Assessment of availability of a Fluid Catalytic Cracking Unit through simulation

This paper presents a systematic approach to estimate the availability of process plants. The study includes a live problem at a Fluid Catalytic Cracking Unit (FCCU) of a refinery requiring high levels of availability for cost-effective operation. The system is modelled as a fault tree which is often used in the analysis of chemical process industries. A numerical evaluation of the fault tree assesses the characertistic safety parameters such as reliability and availability of the system. However, for large and complex systems, such analysis will normally require enormous computational effort, involving the breakdown of the fault tree into minimal cut sets. An alternative approach is to simulate the system using the Monte Carlo method. This paper presents an availability analysis of the Reactor/Regenerator system of the Fluid Catalytic Cracking Unit using the Monte Carlo simulation. The results of the simulation are validated by a comparison with the actual system. The method promises to be a useful tool for assessing the availability of complex systems with alternative configurations.     

Diagnosis Modelling for Dependability Assessment of Fault‐Tolerant Systems Based on Stochastic Activity Networks

The growing demand for safety, reliability, availability and maintainability in modern technological systems has led these systems to become more and more complex. To improve their dependability, many features and subsystems are employed like the diagnosis system, control system, backup systems, and so on. These subsystems have all their own dynamic, reliability and performances and interact with each other in order to provide a dependable and fault‐tolerant system. This makes the dependability analysis and assessment very difficult. This paper proposes a method to completely model the diagnosis procedure in fault‐tolerant systems using stochastic activity networks. Combined with Monte Carlo simulation, this will allow the dependability assessment by including the diagnosis parameters and performances explicitly. Copyright © 2014 John Wiley & Sons, Ltd.     

Procedures of Monte Carlo transport simulation for applications in system engineering

Monte Carlo (MC) simulation is the most promising tool for performing realistic reliability and availability analysis of complex systems. Yet, the efficient use of MC simulation technique is not trivial in large scale applications.This paper considers the two commonly adopted approaches to MC simulation: the direct, component-based approach and the indirect, system-based approach. The mathematical details of the two approaches are worked out in detail, so as to show their probabilistic equivalence. The proper formulation for biasing the simulation is introduced, thus leading to the correct expressions for the statistical weights.Both approaches are applied, in an analog as well as in a biased scheme, to a simple system of the literature and comparisons are made with respect to the computing time and the goodness of the estimate, as measured by the variance of the results.     

Application of the state transition sampling technique to system reliability evaluation

Monte Carlo simulation is becoming an attractive alternative to analytical approaches for reliability evaluation in large electric power systems. Monte Carlo simulation is generally more flexible than an analytical technique when complex operating conditions and system considerations such as multi-derated states, chronology, reservoir operating rules, bus load uncertainty and weather effects need to be incorporated. Monte Carlo techniques are usually classified as being either a sequential or non-sequential method. The basic non-sequential Monte Carlo approach is known as the state sampling method in which the actual frequency of failure is estimated from the number of failures encountered during the simulation process. The actual frequency of failure can be more accurately obtained by using a sequential approach which models the component up and down cycles together with the system load. This paper presents and illustrates the application of the state transition sampling technique. This method can be used to estimate the actual frequency index without requiring an additional enumeration procedure or sampling the component up and down cycles and storing chronological information on the overall state of the system. In this approach the next system state is obtained by allowing a component to undergo transitions from its present state. The procedure focuses on transitions of the whole system rather than on component states or state durations. This technique is usually much faster than the traditional sequential simulation approach. The state transition sampling technique will be illustrated by application to generating capacity and composite generation and transmission system reliability assessment in a representative electric power system. © 1997 John Wiley & Sons, Ltd.     

Optimizing maintenance and repair policies via a combination of genetic algorithms and Monte Carlo simulation

In this paper we present an optimization approach based on the combination of a Genetic Algorithms maximization procedure with a Monte Carlo simulation. The approach is applied within the context of plant logistic management for what concerns the choice of maintenance and repair strategies. A stochastic model of plant operation is developed from the standpoint of its reliability/availability behavior, i.e. of the failure/repair/maintenance processes of its components. The model is evaluated by Monte Carlo simulation in terms of economic costs and revenues of operation. The flexibility of the Monte Carlo method allows us to include several practical aspects such as stand-by operation modes, deteriorating repairs, aging, sequences of periodic maintenances, number of repair teams available for different kinds of repair interventions (mechanical, electronic, hydraulic, etc.), components priority rankings. A genetic algorithm is then utilized to optimize the components maintenance periods and number of repair teams. The fitness function object of the optimization is a profit function which inherently accounts for the safety and economic performance of the plant and whose value is computed by the above Monte Carlo simulation model. For an efficient combination of Genetic Algorithms and Monte Carlo simulation, only few hundreds Monte Carlo histories are performed for each potential solution proposed by the genetic algorithm. Statistical significance of the results of the solutions of interest (i.e. the best ones) is then attained exploiting the fact that during the population evolution the fit chromosomes appear repeatedly many times. The proposed optimization approach is applied on two case studies of increasing complexity.     

Stochastic finite element-based reliability analysis of space frames

In the present paper the weighted integral method in conjunction with Monte Carlo simulation is used for the stochastic finite element-based reliability analysis of space frames. The limit state analysis required at each Monte Carlo simulation is performed using a non-holonomic step-by-step elasto-plastic analysis based on the plastic node method in conjunction with efficient solution techniques. This implementation results in cost effective solutions both in terms of computing time and storage requirements. The numerical results presented demonstrate that this approach provides a realistic treatment for the stochastic finite element-based reliability analysis of large scale three-dimensional building frames.     

Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment

Traditional fault tree (FT) analysis is widely used for reliability and safety assessment of complex and critical engineering systems. The behavior of components of complex systems and their interactions such as sequence- and functional-dependent failures, spares and dynamic redundancy management, and priority of failure events cannot be adequately captured by traditional FTs. Dynamic fault tree (DFT) extend traditional FT by defining additional gates called dynamic gates to model these complex interactions. Markov models are used in solving dynamic gates. However, state space becomes too large for calculation with Markov models when the number of gate inputs increases. In addition, Markov model is applicable for only exponential failure and repair distributions. Modeling test and maintenance information on spare components is also very difficult. To address these difficulties, Monte Carlo simulation-based approach is used in this work to solve dynamic gates. The approach is first applied to a problem available in the literature which is having non-repairable components. The obtained results are in good agreement with those in literature. The approach is later applied to a simplified scheme of electrical power supply system of nuclear power plant (NPP), which is a complex repairable system having tested and maintained spares. The results obtained using this approach are in good agreement with those obtained using analytical approach. In addition to point estimates of reliability measures, failure time, and repair time distributions are also obtained from simulation. Finally a case study on reactor regulation system (RRS) of NPP is carried out to demonstrate the application of simulation-based DFT approach to large-scale problems.     

First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

The first passage failure of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations in the case of external resonance is studied. First, a stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations using generalized harmonic functions is reviewed briefly. Then, a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established from the averaged Itô equations, respectively. The conditional reliability function, and the conditional probability density and conditional mean of the first passage time are obtained from solving these equations together with suitable initial condition and boundary conditions. The comparison between the analytical results and those from Monte Carlo simulation for an example shows that the proposed method works very well. It is also shown by using Monte Carlo simulation that the reliability of the system in the case of external resonance is much lower than that in the non-resonant case.     

Incorporating fuzzy weather-related outages in transmission system reliability assessment

Fuzzy models for weather-related outages of overhead lines and a combined probabilistic and fuzzy technique for transmission system reliability assessment are presented. The region-divided weather states are modelled using a probability approach. This approach and the fuzzy models of weather-related outages are combined and incorporated into a Monte Carlo simulation procedure of transmission system reliability assessment to evaluate membership functions and mean values of reliability indices. The reliability test system is used to demonstrate an application of the proposed models and method. The membership functions of reliability indices provide a wider insight into the fuzziness of weather effects, which cannot be modelled by traditional probability concepts.     

Capacity investment decision by Monte Carlo approach in a cooperation network

This paper proposes a Monte Carlo approach to make the capacity investment decision. The environment concerns the capacity expansion issue for independent plants operating in a collaborative network. The plants that compose the network can share capacity through a negotiation protocol in order to balance under and over utilisation due to the customer demand. The plants apply the capacity expansion process following a periodic review policy. The generic plant makes the decision using a Monte Carlo approach that takes into account the information of the plant and the information of the collaboration with the plants of the network. The Monte Carlo simulator provides the information to each plant to support the capacity investment decision. The proposed approach is compared with a case characterised by information sharing among the plants proposed in literature and a case without information sharing. A simulation environment based on the JAVA package has been developed in order to test the approach in several market conditions. Several customer demand scenarios have been tested. The simulation results highlight these main findings: the robustness of the proposed approach; the reduction of the capacity investment keeping the same level of total profit performance; and the higher utilisation of the cooperation with the other plants of the network.     

基于Bayes小子样二项分布单元可靠性评定的仿真方法

对于小子样二项分布单元可靠度下限评定，经典方法有很大局限性，文中介绍了Bayes方法。并在其基础上提出基于Bayes方法的Monte Carlo仿真方法，示例证明，该方法有很好的应用前途。     

A new reliability analysis method for repairable systems with multifunction modes based on goal‐oriented methodology

This paper proposes a new systematic reliability analysis method for repairable systems with multifunction modes based on the goal‐oriented (GO) method. First, we create a new function GO operator, a new logical GO operator, and a new auxiliary GO operator, deduce their GO operation formulas, and propose some new rules of the GO operation and an exact algorithm with shared signal of the GO method for such systems. Then, we formulate the analysis process of repairable systems with multifunction modes based on the new GO method. Finally, we apply this new GO methodology to reliability analysis of the control system for a heavy vehicle. To verify the feasibility, advantage, and reasonableness of the new GO methodology, we compare its analysis results with those of fault tree analysis and Monte Carlo simulation. We show that the proposed GO method has clear advantages in system reliability modeling and analysis. All in all, this study not only improves the theory of the GO method and widens its application but also provides a new approach for conducting reliability analysis of complex systems quickly and efficiently.     

Comparison of numerical methods for the assessment of production availability of a hybrid system

A finite volume (FV) scheme is proposed in order to compute different probabilistic measures for systems from dynamic reliability field. The FV scheme is tested on a small but realistic benchmark case stemmed from gas industry [Labeau PE, Dutuit Y. Fiabilité dynamique et disponibilité de production: un cas illustratif. Proceedings of λμ 14, Bourges, France, vol. 2. 2004. p. 431–6 [in French]]. The point is to compute the production availability and the annual frequency of loss of nominal production (among other quantities) for a system of gas production. The results of the FV method are compared to those obtained by Monte Carlo simulation, showing the accuracy of the method.     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Computational strategy for the crash design analysis using an uncertain computational mechanical model

The framework of this paper is the robust crash analysis of a motor vehicle. The crash analysis is carried out with an uncertain computational model for which uncertainties are taken into account with the parametric probabilistic approach and for which the stochastic solver is the Monte Carlo method. During the design process, different configurations of the motor vehicle are analyzed. Usual interpolation methods cannot be used to predict if the current configuration is similar or not to one of the previous configurations already analyzed and for which a complete stochastic computation has been carried out. In this paper, we propose a new indicator that allows to decide if the current configuration is similar to one of the previous analyzed configurations while the Monte Carlo simulation is not finished and therefore, to stop the Monte Carlo simulation before the end of computation.     

Algorithm for estimating reliability confidence bounds of multi-state systems

The paper suggests an effective approach for the estimation of reliability confidence bounds based on component reliability and uncertainty data for multi-state systems with binary-capacitated components. The approach presented is based on the implementation of the universal generating function technique. When compared with a pure Monte Carlo simulation approach, the universal generating function (UGF)-based approach is proven to be more effective due to a more precise reliability estimation and a considerably lower computational effort. Examples are given throughout the paper to illustrate the suggested approach.     

Holistic reliability analysis of weighted voting systems from a multi-state perspective

The computation of the reliability of weighted voting systems is an important problem in reliability theory due to its potential application in security, target identification, safety and monitoring areas. Voting systems are used in a wide variety of applications where an acceptance or rejection decision has to be made about a binary proposition presented to the system. For these systems, it is of interest to obtain the probability so that based on the vote of decision-making units, the system aggregates these votes into the right decision when presented with such a proposition. This paper presents a holistic work on weighted voting system reliability by presenting modeling, computation, estimation and optimization techniques. The modeling part takes advantage of the structure of weighted voting systems to present a model of its reliability as a multi-state system. Next, based on the multi-state view of the system, an exact computational approach based on multi-state minimal cut and path vectors is introduced. The paper then acknowledges the computational complexity of the problem and provides a Monte Carlo simulation approach that estimates system reliability accurately and in an efficient computational time. Finally, an optimization heuristic that generates quasi-optimal solutions is presented that is able to solve the problem of maximizing the reliability of a weighted voting system based on a specified number of decision-making units with known reliability characteristics.     

Adaptive surrogate model coupled with stochastic configuration network strategies for time-dependent reliability assessment

Time-dependent reliability assessment is crucial in enhancing product development economics and product performance sustainability throughout the lifecycle. It is still a challenge to accurately and efficiently evaluate the time-dependent reliability of engineering systems. This paper proposes a novel adaptive surrogate model method combining stochastic configuration network (SCN) and Kriging strategies to evaluate time-dependent reliability. SCN has accurate approximation ability and learning efficiency for strongly nonlinear systems that can overcome the conventional time-dependent reliability calculation, which is time-consuming and characterized by low accuracy. The proposed method first applies SCN to establish the response model of the performance function with respect to time and obtain the extreme value of the performance function. Then, Kriging is used to establish the extreme value model of the performance function with respect to the random variables based on the extreme value of performance function. The adaptive process considering the characteristics of random variables samples is adopted to update the extreme value model until the model meets the confidence target. Lastly, Monte Carlo simulation is employed for time-dependent reliability assessment based on the established extreme value model. Three example studies are used to demonstrate the effectiveness of the proposed approach for time-dependent reliability assessment.     

A new system formulation for the tolerance analysis of overconstrained mechanisms

The goal of tolerance analysis is to verify whether design tolerances enable a mechanism to be functional. The current method consists in computing a probability of failure using Monte Carlo simulation combined with an optimization scheme called at each iteration. This time consuming technique is not appropriate for complex overconstrained systems. This paper proposes a transformation of the current tolerance analysis problem formulation into a parallel system probability assessment problem using the Lagrange dual form of the optimization problem. The number of events being very large, a preliminary selective search algorithm is used to identify the most contributing events to the probability of failure value. The First Order Reliability Method (FORM) for systems is eventually applied to compute the probability of failure at low cost. The proposed method is tested on an overconstrained mechanism modeled in three dimensions. Results are consistent with those obtained with the Monte Carlo simulation and the computing time is significantly reduced.     

Effective boundary conditions for carriers in ultrathin SOI channels

We have studied electron backscattering from heavily doped source/drain extensions using both the solution of Boltzmann equation and Monte Carlo simulation, for a simple case of monochromatic incident "beam" of ballistic electrons. For the case of elastic scattering, numerical results for the total reflection coefficient R may be well described by a simple expression which has a clear physical sense within the Landauer formalism of mesoscopic transport. The reduction of R due to inelastic scattering was also analyzed using Monte Carlo simulation. We believe that our work paves a way toward simple and accurate modeling of nanoscale MOSFETs with thin electrode extensions.