Bayesian Belief Network Model Quantification Using Distribution-Based Node Probability and Experienced Data Updates for Software Reliability Assessment

Since digital instrumentation and control systems are expected to play an essential role in safety systems in nuclear power plants (NPPs), the need to incorporate software failures into NPP probabilistic risk assessment has arisen. Based on a Bayesian belief network (BBN) model developed to estimate the number of software faults considering the software development lifecycle, we performed a pilot study of software reliability quantification using the BBN model by aggregating different experts' opinions. In this paper, we suggest the distribution-based node probability table (D-NPT) development method which can efficiently represent diverse expert elicitation in the form of statistical distributions and provides mathematical quantification scheme. Besides, the handbook data on U.S. software development and V&V and testing results for two nuclear safety software were used for a Bayesian update of the D-NPTs in order to reduce the BBN parameter uncertainty due to experts' different background or levels of experience. To analyze the effect of diverse expert opinions on the BBN parameter uncertainties, the sensitivity studies were conducted by eliminating the significantly different NPT estimates among expert opinions. The proposed approach demonstrates a framework that can effectively and systematically integrate different kinds of available source information to quantify BBN NPTs for NPP software reliability assessment

Results and insights of internal fire and internal flood analyses of the Surry Unit 1 Nuclear Power Plant during mid-loop operations

During 1989, the Nuclear Regulatory Commission (NRC) initiated an extensive program to carefully examine the potential risks during low power and shutdown operations. Two plants, Surry (pressurized water reactor) and Grand Gulf (boiling water reactor), were selected as the plants to be studied by Brookhaven National Laboratory (BNL) and Sandia National Laboratories (SNL). The objectives of the program are to assess the risks of severe accidents initiated during plant operational states (POSs) other than full power operation and to compare the estimated core damage frequencies (CDFs), important accident sequences and other qualitative and quantitative results with those accidents initiated during full power operation as assessed in NUREG-1150. The scope of the program includes that of a Level 3 PRA for internal events and a Level 1 PRA for seismically induced and internal fire and flood induced core damage sequences. This paper summarizes the results and highlights of the internal fire and flood analysis documented in Volumes 3 and 4 of NUREG/CR-6144 performed for the Surry plant during mid-loop operation

Perspectives on Low Power and Shutdown Risk

This paper presents results from a program sponsored by the US Nuclear Regulatory Commission to examine the risks from low power and shutdown operations. Significant progress has been made by the industry in reducing such risks; however, important operational events continue to occur. Current perceptions of low power and shutdown risks are discussed in the paper along with an assessment of the current methods for understanding important events and quantifying their associated risk

APPLICATION OF A BAYESIAN BELIEF NETWORK MODEL TO RELIABILITY ASSESSMENT OF NUCLEAR SAFETY-RELATED SOFTWARE

As the instrumentation and control (I&C) systems in nuclear power plants (NPPs) have been replaced with digital-based systems, the need to incorporate software failures into NPP probabilistic risk assessments has arisen. In order to assess the probability of software failure on demand, a Bayesian belief network (BBN) model was developed which estimates the number of defects and the resulting probability of software failure on demand in nuclear safety-related software. To assess the feasibility of the BBN framework, the BBN model was applied to the prototype Integrated Digital Protection System-Reactor Protection System (IDiPS-RPS) to estimate the number of remaining faults and the software failure probability of a target software. The developmental- and V&V-activities carried out during the IDiPS-RPS development process were evaluated based on the well-defined checklist derived by the V&V team and were estimated based on expert elicitation. In addition, the attribute evaluations and the number of FPs of the target software is provided as the inputs for the BBN model. The application results showed the feasibility of using BBNs for quantifying software failure probabilities and several insights were gained from the applications of the BBN model. The proposed BBN framework can be applied to estimate the software failure probability for other safety-related NPP software and provide an insight on modeling the software development process that involves iterations between different development phases

DEVELOPMENT OF A BAYESIAN BELIEF NETWORK MODEL FOR QUANTIFYING SOFTWARE FAILURE PROBABILITY OF A PROTECTION SYSTEM

A Bayesian Belief Network model for quantifying the probability of failure on demand of a protection system due to software failures is presented. It is based on the assumption that the quality in carrying out the software development activities determines the reliability of the software. The oval BBN model is a generic one that can be applied to any safety critical software. It uses the quality evaluation and debugging data of a specific software program to estimate the number of faults injected and the number of faults detected and removed in each phase of the development process. The estimated number of faults is then converted into a software failure probability using a Fault Size Distribution

Development of a Bayesian Belief Network Model for the Software Reliability Assessment of Nuclear Digital I&C Safety Systems

Since the digital instrumentation and control systems are expected to play an important role for the safety systems in nuclear power plants (NPPs), the need has emerged to not only establish a basis for incorporating software behavior into digital I&C system reliability models, but also to quantify the failure probability of the software used in NPP digital protection systems. In this study, a Bayesian belief network (BBN) model is developed to quantitatively assess software reliability by estimating the number of faults in a software program considering its software development life cycle (SDLC). The model structure and parameters are established based on the information applicable to NPP safety-related systems and the evidence used to construct and quantify the BBN model was collected from three stages of expert elicitation. The software failure probability is estimated from the number of residual defects in a software program at the end of SDLC phase. As case study, the BBN model was applied to quantify the software reliability of a typical digital protection software having the size of 50 function points and having the Medium development and validation and verification (V&V) qualities. The developed model can be applied to estimate the failure probability for both developing and deployed safety-related NPP software, and such results can be used to evaluate the quality of the digital I&C systems in addition to estimating potential reactor risk due to software failure

Development of a Bayesian belief network model for software reliability quantification of digital protection systems in nuclear power plants

As the instrumentation and control (I&C) systems in nuclear power plants (NPPs) have been replaced with digital-based systems, the need has emerged to not only establish a basis for incorporating software behavior into digital I&C system reliability models, but also to quantify the software reliability used in NPP digital protection systems. Therefore, a Bayesian belief network (BBN) model which estimates the number of faults in a software considering its software development life cycle (SDLC) is developed in this study. The model structure and parameters are established based on the information applicable to safety-related systems and expert elicitation. The evidence used in the model was collected from three stages of expert elicitation. To assess the feasibility of using BBN in NPP digital protection software reliability quantification, the BBN model was applied to the Integrated Digital Protection System-Reactor Protection System and estimated the number of defects at each SDLC phase and further assessed the software failure probability. The developed BBN model can be employed to estimate the reliability of deployed safety-related NPP software and such results can be used to evaluate the quality of the digital I&C systems in addition to estimating the potential reactor risk due to software failure

Total plaque score helps to determine follow-up strategy for carotid artery stenosis progression in head and neck cancer patients after radiation therapy.

BackgroundTo identify predictors of carotid artery stenosis (CAS) progression in head and neck cancer (HNC) patients after radiation therapy (RT).MethodsWe included 217 stroke-naïve HNC patients with mild carotid artery stenosis after RT in our hospital. These patients underwent annual carotid duplex ultrasound (CDU) studies to monitor CAS progression. CAS progression was defined as the presence of ≥50% stenosis of the internal/common carotid artery on follow-up CDU. We recorded total plaque score (TPS) and determined the cut-off TPS to predict CAS progression. We categorized patients into high (HP) and low plaque (LP) score groups based on their TPS at enrolment. We analyzed the cumulative events of CAS progression in the two groups.ResultsThe TPS of the CDU study at enrolment was a significant predictor for CAS progression (adjusted odds ratio [aOR] = 1.69, p = 0.002). The cut-off TPS was 7 (area under the curve: 0.800), and a TPS ≥ 7 strongly predicted upcoming CAS progression (aOR = 41.106, p = 0.002). The HP group had a higher risk of CAS progression during follow-up (adjusted hazard ratio = 6.15; 95% confident interval: 2.29-16.53) in multivariable Cox analysis, and also a higher trend of upcoming ischemic stroke (HP vs. LP: 8.3% vs. 2.2%, p = 0.09).ConclusionsHNC patients with a TPS ≥ 7 in any CDU study after RT are susceptible to CAS progression and should receive close monitoring within the following 2 years