System Reliability Analysis

System Reliability Analysis Mahesh Pandey and Mikko Jyrkama

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 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 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

Example Example: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

Solution 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 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. • Solution: • First combine the parallel components 2 and 3 • The probability of failure is • The reliability is 2 1 3 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) Fundamentals of Reliability © M. Pandey, University of Waterloo

System Reliability Analysis