An evaluation of the multi-state node networks reliability using the traditional binary-state networks reliability algorithm

A system where the components and system itself are allowed to have a number of performance levels is called the Multi-state system (MSS). A multi-state node network (MNN) is a generalization of the MSS without satisfying the flow conservation law. Evaluating the MNN reliability arises at the design and exploitation stage of many types of technical systems. Up to now, the known existing methods can only evaluate a special MNN reliability called the multi-state node acyclic network (MNAN) in which no cyclic is allowed. However, no method exists for evaluating the general MNN reliability. The main purpose of this article is to show first that each MNN reliability can be solved using any the traditional binary-state networks (TBSN) reliability algorithm with a special code for the state probability. A simple heuristic SDP algorithm based on minimal cuts (MC) for estimating the MNN reliability is presented as an example to show how the TBSN reliability algorithm is revised to solve the MNN reliability problem. To the author's knowledge, this study is the first to discuss the relationships between MNN and TBSN and also the first to present methods to solve the exact and approximated MNN reliability. One example is illustrated to show how the exact MNN reliability is obtained using the proposed algorithm.     

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.     

Element substitution algorithm for general two-terminal network reliability analyses

The computation of the reliability of two-terminal networks is a classical reliability problem. For these types of problems, one is interested, from a general perspective, in obtaining the probability that two specific nodes can communicate. This paper presents a holistic algorithm for the analysis of general networks that follow a two-terminal rationale. The algorithm is based on a set replacement approach and an element inheritance strategy that effectively obtains the minimal cut sets associated with a given network. The vast majority of methods available for obtaining two-terminal reliability are generally based on assumptions about the performance of the network. Some methods assume network components can be in one of two states: (i) either completely failed; or (ii) perfectly functioning, others usually assume that nodes are perfectly reliable and thus, these methods have to be complemented or transformed to account for node failure, and the remaining methods assume minimal cut sets can be readily computed in order to analyze more complex network and component behavior. The algorithm presented in this paper significantly differs from previous approaches available in the literature in the sense that it is based on a predecessor matrix and an element substitution technique that allows for the exact computation of minimal cut sets and the immediate inclusion of node failure without any changes to the pseudo-code. Several case networks are used to validate and illustrate the algorithms.     

A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies

This paper deals with multi-state systems (MSS), whose performance can settle on different levels, e.g. 100%, 80%, 50% of the nominal capacity, depending on the operative conditions of the constitutive multi-state elements. Examples are manufacturing, production, power generation and gas and oil transportation systems. Often in practice, MSS are such that operational dependencies exist between the system state and the state of its components. For example, in a production line of nodal series structure, with no buffers between the nodes, if one of the nodes throughput changes (e.g. switches from 100% to 50% due to a deterministic or stochastic transition of one of its components), the other nodes must be reconfigured (i.e. their components must deterministically change their states) so as to provide the same throughput.In this paper, we present a Monte Carlo simulation technique which allows modelling the complex dynamics of multi-state components subject to operational dependencies with the system overall state. A correlation method is tailored to model the automatic change of state of the relevant components following a change in one of the system nodes. The proposed technique is verified on a simple case study of literature.     

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.     

Study of strength and its reliability of SiC fiber bundle by experimental and Monte-Carlo simulation approach

Tensile tests and Monte-Carlo simulation on the strength and its reliability of the SiC_CVD (formed by chemical vapor deposition) fiber bundle were performed. The experimental and simulation results were compared and analyzed by fiber bundle strength theories. The experimental results showed that the strength of the SiC_CVD fiber bundle was decreased as the number of fibers in the bundle was increased; while in the process, Weibull shape parameter of the bundle strength was increased. The experimental results were in good agreement with the Monte-Carlo simulation. In addition, Monte-Carlo simulation was used to clarify the detailed relationship between the strength of the SiC_CVD bundle and the number of fibers in the bundle and the simulation results were compared with that of Coleman theory. The comparison revealed that the strength of the SiC_CVD bundle converged to the value of Coleman theory as the number of fibers in the bundle increased; at the same time, the rate of convergence was increased as Weibull shape parameter was increased. Furthermore, the relationship between the strength of the SiC_CVD fiber bundle and Weibull shape parameter of the SiC_CVD fiber strength was also examined. It was found that the strength of the SiC_CVD fiber bundle increased as Weibull shape parameter was increased although the number of fibers in the bundle was countable. Finally, the breaking-down process and the number of broken-fibers in the bundle depended on the number of fibers the bundle and Weibull shape parameter of the SiC_CVD fiber strength.     

Approximate multi-state reliability expressions using a new machine learning technique

The machine-learning-based methodology, previously proposed by the authors for approximating binary reliability expressions, is now extended to develop a new algorithm, based on the procedure of Hamming Clustering, which is capable to deal with multi-state systems and any success criterion. The proposed technique is presented in details and verified on literature cases: experiment results show that the new algorithm yields excellent predictions.     

Estimation of the importance measures of multi-state elements by Monte Carlo simulation

A generalization of some frequently used importance measures has been proposed by some of the authors for application to multi-state systems constituted by multi-state elements. This paper deals with the Monte Carlo (MC) estimation of these measures, which entails evaluating the system output performance under restrictions on the performance levels of its multi-state elements. Simulation procedures are proposed according to two different performance-restriction approaches. Further, the flexibility of the MC method is exploited to account for load-sharing and operational dependencies among parallel elements. The approach is tested on a multi-state transmission system of literature.     

Multi-state component criticality analysis for reliability improvement in multi-state systems

This paper evaluates and implements composite importance measures (CIM) for multi-state systems with multi-state components (MSMC). Importance measures are frequently used as a means to evaluate and rank the impact and criticality of individual components within a system yet they are less often used as a guide to prioritize system reliability improvements. For multi-state systems, previously developed measures sometimes are not appropriate and they do not meet all user needs. This study has two inter-related goals: first, to distinguish between two types of importance measures that can be used for evaluating the criticality of components in MSMC with respect to multi-state system reliability, and second, based on the CIM, to develop a component allocation heuristic to maximize system reliability improvements. The heuristic uses Monte-Carlo simulation together with the max-flow min-cut algorithm as a means to compute component CIM. These measures are then transformed into a cost-based composite metric that guides the allocation of redundant elements into the existing system. Experimental results for different system complexities show that these new CIM can effectively estimate the criticality of components with respect to multi-state system reliability. Similarly, these results show that the CIM-based heuristic can be used as a fast and effective technique to guide system reliability improvements.     

A joint reliability-redundancy optimization approach for multi-state series-parallel systems

In this paper, we present a practical approach for the joint reliability-redundancy optimization of multi-state series-parallel systems. In addition to determining the optimal redundancy level for each parallel subsystem, this approach also aims at finding the optimal values for the variables that affect the component state distributions in each subsystem. The key point is that technical and organizational actions can affect the state transition rates of a multi-state component, and thus affect the state distribution of the component and the availability of the system. Taking this into consideration, we present an approach for determining the optimal versions and numbers of components and the optimal set of technical and organizational actions for each subsystem of a multi-state series-parallel system, so as to minimize the system cost while satisfying the system availability constraint. The approach might be considered to be the multi-state version of the joint system reliability-redundancy optimization methods.     

Reliability approach to the tensile strength of unidirectional CFRP composites by Monte-Carlo simulation in a shear-lag model

A numerical technique based on the Monte-Carlo method in a shear-lag model is developed to simulate the tensile strength and fracture process for a unidirectional carbon-fiber-reinforced-plastic (CFRP) composite. The technique improves on the conventional approach by using an r_min method that can determine the stresses working on the fiber and matrix elements as the damage progresses. The r_min method is based on tracking the incremental ratio of the strength of an element to its stress. The present model includes the effect of the sliding frictional forces around fiber breaks caused by debonding between the fiber and matrix. Statistical properties of the tensile strength were obtained through simulation runs involving 100 samples for each value of the frictional force parameter. Also studied was the size effect in composite strength with increasing numbers of fibers, N, where it was found numerically that mean strength varies linearly as 1/[ln(N)]^1/2 and coefficient of variation varies linearly as 1/ln(N), as suggested from a simple theory.     

Extended block diagram method for a multi-state system reliability assessment

The presented method extends the classical reliability block diagram method to a repairable multi-state system. It is very suitable for engineering applications since the procedure is well formalized and based on the natural decomposition of the entire multi-state system (the system is represented as a collection of its elements). Until now, the classical block diagram method did not provide the reliability assessment for the repairable multi-state system. The straightforward stochastic process methods are very difficult for engineering application in such cases due to the “dimension damnation”—huge number of system states. The suggested method is based on the combined random processes and the universal generating function technique and drastically reduces the number of states in the multi-state model.     

A universal generating function approach for the analysis of multi-state systems with dependent elements

The paper extends the universal generating function technique used for the analysis of multi-state systems to the case when the performance distributions of some elements depend on states of another element or group of elements.     

Homogeneous redundancy optimization in multi-state series-parallel systems: A heuristic approach

This paper presents a heuristic for a series-parallel system, exhibiting a multi-state behavior, minimizing the cost in order to provide a desired level of reliability. System reliability is defined as the ability to satisfy consumer demands which is presented as a piecewise cumulative load curve. The components are binary and chosen from a list of products available on the market, and are characterized in terms of their feeding capacity, reliability and cost. The solution approach makes use of a homogeneous collection of components to provide redundancy in a subsystem. The algorithm is applied to power systems found in the literature for various levels of reliability requirement. The heuristic offers a straightforward analysis and is efficient both in terms of solution quality and computational time, as compared to existing genetic algorithms and heuristics. Thus, the developed heuristic is attractive, and it can be easily and efficiently applied to numerous real-life systems.     

3-TPT平台误差的蒙特卡洛模拟

 通过对3-TPT五自由度并联机床机构进行分析,建立了误差分析数学模型,在此基础上,利用蒙特卡洛技术模拟分析了驱动杆杆长误差、虎克铰间隙对运动平台误差的影响。结果表明,该并联机构的输出误差较小,满足精度要求。此研究为实际误差的补偿及机构设计参数的优化奠定了理论基础,同时也为并联机构的误差估计提供了一种方法。     

Monte Carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components

In the present paper, we consider some frequently used importance measures, in their generalized form proposed by the authors for application to multi-state systems constituted by multi-state components. To catch the dynamics of multi-state systems, Monte Carlo simulation has been utilized. A simulation approach has been presented which allows estimating of all the importance measures of the components at a given performance level in a single simulation, provided that the components are independent. The effects of different performance demands made on the system on the importance of its multi-state components have been examined with respect to a simple multi-state series–parallel system. The results have shown that a performance level of a component may be more critical for the achievement of a system performance and less critical for another.     

A multi-state Markov model for a short-term reliability analysis of a power generating unit

This paper presents a multi-state Markov model for a coal power generating unit. The paper proposes a technique for the estimation of transition intensities (rates) between the various generating capacity levels of the unit based on field observation. The technique can be applied to such units where output generating capacity is uniformly distributed. In order to estimate the transition intensities a special Markov chain embedded in the observed capacity process was defined. By using this technique, all transition intensities can be estimated from the observed realization of the unit generating capacity stochastic process. The proposed multi-state Markov model was used to calculate important reliability indices such as the Forced Outage Rate (FOR), the Expected Energy Not Supplied (EENS) to consumers, etc. These indices were found for short-time periods (about 100 h). It was shown that these indices are sensibly different from those calculated for a long-term range. Such Markov models could be very useful for power system security analysis and short-term operating decisions.     

Monte-Carlo simulation of upconversion processes in erbium-doped materials

Nonlinear upconversion quenching in Er-doped materials has been studied with use of Monte-Carlo modeling. Structure models allowed one to consider homogeneous Er³⁺ ions space distributions as well as clustering. Two variants of the simulation algorithm have been developed which took into account an evolution of one excitation or evolutions of all excitations simultaneously. The obtained results provided quantitative data on the influence of the following factors on the upconversion efficiency: (a) erbium content, (b) migration of excitation, (c) pump power, and (d) duration of pulse pumping.     

Evaluation of failure probabilities of mechanical systems under seismic action by the Monte-Carlo simulation method

Direct Monte-Carlo simulation method plays an important role in modern computational methods. For a large class of multidimensional problems of radiative transport theory, the procedure is the only available method allowing the consideration of all varieties of geometric and physical presumptions. This gives rise to computational investigation of actual and practical problems such as neutron-transport problem, reactor shielding, and impurity diffusion in random fields. The method enables the determination of the first-passage probability that the system response exceeds prescribed safe domain. In this paper, the failure probabilities of a plate subjected to seismic load are determined using this simulation method. For the purpose of reliability analysis, the von Mises criterion is used to determine the limit state failure. For the seismic load, the statistical model of earthquake-induced ground acceleration proposed by Ruiz and Penzien is used. Translated from Problemy Prochnosti, No. 6, pp. 54–70, November–December, 2008.     

Computer simulation for quality and reliability engineering

Computer simulation has been used widely in many industries for many applications. A simulation model mimics a real world system, enabling an investigation of its operation. More recently simulation models have incorporated a visual display and interactive features to aid understanding and enhance the investigation. Computer simulation has many potential uses in quality and reliability engineering, for instance, modelling equipment failures, quality control strategies, maintenance requirements and operational logistics. A case study shows how simulation has been used to study the throughput, flexibility and robustness of a manufacturing plant design. Alternative simulation software packages are briefly discussed.