Multi-State Reliability Analysis of Nuclear Power Plant Systems

The probabilistic safety assessment of engineering systems involving high-consequence low-probability events is stochastic in nature due to uncertainties inherent in time to an event. The event could be a failure, repair, maintenance or degradation associated with system ageing. Accurate reliability prediction accounting for these uncertainties is a precursor to considerably good risk assessment model. Stochastic Markov reliability models have been constructed to quantify basic events in a static fault tree analysis as part of the safety assessment process. The models assume that a system transits through various states and that the time spent in a state is statistically random. The system failure probability estimates of these models assuming constant transition rate are extensively utilized in the industry to obtain failure frequency of catastrophic events. An example is core damage frequency in a nuclear power plant where the initiating event is loss of cooling system. However, the assumption of constant state transition rates for analysis of safety critical systems is debatable due to the fact that these rates do not properly account for variability in the time to an event. An ill-consequence of such an assumption is conservative reliability prediction leading to addition of unnecessary redundancies in modified versions of prototype designs, excess spare inventory and an expensive maintenance policy with shorter maintenance intervals. The reason for this discrepancy is that a constant transition rate is always associated with an exponential distribution for the time spent in a state. The subject matter of this thesis is to develop sophisticated mathematical models to improve predictive capabilities that accurately represent reliability of an engineering system. The generalization of the Markov process called the semi-Markov process is a well known stochastic process, yet it is not well explored in the reliability analysis of nuclear power plant systems. The continuous-time, discrete-state semi-Markov process model is a stochastic process model that describes the state transitions through a system of integral equations which can be solved using the trapezoidal rule. The primary objective is to determine the probability of being in each state. This process model ensures that time spent in the states can be represented by a suitable non-exponential distribution thus capturing the variability in the time to event. When exponential distribution is assumed for all the state transitions, the model reduces to the standard Markov model. This thesis illustrates the proposed concepts using basic examples and then develops advanced case studies for nuclear cooling systems, piping systems, digital instrumentation and control (I&C) systems, fire modelling and system maintenance. The first case study on nuclear component cooling water system (NCCW) shows that the proposed technique can be used to solve a fault tree involving redundant repairable components to yield initiating event probability quantifying the loss of cooling system. The time-to-failure of the pump train is assumed to be a Weibull distribution and the resulting system failure probability is validated using a Monte Carlo simulation of the corresponding reliability block diagram. Nuclear piping systems develop flaws, leaks and ruptures due to various underlying damage mechanisms. This thesis presents a general model for evaluating rupture frequencies of such repairable piping systems. The proposed model is able to incorporate the effect of aging related degradation of piping systems. Time dependent rupture frequencies are computed and the influence of inspection intervals on the piping rupture probability is investigated. There is an increasing interest worldwide in the installation of digital instrumentation and control systems in nuclear power plants. The main feedwater valve (MFV) controller system is used for regulating the water level in a steam generator. An existing Markov model in the literature is extended to a semi-Markov model to accurately predict the controller system reliability. The proposed model considers variability in the time to output from the computer to the controller with intrinsic software and mechanical failures. State-of-the-art time-to-flashover fire models used in the nuclear industry are either based on conservative analytical equations or computationally intensive simulation models. The proposed semi-Markov based case study describes an innovative fire growth model that allows prediction of fire development and containment including time to flashover. The model considers variability in time when transiting from one stage of the fire to the other. The proposed model is a reusable framework that can be of importance to product design engineers and fire safety regulators. Operational unavailability is at risk of being over-estimated because of assuming a constant degradation rate in a slowly ageing system. In the last case study, it is justified that variability in time to degradation has a remarkable effect on the choice of an effective maintenance policy. The proposed model is able to accurately predict the optimal maintenance interval assuming a non-exponential time to degradation. Further, the model reduces to a binary state Markov model equivalent to a classic probabilistic risk assessment model if the degradation and maintenance states are eliminated. In summary, variability in time to an event is not properly captured in existing Markov type reliability models though they are stochastic and account for uncertainties. The proposed semi-Markov process models are easy to implement, faster than intensive simulations and accurately model the reliability of engineering systems

Techniques for the realization of ultra- reliable spaceborne computer Final report

Bibliography and new techniques for use of error correction and redundancy to improve reliability of spaceborne computer

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

Managing the restoration of membranes in reverse osmosis desalination using a digital twin

This thesis studies degradation and restoration policies for a pressure vessel in a reverse osmosis (RO) desalination plant. In the study context, biofouling is the primary cause of the degradation of the RO membrane elements, amplified by seasonal algal blooms. This research developed a decision support system (DSS) for evaluating membrane restoration strategy. The engine of the DSS is a digital twin (DT), a virtual representation of wear (degradation) and restoration of membrane elements in a RO pressure vessel. The basis of the DT is a mathematical model that describes an RO pressure vessel as a novel multi-component system in which the hidden wear-states of individual elements (components) are quantified, and elements can be swapped or replaced. This contrasts with the contemporary presentation of a membrane system as a single system in the literature. The parameters of the model are estimated using statistical methods. The research approach is described in the context of a case study on the Carlsbad Desalination Plant in California. Results show a good fit between the observed and the modelled wear-states. Competing policies are compared based on risk, cost, downtime, and the number of stoppages. Projections indicate that a significant cost-saving can be achieved while not compromising the integrity of the plant. Alternative policies 11 and 12 showed better wear management than the current policy 10 of the maintenance company while reducing costs between $0.7 to$1.7 million for the next five years.The research in the thesis contributes toward maintenance modelling. New models of multivariate degradation and imperfect repair are presented. The research makes an important contribution to desalination and water treatment engineering, providing a unique membrane maintenance management approach currently absent from the literature. The thesis also contributes to the maintenance theory. It proposes a general approach for applying a decision support system (DSS) for maintenance requirements analysis, involving a digital twin (DT) for wear and repair projections when wear is stochastic, and repair effects are not immediately apparent. The essential elements of a DSS are discussed. This research encourages a dialogue between researchers of maintenance theory and modelling and practitioners of maintenance planning about decision support systems and digital twins that not only project the when but also evaluate the what in maintenance strategy. The presented concept of a DSS driven by a DT for maintenance requirement analysis has valuable practical implications, and the thesis, in discussing this concept, makes an essential contribution to the discussion about Industry 4.0, digital twins, and maintenance

Bootstrapping computation of availability for a repairable system with standby subject to imperfect switching

我們考慮一個具有不完美備元可修理系統，此系統包含四個主要和二個備用可修理機器。本文主要討論以五種拔靴法為基礎建構其可用度的信賴區間。我們假設主要和備用機器損壞的時間間隔服從指數分配，修護時間服從四種不同的分配：指數、伽瑪、均勻、混和分配，接著使用遞迴法和輔助變數技巧求得系統在穩態時的可用度，下一步則採用以拔靴法為基礎，利用標準拔靴法(standard bootstrap)、百分比拔靴法(percentile bootstrap)、誤差修正百分比拔靴法(bias-corrected percentile bootstrap)、加速並修正誤差百分比拔靴法(bias-corrected and accelerated percentile bootstrap) 以及樞 紐拔靴法(bootstrap pivotal) 等五種方法建構並計算出其信賴區間、覆蓋率和信賴長度以便探討它們的表現，最後，以一些實驗數據來說明結論。This paper deals with the availability behavior of a repairable system in which standby switched to primary is subject to breakdowns. The time-to-failure of the four primary and two standby units are assumed to be exponentially and generally distributed. In addtion, the repair time of service station follow four common distributions: exponential(EXP), Gamma(G), Uniform(U), Mixture(M). We use a recursive method, and the supplementary variable technique to develop the steadystate availability, Av. The estimator Aˆv is strongly consistent and asymptotically normal. The interval estimations of Av are constructed by five bootstrap approaches: standard bootstrap confidence interval(SB), the percentile bootstrap confidence interval(PB), the bias-corrected percentile bootstrap confidence interval(BCPB), the bias-corrected and accelerated confidence interval(BCa) and bootstrap pivot confidence interval(BP). Finally, some simulation computations are conducted in order to describe the performances of Aˆv on various interval estimation by calculating the coverage percentage and the average length of intervals.Contents 1 Introduction 1 2 Description of the system 3 3 Availability analysis of the system 5 4 Estimation of availability Av 12 5 Bootstrap estimation of Av 14 5.1 SB confidence interval . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2 PB confidence interval . . . . . . . . . . . . . . . . . . . . . . . . 15 5.3 BCPB bootstrap confidence interval . . . . . . . . . . . . . . . . 15 5.4 BCa confidence interval . . . . . . . . . . . . . . . . . . . . . . . . 16 5.5 BP confidence interval . . . . . . . . . . . . . . . . . . . . . . . . 16 6 Simulation study 18 7 Concluding remarks 21 References 2

Bootstrapping Computation of Availability for a Repairable System with Standby Subject to Imperfect Switching

This article deals with the availability behavior of a repairable system in which standby switched to primary is subject to breakdowns. The time-to-failure of the four primary and two standby units are assumed to be exponentially and generally distributed. In addtion, the repair time of service station follow four common distributions: exponential (EXP), Gamma (G), Uniform (U), and Mixture (M). We use a recursive method, and the supplementary variable technique to develop the steady-state availability, Av. The estimator [image omitted] is strongly consistent and asymptotically normal. The interval estimations of Av are constructed by five bootstrap approaches: standard bootstrap confidence interval (SB), the percentile bootstrap confidence interval (PB), the bias-corrected percentile bootstrap confidence interval (BCPB), the bias-corrected and accelerated confidence interval (BCa), and bootstrap pivot confidence interval (BP). Finally, some simulation computations are conducted in order to describe the performances of [image omitted] on various interval estimation by calculating the coverage percentage and the average length of intervals

Reliability Abstracts and Technical Reviews January - December 1970

Reliability Abstracts and Technical Reviews is an abstract and critical analysis service covering published and report literature on reliability. The service is designed to provide information on theory and practice of reliability as applied to aerospace and an objective appraisal of the quality, significance, and applicability of the literature abstracted

Risk Management for the Future

A large part of academic literature, business literature as well as practices in real life are resting on the assumption that uncertainty and risk does not exist. We all know that this is not true, yet, a whole variety of methods, tools and practices are not attuned to the fact that the future is uncertain and that risks are all around us. However, despite risk management entering the agenda some decades ago, it has introduced risks on its own as illustrated by the financial crisis. Here is a book that goes beyond risk management as it is today and tries to discuss what needs to be improved further. The book also offers some cases