Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation

Several generalizations of the two-parameter Weibull model have been proposed to model data sets that exhibit complex non-monotone shapes of hazard rate function. The present paper focuses on one such generalization referred to as the Weibull extension model in the literature. Complete Bayesian analysis of the model has been provided using Markov chain Monte Carlo simulation. Finally, a thorough study has been conducted for checking the adequacy of the model for a given data set using some of the graphical and numerical methods based on predictive simulation ideas. A real data set is considered for illustration.     

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.     

Numerical simulation of point-to-plane corona discharge using a Monte Carlo method

Monte Carlo simulation techniques are used to study the dynamical properties of charged particles in point-to-plane corona discharge. The numerical model includes the release of electron-ion pairs by photoionization and secondary electron emission from cathode as well as the first Townsend ionization. The simulation results of negative corona discharge in nitrogen show that electron avalanche takes place in the region of high electric field near pin electrode and the photoionization is the essential mechanism to sustain the discharge as well as electron impact ionization.     

A spectral representation based model for Monte Carlo simulation

A new model is proposed for generating samples of real-valued stationary Gaussian processes. The model is based on the spectral representation theorem stating that a weakly stationary process can be viewed as a superposition of harmonics with random properties. The classical use of this theorem for Monte Carlo simulation is based on models consisting of a superposition of harmonics with fixed frequencies but random amplitude and phase. The resulting samples have the same period depending on the discretization of the frequency band. In contrast, the proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods depending on the particular sample values of the harmonic frequencies.

A band limited Gaussian white noise process is used to illustrate the proposed Monte Carlo simulation algorithm and demonstrate that the estimates of the covariance function based on the samples of the proposed model are not periodic.     

Biased Monte Carlo unavailability analysis for systems with time-dependent failure rates

In this paper we consider systems made of components with time-dependent failure rates. A proper analysis of the time-dependent failure behaviour is very important for considerations of life-extension of safety critical systems such as nuclear power plants. This problem is tackled by Monte Carlo simulation which does not suffer from the additional complexity introduced by the model parameters' time inhomogeneity.The high reliability of the systems typically encountered in practice entails resorting to biasing techniques for favouring the events of interest. In this work, we investigate the possibility of biasing the system failures to be distributed in time according to exponential laws. The drawbacks encountered in such procedure have driven us towards the adoption of biasing schemes relying on uniform distributions which distribute failures over the system life more evenly.     

First-order differential sensitivity analysis of a nuclear safety system by Monte Carlo simulation

In this paper we employ a Monte Carlo method to compute the first-order, differential sensitivity indexes of the basic events characterizing the reliability behavior of the containment spray injection system of a nuclear power plant. An exemplification is provided as to how the obtained sensitivity indexes can be used to drive improvements in the system design and operation.     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.     

Comparison of Weibull small samples using Monte Carlo simulations

The evaluation of the functional reliability of different designs is a common task and times to failure can be compared using the likelihood ratio test. In the microelectronics industry, as in many others, the high cost of testing places severe restrictions on the sample size. Moreover, the products in these tests are often new and do not have previous reliability histories. These factors make the selection of the Type I and Type II errors in comparison tests very difficult. This paper presents the Monte Carlo simulation results of Type II errors for the likelihood ratio test of comparison as a function of the Type I error and the (small) sample size. Our conclusions are summarized as follows: (1) the common microelectronics industry standard sample size of 32 is often insufficient to reach satisfactory conclusions; (2) small sample tests should only be used for prescreening for significant differences; and (3) when only small samples are available, the Type I and the Type II errors must be selected carefully to prevent misleading conclusions. Copyright © 2006 John Wiley & Sons, Ltd.     

Prediction of micro-channel flows using direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is a particle-based numerical modeling technique. It is recently used for simulating gaseous flow in micro-electro-mechanical-systems (MEMS) where micron-scale features become important. In this paper, numerical simulations of fluid flow in micro-channels are carried out using the DSMC method. The details in determining the parameters critical for DSMC applications in micro-channels are provided. Streamwise velocity distributions in the slip-flow regime are compared with the analytical solution based on the Navier–Stokes equations with slip velocity boundary condition. Satisfactory agreements have been achieved. Effects of the entrance and exit regions on simulation results are discussed. Simulations are then extended to transition flow regime (Kn>0.1) and compared with the analytical solution. It is shown that the results are distinguished with the analytical solutions, which fail to predict the flow due to the break down of continuum assumption. It is indicated that the gradient of the pressure along the channel direction dominates the motion of the fluid flow.     

Node placement for triangular mesh generation by Monte Carlo simulation

A new approach of node placement for unstructured mesh generation is proposed. It is based on the Monte Carlo method to position nodes for triangular or tetrahedral meshes. Surface or volume geometries to be meshed are treated as atomic systems, and mesh nodes are considered as interacting particles. By minimizing system potential energy with Monte Carlo simulation, particles are placed into a near‐optimal configuration. Well‐shaped triangles or tetrahedra can then be created after connecting the nodes by constrained Delaunay triangulation or tetrahedrization. The algorithm is simple, easy to implement, and works in an almost identical way for 2D and 3D meshing. Copyright © 2005 John Wiley & Sons, Ltd.     

Production rate of synchronous transfer lines using Monte Carlo simulation

In this paper, we consider unpaced synchronous transfer lines producing a single product. The transfer line stations are arranged in a series con?guration, have no buffers, and are subject to operation-dependent failures. Throughput is an important performance measure for transfer lines, and we have adopted that measure. Analytical methods for determining capacity of such transfer lines are available only for the simplest systems, but we show Monte Carlo simulation to be a fast, flexible, easy, and accurate method of estimating throughput in lines of any length and having a wide range of operating characteristics.     

光子在闪烁晶体中传输的蒙特卡罗模拟

为了找到构筑闪烁晶体探测器的优化方法，使用蒙特卡罗方法对闪烁晶体BGO（Bi4Ge3O12，锗酸铋）的光收集效率进行了模拟研究。模拟结果表明：入射面为粗糙面，其余为抛光面，同时外层包装上高反射率的材料，可得到最大的光输出（约59．1％的光子被收集）；耦合剂的折射率的得到高的光输出也起着非常重要的作用。     

磁性多层膜系统自旋重取向行为的Monte Carlo模拟

依据Heisenberg模型,利用Monte　Carlo方法模拟了磁性多层膜系统的自旋重取向行为,研究了各向异性、偶极相互作用以及外磁场对系统自旋取向的影响。通过模拟计算,获得了系统组态、磁分量等随偶极相互作用、外加磁场和温度的变化规律,重点研究了磁性多层膜系统在外磁场作用下的磁滞现象。     

Genetic algorithms and Monte Carlo simulation for optimal plant design

We present an approach to the optimal plant design (choice of system layout and components) under conflicting safety and economic constraints, based upon the coupling of a Monte Carlo evaluation of plant operation with a Genetic Algorithms-maximization procedure. The Monte Carlo simulation model provides a flexible tool, which enables one to describe relevant aspects of plant design and operation, such as standby modes and deteriorating repairs, not easily captured by analytical models. The effects of deteriorating repairs are described by means of a modified Brown–Proschan model of imperfect repair which accounts for the possibility of an increased proneness to failure of a component after a repair. The transitions of a component from standby to active, and vice versa, are simulated using a multiplicative correlation model. The genetic algorithms procedure is demanded to optimize a profit function which accounts for the plant safety and economic performance and which is evaluated, for each possible design, by the above Monte Carlo simulation.In order to avoid an overwhelming use of computer time, for each potential solution proposed by the genetic algorithm, we perform only few hundreds Monte Carlo histories and, then, exploit the fact that during the genetic algorithm population evolution, the fit chromosomes appear repeatedly many times, so that the results for the solutions of interest (i.e. the best ones) attain statistical significance.     

Monte Carlo simulation of nucleation and growth of thin films

We study thin film growth using a lattice-gas, solid-on-solid model employing the Monte Carlo technique. The model is applied to chemical vapour deposition (CVD) by including the rate of arrival of the precursor molecules and their dissociation. We include several types of migration energies including the edge migration energy which allows the diffusive movement of the monomer along the interface of the growing film, as well as a migration energy which allows for motion transverse to the interface. Several well-known features of thin film growth are mimicked by this model, including some features of thin copper films growth by CVD. Other features reproduced are—compact clusters, fractal-like clusters, Frank-van der Merwe layer-by-layer growth and Volmer-Weber island growth. This method is applicable to film growth both by CVD and by physical vapour deposition (PVD).     

The fatigue limit: An analytical solution to a Monte Carlo problem

A new extreme value distribution based on log-normally distributed defects is presented. From this, an analytical solution to the random defect Monte Carlo problem in form of a distribution function characterizing the fatigue limit of an arbitrary component is derived. Surface defects, defined as internal defects intersecting a free surface, are incorporated into the model through an original analytical approach. The presented model is physically based and simple to implement and apply.Furthermore, the model was applied to a series of fatigue limit experiments found in the literature. The fatigue limit predictions were in good agreement with experimental results.     

A Monte Carlo simulation model for stationary non-Gaussian processes

A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second order correlation functions than translation processes. The paper also develops an algorithm for generating samples of any non-Gaussian process in the class of mixtures of translation processes. The algorithm is based on the sampling representation theorem for stochastic processes and properties of the conditional distributions. Examples are presented to illustrate the proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes.     

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.     

A study using Monte Carlo Simulation for failure probability calculation in Reliability-Based Optimization

In this study, a Reliability-Based Optimization (RBO) methodology that uses Monte Carlo Simulation techniques, is presented. Typically, the First Order Reliability Method (FORM) is used in RBO for failure probability calculation and this is accurate enough for most practical cases. However, for highly nonlinear problems it can provide extremely inaccurate results and may lead to unreliable designs. Monte Carlo Simulation (MCS) is usually more accurate than FORM but very computationally intensive. In the RBO methodology presented in this paper, limit state approximations are used in conjunction with MCS techniques in an approximate MCS-based RBO that facilitates the efficient calculation of the probabilities of failure. A FORM-based RBO is first performed to obtain the initial limit state approximations. A Symmetric Rank-1 (SR1) variable metric algorithm is used to construct and update the quadratic limit state approximations. The approximate MCS-based RBO uses a conditional-expectation-based MCS, that was chosen over indicator-based MCS because of the smoothness of the probability of failure estimates and the availability of analytic sensitivities. The RBO methodology was implemented for an analytic test problem and a higher-dimensional, control-augmented-structure test problem. The results indicate that the SR1 algorithm provides accurate limit state approximations (and therefore accurate estimates of the probabilities of failure) for these test problems. It was also observed that the RBO methodology required two orders of magnitude fewer analysis calls than an approach that used exact limit state evaluations for both test problems.     

Monte Carlo simulation of grating-based neutron phase contrast imaging at CPHS

Since the launching of the Compact Pulsed Hadron Source (CPHS) project of Tsinghua University in 2009, works have begun on the design and engineering of an imaging/radiography instrument for the neutron source provided by CPHS. The instrument will perform basic tasks such as transmission imaging and computerized tomography. Additionally, we include in the design the utilization of coded-aperture and grating-based phase contrast methodology, as well as the options of prompt gamma-ray analysis and neutron-energy selective imaging. Previously, we had implemented the hardware and data-analysis software for grating-based X-ray phase contrast imaging. Here, we investigate Geant4-based Monte Carlo simulations of neutron refraction phenomena and then model the grating-based neutron phase contrast imaging system according to the classic-optics-based method. The simulated experimental results of the retrieving phase shift gradient information by five-step phase-stepping approach indicate the feasibility of grating-based neutron phase contrast imaging as an option for the cold neutron imaging instrument at the CPHS.