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NASA NTRS2012

Comparison of TRMM 2A25 Products Version 6 and Version 7 with NOAA/NSSL Ground Radar-Based National Mosaic QPE

Characterization of the error associated to satellite rainfall estimates is a necessary component of deterministic and probabilistic frameworks involving spaceborne passive and active microwave measurements for applications ranging from water budget studies to forecasting natural hazards related to extreme rainfall events. We focus here on the error structure of Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) quantitative precipitation estimation (QPE) at ground. The problem was addressed in a previous paper by comparison of 2A25 version 6 (V6) product with reference values derived from NOAA/NSSL's ground radar-based National Mosaic and QPE system (NMQ/Q2). The primary contribution of this study is to compare the new 2A25 version 7 (V7) products that were recently released as a replacement of V6. This new version is considered superior over land areas. Several aspects of the two versions are compared and quantified including rainfall rate distributions, systematic biases, and random errors. All analyses indicate V7 is an improvement over V6.

Kirstetter, Pierre-Emmanuel↗

DOE OSTI2015

Development of criticality risk evaluation method for fuel debris in Fukushima Dai-ichi NPS - 14373

After the accident of Fukushima Dai-ichi Nuclear Power Station, there has been still damaged nuclear fuel in the reactor buildings, which is called 'fuel debris' and contains an amount of fissile materials show that it is currently subcritical, which must be kept until finishing retrieval work. In the latest plan, retrieving fuel debris is to start in 2025. The International Research Institute for Nuclear Decommissioning, IRID, has been developing the technology for decontamination in reactor building. A developed method will be reviewed and granted by the Nuclear Regulatory Authority in Japan, NRA, before the start of the retrieving. Criticality risk information will be needed for decision making on following two subcriticality issues, -Criticality control of fuel debris to keep is subcritical until the end of retrieval work. -Safe operation for retrieving fuel debris to keep it subcritical. Because fuel debris has been out of criticality control and the key condition for its current subcriticality is unknown, it is important to obtain criticality risk information as soon as possible. Applying conventional Probabilistic Safety Assessment, PSA, to fuel debris is difficult, because it is based on the probability of becoming out of criticality control due to troubles such as equipment failure, operation mistake and so on. A new method, which has been developed by Japan Atomic Energy Agency to technically support the NRA, is designed to estimate criticality risk based on a probability distribution of k{sub eff} due to uncertainty of composition and geometry of fuel debris, which method will provide risk information for the two subcriticality issues as well as for the tolerance level of criticality risk if it is unavoidable. Developed method contains four steps: two steps of analysis of criticality risk and two steps of quantification of the risk. A procedure of risk quantification has been defined, in which systematic analysis of criticality risk can be done by making 'status matrix'. A trial analysis by using the procedure shows that some events which can initiate criticality are able to be supposed to happen during maintenance period until the beginning of retrieving fuel debris, and that analysis also indicates countermeasures should be considered as soon as possible in order to reduce criticality risk for public and workers. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Estimation of iodine nutrition and thyroid function status in late-gestation pregnant women in the United States: Development and application of a population-based pregnancy model

Previously, a deterministic biologically-based dose-response (BBDR) pregnancy model was developed to evaluate moderate thyroid axis disturbances with and without thyroid-active chemical exposure in a near-term pregnant woman and fetus. In the current study, the existing BBDR model was adapted to include a wider functional range of iodine nutrition, including more severe iodine deficiency conditions, and to incorporate empirically the effects of homeostatic mechanisms. The extended model was further developed into a population-based model and was constructed using a Monte Carlo-based probabilistic framework. In order to characterize total (T4) and free (fT4) thyroxine levels for a given iodine status at the population-level, the distribution of iodine intake for late-gestation pregnant women in the U.S was reconstructed using various reverse dosimetry methods and available biomonitoring data. The range of median (mean) iodine intake values resulting from three different methods of reverse dosimetry tested was 196.5–219.9 μg of iodine/day (228.2–392.9 μg of iodine/day). There was minimal variation in model-predicted maternal serum T4 and ft4 thyroxine levels from use of the three reconstructed distributions of iodine intake; the range of geometric mean for T4 and fT4, was 138–151.7 nmol/L and 7.9–8.7 pmol/L, respectively. The average value of the ratio of the 97.5th percentile to the 2.5th percentile equaled 3.1 and agreed well with similar estimates from recent observations in third-trimester pregnant women in the U.S. In addition, the reconstructed distributions of iodine intake allowed us to estimate nutrient inadequacy for late-gestation pregnant women in the U.S. via the probability approach. The prevalence of iodine inadequacy for third-trimester pregnant women in the U.S. was estimated to be between 21% and 44%. Taken together, the current work provides an improved tool for evaluating iodine nutritional status and the corresponding thyroid function status in pregnant women in the U.S. This model enables future assessments of the relevant risk of thyroid hormone level perturbations due to exposure to thyroid-active chemicals at the population-level. - Highlights: • A population-based thyroid function model for pregnant women was developed. • The model was used specifically study the late-gestation pregnant women in the U.S. • The prevalence of iodine inadequacy was estimated in the sub-population studied. • Developed model well predicts trimester-specific thyroid hormone reference ranges. • The model can be further used to study thyroid perturbations at a population level.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Application of Point Precipitation Frequency Estimates to Watersheds

This report documents work sponsored by the U.S. Nuclear Regulatory Commission (NRC) at the Oak Ridge National Laboratory (ORNL) as part of the RES project, “Application of Point Precipitation Frequency Estimates to Watersheds.” This project was implemented as part of the Probabilistic Flood Hazard Assessment (PFHA) Research Program. The objective of the PFHA Research Program is to develop tools and guidance on the use of PFHA methods to risk-inform NRC’s licensing of new facilities as well as licensing and oversight of currently operating facilities as they relate to flooding hazards. Many nuclear power plants (NPPs) are located on or near rivers so riverine flooding hazards need to be considered in their design and operation. Probabilistic riverine flood models are important tools for realistic assessment of flooding risks. However, these models require areal estimates of the depth, duration, and frequency of rainfall distributed over the watershed, which are not often available. Point precipitation frequency estimates are more widely available. For example, the National Oceanic and Atmospheric Administration (NOAA) has published NOAA Atlas 14, which provides point precipitation frequency estimates for 5-minute through 60-day durations at average recurrence intervals of 1-year through 1,000-year. The research documented in this report addresses areal reduction factors (ARFs), which can be used to convert the widely available point precipitation frequency estimates, to estimates of areal precipitation frequency over a watershed. The most widely used ARF source is Technical Paper 29 (TP-29) published by the then U.S. Weather Bureau in 1958. However, both the methods and the underlying precipitation data used to produce TP-29 are seriously out of date. For example, due to the small gauge network available at the time of TP-29’s compilation, ARF estimates developed are only for watersheds smaller than about 400 square miles. Due to the relatively short record lengths of precipitation data available, frequency considerations could not be accurately determined. Other factors such as regional climate and seasonality were not addressed. Several newer methods have been published since TP-29 was developed and both the type and quantity of precipitation data have increased significantly, along with computational resources and analytical tools such as geographic information systems. This report reviewed and assessed the available precipitation products and methods for conducting ARF analysis. The work applied up-to-date precipitation data products and analysis methods with a novel watershed-based approach to investigate how ARF estimates vary across different methods, data sources, geographical locations, return periods, and seasons. The overall findings reported here regarding basic ARF trends are in line with other recent studies showing that ARFs decrease with increasing area, increase with increasing duration, and decrease with increasing return period. This study found significant differences among the available ARF methods. This work also found a strong geographical variability across different US hydrologic regions, suggesting that the ARF are specific to regional climate patterns and geographical characteristics and should not be applied arbitrarily to other locations. The results also reveal the importance of data record length, especially for high return level ARFs. The work reported in NUREG/CR-7271 will assist NRC staff in assessing different classes of ARF methods in conjunction with available rainfall data sets. It will also support the development of guidance for application of point precipitation data in PFHAs. It should be noted that the ARF values presented in this report for any location or region were developed for the purposes of comparing methods and investigating the factors that influence ARFs. They should not be considered official and should not be used in leu of a site-specific analysis.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

SU-G-JeP2-02: A Unifying Multi-Atlas Approach to Electron Density Mapping Using Multi-Parametric MRI for Radiation Treatment Planning

Purpose: MRI has a number of advantages over CT as a primary modality for radiation treatment planning (RTP). However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. In the work, a reliable method to map electron density is developed by leveraging the differential contrast of multi-parametric MRI. Methods: We propose a probabilistic Bayesian approach for electron density mapping based on T1 and T2-weighted MRI, using multiple patients as atlases. For each voxel, we compute two conditional probabilities: (1) electron density given its image intensity on T1 and T2-weighted MR images, and (2) electron density given its geometric location in a reference anatomy. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function using the Bayesian formalism. The mean value of the posterior probability density function provides the estimated electron density. Results: We evaluated the method on 10 head and neck patients and performed leave-one-out cross validation (9 patients as atlases and remaining 1 as test). The proposed method significantly reduced the errors in electron density estimation, with a mean absolute HU error of 138, compared with 193 for the T1-weighted intensity approach and 261 without density correction. For bone detection (HU>200), the proposed method had an accuracy of 84% and a sensitivity of 73% at specificity of 90% (AUC = 87%). In comparison, the AUC for bone detection is 73% and 50% using the intensity approach and without density correction, respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection based on multi-parametric MRI of the head with highly heterogeneous anatomy. This could allow for accurate dose calculation and reference image generation for patient setup in MRI-based radiation treatment planning.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2011

Toward a Framework for Systematic Error Modeling of NASA Spaceborne Radar with NOAA/NSSL Ground Radar-Based National Mosaic QPE

Characterization of the error associated to satellite rainfall estimates is a necessary component of deterministic and probabilistic frameworks involving space-born passive and active microwave measurement") for applications ranging from water budget studies to forecasting natural hazards related to extreme rainfall events. We focus here on the error structure of NASA's Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) quantitative precipitation estimation (QPE) at ground. The problem is addressed by comparison of PR QPEs with reference values derived from ground-based measurements using NOAA/NSSL ground radar-based National Mosaic and QPE system (NMQ/Q2). A preliminary investigation of this subject has been carried out at the PR estimation scale (instantaneous and 5 km) using a three-month data sample in the southern part of US. The primary contribution of this study is the presentation of the detailed steps required to derive trustworthy reference rainfall dataset from Q2 at the PR pixel resolution. It relics on a bias correction and a radar quality index, both of which provide a basis to filter out the less trustworthy Q2 values. Several aspects of PR errors arc revealed and quantified including sensitivity to the processing steps with the reference rainfall, comparisons of rainfall detectability and rainfall rate distributions, spatial representativeness of error, and separation of systematic biases and random errors. The methodology and framework developed herein applies more generally to rainfall rate estimates from other sensors onboard low-earth orbiting satellites such as microwave imagers and dual-wavelength radars such as with the Global Precipitation Measurement (GPM) mission.

Kirstettier, Pierre-Emmanual↗

DOE OSTI2016

SU-F-J-187: The Statistical NTCP and TCP Models in the Proton Therapy

Purpose: The statistical models (SM) are typically used as a subjective description of a population for which there is only limited sample data, and especially in cases where the relationship between variables is known. The normal tissue complications and tumor control are frequently stochastic effects in the Radiotherapy (RT). Based on probabilistic treatments, it recently has been formulated new NTCP and TCP models for the RT. Investigating the particular requirements for their clinical use in the proton therapy (PT) is the goal of this work. Methods: The SM can be used as phenomenological or mechanistic models. The former way allows fitting real data and getting theirparameters. In the latter one, we should do efforts for determining the parameters through the acceptable estimations, measurements, and/or simulation experiments. Experimental methodologies for determination of the parameters have been developed from the fraction cells surviving the proton irradiation curves in tumor and OAR, and precise RBE models are used for calculating the variable of effective dose. As the executions of these methodologies have a high costs, so we have developed computer tools enable to perform simulation experiments as complement to limitations of the real ones. Results: The requirements for the use of the SM in the PT, such as validation and improvement of the elaborated and existent methodologies for determining the SM parameters and effective dose respectively, were determined. Conclusion: The SM realistically simulates the main processes in the PT, and for this reason these can be implemented in this therapy, which are simples, computable and they have other advantages over some current models. It has been determined some negative aspects for some currently used probabilistic models in the RT, like the LKB NTCP and others derived from logistic functions; which can be improved with the proposed methods in this study.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

PROBABILISTIC MODEL OF BEAM–PLASMA INTERACTION IN RANDOMLY INHOMOGENEOUS PLASMA

We propose a new model that describes beam–plasma interaction in the presence of random density fluctuations with a known probability distribution. We use the property that, for the given frequency, the probability distribution of the density fluctuations uniquely determines the probability distribution of the phase velocity of waves. We present the system as discrete and consisting of small, equal spatial intervals with a linear density profile. This approach allows one to estimate variations in wave energy density and particle velocity, depending on the density gradient on any small spatial interval. Because the characteristic time for the evolution of the electron distribution function and the wave energy is much longer than the time required for a single wave–particle resonant interaction over a small interval, we determine the description for the relaxation process in terms of averaged quantities. We derive a system of equations, similar to the quasi-linear approximation, with the conventional velocity diffusion coefficient D and the wave growth rate γ replaced by the average in phase space, by making use of the probability distribution for phase velocities and by assuming that the interaction in each interval is independent of previous interactions. Functions D and γ are completely determined by the distribution function for the amplitudes of the fluctuations. For the Gaussian distribution of the density fluctuations, we show that the relaxation process is determined by the ratio of beam velocity to plasma thermal velocity, the dispersion of the fluctuations, and the width of the beam in the velocity space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Sizing ramping reserve using probabilistic solar forecasts: A data-driven method

Ramping products have been introduced or proposed in several U.S. power markets to mitigate the impact of load and renewable uncertainties on market efficiency and reliability. Current methods often rely on historical data to estimate the requirements of ramping products and fail to take into account the effects of the latest weather conditions and their uncertainties, which could lead to overly conservative or insufficient requirements. This study proposes a k-nearest-neighbor-based method to give weather-informed estimates of ramping needs based on short-term probabilistic solar irradiance forecasts. Forecasts from multiple sites are employed in conjunction with principal component analysis to derive numerical classifiers to characterize system-level weather conditions. In addition, we develop a data-driven method to optimize the model parameters in a rolling-forward manner. By using real-world data from the California Independent System Operator, we design two metrics to evaluate method performance: 1) frequency of shortage and 2) oversupply of ramping product. Our proposed method presents advantages in comparison with the baseline and a set of benchmark methods: without compromising system reliability, it reduces system ramping requirements by up to 25%, therefore improving both system reliability and economics.

14 SOLAR ENERGY↗

DOE OSTI2015

Improved Sampling Algorithms in the Risk-Informed Safety Margin Characterization Toolkit

The RISMC approach is developing advanced set of methodologies and algorithms in order to perform Probabilistic Risk Analyses (PRAs). In contrast to classical PRA methods, which are based on Event-Tree and Fault-Tree methods, the RISMC approach largely employs system simulator codes applied to stochastic analysis tools. The basic idea is to randomly perturb (by employing sampling algorithms) timing and sequencing of events and internal parameters of the system codes (i.e., uncertain parameters) in order to estimate stochastic parameters such as core damage probability. This approach applied to complex systems such as nuclear power plants requires to perform a series of computationally expensive simulation runs given a large set of uncertain parameters. These types of analysis are affected by two issues. Firstly, the space of the possible solutions (a.k.a., the issue space or the response surface) can be sampled only very sparsely, and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Secondly, large amounts of data are generated and tools to generate knowledge from such data sets are not yet available. This report focuses on the first issue and in particular employs novel methods that optimize the information generated by the sampling process by sampling unexplored and risk-significant regions of the issue space: adaptive (smart) sampling algorithms. They infer system response from surrogate models constructed from existing samples and predict the most relevant location of the next sample. It is therefore possible to understand features of the issue space with a small number of carefully selected samples. In this report, we will present how it is possible to perform adaptive sampling using the RISMC toolkit and highlight the advantages compared to more classical sampling approaches such Monte-Carlo. We will employ RAVEN to perform such statistical analyses using both analytical cases but also another RISMC code: RELAP-7.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Efficient screening of rare large pit anomalies on polished surfaces using a minimalist sampling scheme

Lawrence Livermore National Laboratory (LLNL) has made significant strides in generating clean energy through its inertial confinement fusion (ICF) experiments. These experiments rely on high-density carbon (HDC) coated shells to encapsulate the fusion fuel. The success of these experiments is heavily dependent on the surface quality of these shells, as even minor imperfections, such as deep pits, can negatively impact fusion yield. Ensuring the required smoothness involves an extensive surface-finishing process that spans approximately 20 stages, making it both time-intensive and resource-demanding. A critical challenge in this process is the need for high-resolution scans to detect rare deep pits, which can be costly and impractical if performed on every shell. This highlights the necessity of developing more efficient scanning methods to optimize time and cost without compromising accuracy. To address these challenges, we introduce a novel approach that employs the multivariate Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to provide a probabilistic upper bound on the error in estimating pit distribution characteristics via a Kernel Density Estimator (KDE). This error bound enables efficient and reliable estimation of pit distribution characteristics at a specified statistical confidence level using a minimal number of surface scans. The integrated DKW-KDE approach was validated through surface-finishing experiments across two batches of HDC-coated shells, demonstrating consistent and robust performance across multiple stages of the surface-finishing experiments. The validation studies suggest that the integrated DKW-KDE approach achieves comparable accuracy in estimating the risk of deleterious large pits with six scans, thus conserving time and resources. Further evaluations show that performance remains consistent across batches and over multiple polishing stages. In conclusion, based on these findings, one can leverage the minimal-scan insights to strategically improve the bottleneck inspection process, thus enhancing the productivity and quality of shell polishing and similar challenging manufacturing processes.

Inertial confinement fusion↗

DOE OSTI2021

Extending quantum probabilistic error cancellation by noise scaling

Here, we propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device’s noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

In this study, the computational burden of a large-eddy simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, will greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, it is shown how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. Lastly, it is also demonstrated how the improved statistical model adds critical insight to the performance of the model.

42 ENGINEERING↗

NASA NTRS1987

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system structural components

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

Cruse, T. A.↗

NASA NTRS1988

Probabilistic Structural Analysis Methods for select space propulsion system structural components (PSAM)

Cruse, T. A.↗

NASA NTRS2002

Development of Advanced Life Cycle Costing Methods for Technology Benefit/Cost/Risk Assessment

The overall objective of this three-year grant is to provide NASA Langley's System Analysis Branch with improved affordability tools and methods based on probabilistic cost assessment techniques. In order to accomplish this objective, the Aerospace Systems Design Laboratory (ASDL) needs to pursue more detailed affordability, technology impact, and risk prediction methods and to demonstrate them on variety of advanced commercial transports. The affordability assessment, which is a cornerstone of ASDL methods, relies on the Aircraft Life Cycle Cost Analysis (ALCCA) program originally developed by NASA Ames Research Center and enhanced by ASDL. This grant proposed to improve ALCCA in support of the project objective by updating the research, design, test, and evaluation cost module, as well as the engine development cost module. Investigations into enhancements to ALCCA include improved engine development cost, process based costing, supportability cost, and system reliability with airline loss of revenue for system downtime. A probabilistic, stand-alone version of ALCCA/FLOPS will also be developed under this grant in order to capture the uncertainty involved in technology assessments. FLOPS (FLight Optimization System program) is an aircraft synthesis and sizing code developed by NASA Langley Research Center. This probabilistic version of the coupled program will be used within a Technology Impact Forecasting (TIF) method to determine what types of technologies would have to be infused in a system in order to meet customer requirements. A probabilistic analysis of the CER's (cost estimating relationships) within ALCCA will also be carried out under this contract in order to gain some insight as to the most influential costs and the impact that code fidelity could have on future RDS (Robust Design Simulation) studies.

Yackovetsky, Robert↗

DOE OSTI2014

Comparison of a Traditional Probabilistic Risk Assessment Approach with Advanced Safety Analysis

As part of the Light Water Sustainability Program (LWRS) [1], the purpose of the Risk Informed Safety Margin Characterization (RISMC) [2] Pathway research and development (R&D) is to support plant decisions for risk-informed margin management with the aim to improve economics, reliability, and sustain safety of current NPPs. In this paper, we describe the RISMC analysis process illustrating how mechanistic and probabilistic approaches are combined in order to estimate a safety margin. We use the scenario of a “station blackout” (SBO) wherein offsite power and onsite power is lost, thereby causing a challenge to plant safety systems. We describe the RISMC approach, illustrate the station blackout modeling, and contrast this with traditional risk analysis modeling for this type of accident scenario. We also describe our approach we are using to represent advanced flooding analysis.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

A Statistical Testing Approach for Quantifying Software Reliability; Application to an Example System

The U.S. Nuclear Regulatory Commission (NRC) encourages the use of probabilistic risk assessment (PRA) technology in all regulatory matters, to the extent supported by the state-of-the-art in PRA methods and data. Although much has been accomplished in the area of risk-informed regulation, risk assessment for digital systems has not been fully developed. The NRC established a plan for research on digital systems to identify and develop methods, analytical tools, and regulatory guidance for (1) including models of digital systems in the PRA's of nuclear power plants (NPPs), and, (2) incorporating digital systems in the NRC's risk-informed licensing and oversight activities. Under NRC's sponsorship, Brookhaven National Laboratory (BNL) explored approaches for addressing the failures of digital instrumentation and control (I and C) systems in the current NPP PRA framework. Specific areas investigated included PRA modeling digital hardware , development of a philosophical basis for defining software failure , and identification of desirable attributes of quantitative software reliability methods . Based on the earlier research, statistical testing is considered a promising method for quantifying software reliability. It is widely recognized that software failures are due to the triggering of pre-existing defects by the software's operational environment. Software defects can arise from errors made in user requirements or coding errors introduced during the developmental process. The software's operational environment includes factors such as the time history of digital system inputs, communication interfaces, the internal state of the digital system, and external conditions. Thus, software reliability is a function of both the number of pre-existing defects and the presence of a triggering condition caused by the manner in which the software is used. In this paper, we describe a statistical software-testing approach for quantifying software reliability and applied it to the loop-operating control system (LOCS) of an experimental loop of the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). The work involved collaboration between BNL and INL. The objectives of the study include: (1) Development of a statistical testing approach for estimating software failure probability on demand, the results of which are suitable for including in a probabilistic risk assessment (PRA); and, (2) Application of the approach to the LOCS to estimate its failure probability, and obtain insights into the feasibility, practicality, and usefulness of the estimation in models of digital systems for inclusion in nuclear power plants' PRAs. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗