Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual link failure after some amount of elapsed time. The descriptor loss of assured safety (LOAS) is used because failure of the WL system places the entire system in an inoperable configuration while failure of the SL system before failure of the WL system, although undesirable, does not necessarily result in an unintended operation of the entire system. Thus, safety is “assured” by failure of the WL system before failure of the SL system. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation, approximation and illustration of PLOAS with (a) constant delay times, (b) aleatory uncertainty in delay times, and (c) delay times defined by functions of link properties at occurrence times for link failure precursors, and (iii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.
The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/ WL failure time margins defined by (time at which SL failure potentially causes LOAS) - (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) - (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) - (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS).
The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/WL failure time margins defined by (time at which SL failure potentially causes LOAS) – (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS).
The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) time at which LOAS occurs for a one WL/two SL system, (ii) time at which a two-link system fails, (iii) temperature at which a two-link system fails, and (iv) temperature at which LOAS occurs for a one WL/two SL system. The presented results can be generalized to systems with more than one WL and two SLs.
Representations for margins associated with loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems involving multiple time-dependent failure modes are developed. The following topics are described: (i) defining properties for WLs and SLs, (ii) background on cumulative distribution functions (CDFs) for link failure time, link property value at link failure, and time at which LOAS occurs, (iii) CDFs for failure time margins defined by (time at which SL system fails) − (time at which WL system fails), (iv) CDFs for SL system property values at LOAS, (v) CDFs for WL/SL property value margins defined by (property value at which SL system fails) − (property value at which WL system fails), and (vi) CDFs for SL property value margins defined by (property value of failing SL at time of SL system failure) − (property value of this SL at time of WL system failure). Included in this presentation is a demonstration of a verification strategy based on defining and approximating the indicated margin results with (i) procedures based on formal integral representations and associated quadrature approximations and (ii) procedures based on algorithms for sampling-based approximations.
Representations are developed and illustrated for the distribution of link property values at the time of link failure in the presence of aleatory uncertainty in link properties. The following topics are considered: (i) defining properties for weak links and strong links, (ii) cumulative distribution functions (CDFs) for link failure time, (iii) integral-based derivation of CDFs for link property at time of link failure, (iv) sampling-based approximation of CDFs for link property at time of link failure, (v) verification of integral-based and sampling-based determinations of CDFs for link property at time of link failure, (vi) distributions of link properties conditional on time of link failure, and (vii) equivalence of two different integral-based derivations of CDFs for link property at time of link failure.
The Spent Fuel and Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Fuel Cycle Technology (FCT) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). Two high priorities for SFWST disposal R&D are design concept development and disposal system modeling. These priorities are directly addressed in the SFWST Geologic Disposal Safety Assessment (GDSA) control account, which is charged with developing a geologic repository system modeling and analysis capability, and the associated software, GDSA Framework, for evaluating disposal system performance for nuclear waste in geologic media. GDSA Framework is supported by SFWST Campaign and its predecessor the Used Fuel Disposition (UFD) campaign.
The following topics are considered in this presentation: (i) Overview of evidence theory, (ii) Representation of loss of assured safety (LOAS) with evidence theory for a 1 SL, 1 WL system, (iii) Description of 2 SLs and 1 WL used for illustration, (iv) Plausibility and belief for LOAS and associated sampling-based verification calculations for a 2 SL, 1 WL system, (iv) Plausibility and belief for margins associated with LOAS for a 2 SL, 1 WL system, (v) Plausibility and belief for LOAS for a 2 SL, 2 WL system, (vi) Incorporation of evidence spaces for link temperature curves into LOAS calculations, (vii) Plausibility and belief for LOAS for WL/SL systems with SL subsystems, and (viii) Sampling-based procedures for the estimation of plausibility and belief. 2
Representations are developed and illustrated for the distribution of link property values at the time of link failure in the presence of aleatory uncertainty in link properties. The following topics are considered: (i) defining properties for weak links and strong links, (ii) cumulative distribution functions (CDFs) for link failure time, (iii) integral-based derivation of CDFs for link property at time of link failure, (iv) sampling-based approximation of CDFs for link property at time of link failure, (v) verification of integral-based and sampling-based determinations of CDFs for link property at time of link failure, (vi) distributions of link properties conditional on time of link failure, and (vii) equivalence of two different integral-based derivations of CDFs for link property at time of link failure.
Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual failure after some amount of elapsed time. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation of PLOAS with constant delay times, (iii) Approximation and illustration of PLOAS with constant delay times, (iv) Formal representation of PLOAS with aleatory uncertainty in delay times, (v) Approximation and illustration of PLOAS with aleatory uncertainty in delay times, (vi) Formal representation of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, (vii) Approximation and illustration of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, and (viii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.
Representations for margins associated with loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems involving multiple time-dependent failure modes are developed. The following topics are described: (i) defining properties for WLs and SLs, (ii) background on cumulative distribution functions (CDFs) for link failure time, link property value at link failure, and time at which LOAS occurs, (iii) CDFs for failure time margins defined by (time at which SL system fails) – (time at which WL system fails), (iv) CDFs for SL system property values at LOAS, (v) CDFs for WL/SL property value margins defined by (property value at which SL system fails) – (property value at which WL system fails), and (vi) CDFs for SL property value margins defined by (property value of failing SL at time of SL system failure) – (property value of this SL at time of WL system failure). Included in this presentation is a demonstration of a verification strategy based on defining and approximating the indicated margin results with (i) procedures based on formal integral representations and associated quadrature approximations and (ii) procedures based on algorithms for sampling-based approximations.
Weak link (WL)/strong link (SL) systems are important parts of the overall operational design of high - consequence systems. In such designs, the SL system is very robust and is intended to permit operation of the entire system under, and only under, intended conditions. In contrast, the WL system is intended to fail in a predictable and irreversible manner under accident conditions and render the entire system inoperable before an accidental operation of the SL system. The likelihood that the WL system will fail to d eactivate the entire system before the SL system fails (i.e., degrades into a configuration that could allow an accidental operation of the entire system) is referred to as probability of loss of assured safety (PLOAS). This report describes the Fortran 90 program CPLOAS_2 that implements the following representations for PLOAS for situations in which both link physical properties and link failure properties are time - dependent: (i) failure of all SLs before failure of any WL, (ii) failure of any SL before f ailure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The effects of aleatory uncertainty and epistemic uncertainty in the definition and numerical evaluation of PLOAS can be included in the calculations performed by CPLOAS_2. Keywords: Aleatory uncertainty, CPLOAS_2, Epistemic uncertainty, Probability of loss of assured safety, Strong link, Uncertainty analysis, Weak link
A conceptual structure for performance assessments (PAs) for radioactive waste disposal facilities and other complex engineered facilities based on the following three basic conceptual entities is described: EN1, a probability space that characterizes aleatory uncertainty; EN2, a function that predicts consequences for individual elements of the sample space for aleatory uncertainty; and EN3, a probability space that characterizes epistemic uncertainty. The implementation of this structure is illustrated with results from PAs for the Waste Isolation Pilot Plant and the proposed Yucca Mountain repository for high-level radioactive waste.
Several simple test problems are used to explore the following approaches to the representation of the uncertainty in model predictions that derives from uncertainty in model inputs: probability theory, evidence theory, possibility theory, and interval analysis. Each of the test problems has rather diffuse characterizations of the uncertainty in model inputs obtained from one or more equally credible sources. These given uncertainty characterizations are translated into the mathematical structure associated with each of the indicated approaches to the representation of uncertainty and then propagated through the model with Monte Carlo techniques to obtain the corresponding representation of the uncertainty in one or more model predictions. The different approaches to the representation of uncertainty can lead to very different appearing representations of the uncertainty in model predictions even though the starting information is exactly the same for each approach. To avoid misunderstandings and, potentially, bad decisions, these representations must be interpreted in the context of the theory/procedure from which they derive.
Uncertainty and sensitivity analysis results obtained in the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) are presented for two-phase flow in the vicinity of the repository under disturbed conditions resulting from drilling intrusions. Techniques based on Latin hypercube sampling, examination of scatterplots, stepwise regression analysis, partial correlation analysis and rank transformations are used to investigate brine inflow, gas generation repository pressure, brine saturation and brine and gas outflow. Of the variables under study, repository pressure and brine flow from the repository to the Culebra Dolomite are potentially the most important in PA for the WIPP. Subsequent to a drilling intrusion repository pressure was dominated by borehole permeability and generally below the level (i.e., 8 MPa) that could potentially produce spallings and direct brine releases. Brine flow from the repository to the Culebra Dolomite tended to be small or nonexistent with its occurrence and size also dominated by borehole permeability.