University
8. 8. 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 toolFundamentals ofReliability© M. Pandey, University
9. 9. 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 modeFundamentals ofReliability© M. Pandey, University
10. 10. 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 detailFundamentals ofReliability© M. Pandey, University
11. 11. Example theExample: Considerfollowing water heater systemused in a residential home.The objective is to conducta failure modes and effectsanalysis (FMEA) for thesystem.Fundamentals ofReliability© M. Pandey, University
12. 12. 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 tableFundamentals ofReliability© M. Pandey, University
13. 13. Component Failure Effects on Effects on Consequence Failure Detection Compensating Mode other whole system Category Likelihood Method ProvisionsPressure Solution Jammed components Increased gas Loss of hot I - Safe Reasonably Observe at Shut off waterrelief valve open flow and water, more probable pressure supply, reseal thermostat cold water relief valve or replace relief operation input and gas valve Jammed None None I - Safe Probable Manual No conseq. closed testing unless combined with other failure modesGas valve Jammed Burner Water temp. III - Critical Reasonably Water at Open hot water open continues to and pressure probable faucet too faucet to relieve operate, increase; water hot; pressure pres., shut off pressure relief turns to steam relief valve gas; pressure valve opens open (obs.) relief valve compensates Jammed Burner ceases System fails to I - Safe Remote Observe at closed to operate produce hot faucet (cold water water)Thermostat Fails to Burner Water temp. III - Critical Remote Water at Open hot water react to continues to rises; water faucet too hot faucet to relieve temp. operate, turns to steam pressure; rise pressure relief pressure relief valve opens valve compensates Fundamentals of to Water Fails to react to Burner fails function temperature I - Safe Remote Observe at faucet (cold temp. too low water) Reliability drop © M. Pandey, University
14. 14. Reliability Block DiagramsFundamentals ofReliability© M. Pandey, University
15. 15. 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 systemsFundamentals ofReliability© M. Pandey, University
16. 16. 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 1 2 Failure is defined as the union of the individual component failures where Q denotes the probability of failure For small failure probabilitiesFundamentals ofReliability© M. Pandey, University
17. 17. 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 seriesFundamentals ofReliability© M. Pandey, University
18. 18. 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 reliabilitiesFundamentals ofReliability© M. Pandey, University
19. 19. 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 1 2 Failure is defined by the intersection of the individual (component) failure events Assuming independenceFundamentals ofReliability© M. Pandey, University
20. 20. 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 isFundamentals ofReliability© M. Pandey, University
21. 21. Example Problem and probability of failure for theExample: Compute the reliabilityfollowing system. Assume the failure probabilities for thecomponents are Q1 = 0.01, Q2 = 0.02 and Q3 = 0.03. 2 1 3 Solution:  First combine the parallel components 2 and 3  The probability of failure is  The reliability isFundamentals ofReliability© M. Pandey, University
22. 22. 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 isFundamentals ofReliability© M. Pandey, University
23. 23. 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 linkFundamentals ofReliability© M. Pandey, University
24. 24. 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)Fundamentals ofReliability© M. Pandey, University