Multi-state Reliability Model Research Articles

A fuzzy expectation maximization based method for estimating the parameters of a multi-state degradation model from imprecise maintenance outcomes

Multi-State (MS) reliability models are used in practice to describe the evolution of degradation in industrial components and systems. To estimate the MS model parameters, we propose a method based on the Fuzzy Expectation-Maximization (FEM) algorithm, which integrates the evidence of the field inspection outcomes with information taken from the maintenance operators about the transition times from one state to another. Possibility distributions are used to describe the imprecision in the expert statements. A procedure for estimating the Remaining Useful Life (RUL) based on the MS model and conditional on such imprecise evidence is, then, developed. The proposed method is applied to a case study concerning the degradation of pipe welds in the coolant system of a Nuclear Power Plant (NPP). The obtained results show that the combination of field data with expert knowledge can allow reducing the uncertainty in degradation estimation and RUL prediction.

Multi-state time-varying reliability evaluation of smart grid with flexible demand resources utilizing Lz transform

With the expanding proportion of renewable energy generation and development of smart grid technologies, flexible demand resources (FDRs) have been utilized as an approach to accommodating renewable energies. However, multiple uncertainties of FDRs may influence reliable and secure operation of smart grid. Multi-state reliability models for a single FDR and aggregating FDRs have been proposed in this paper with regard to responsive abilities for FDRs and random failures for both FDR devices and information system. The proposed reliability evaluation technique is based on Lz transform method which can formulate time-varying reliability indices. A modified IEEE-RTS has been utilized as an illustration of the proposed technique.

Multi-state reliability assessment for hydraulic lifting system based on the theory of dynamic Bayesian networks

Mechanical systems and their components usually have multiple failure modes and different performance states. Most existing system reliability modelling theories are developed on the basis of binary logic, which lack sufficient ability to describe the above phenomena. In this article, dynamic Bayesian network theory is employed to evaluate the multi-state reliability of a hydraulic lifting system. First, failure mode and effect analysis and structural analysis and design technique are comprehensively applied to analyse the functionalities and failure modes of the components. Afterwards, the time factor is integrated into the model by considering the state transition of the components. In this way, the multi-state reliability model of the system is established by dynamic Bayesian network. The reliability assessment and diagnostic analysis are performed by taking advantage of the dynamic Bayesian network’s bi-directional reasoning ability, and the results are in good agreement with actual situation. It shows that the proposed approach is effective and convenient for multi-state reliability modelling and analysis for mechanical systems.

Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models

ABSTRACTThis paper considers the estimation of the stress–strength reliability of a multi-state component or of a multi-state system where its states depend on the ratio of the strength and stress variables through a kernel function. The article presents a Bayesian approach assuming the stress and strength as exponentially distributed with a common location parameter but different scale parameters. We show that the limits of the Bayes estimators of both location and scale parameters under suitable priors are the maximum likelihood estimators as given by Ghosh and Razmpour [15]. We use the Bayes estimators to determine the multi-state stress–strength reliability of a system having states between 0 and 1. We derive the uniformly minimum variance unbiased estimators of the reliability function. Interval estimation using the bootstrap method is also considered. Under the squared error loss function and linex loss function, risk comparison of the reliability estimators is carried out using extensive simulations.

Reliability models of wind farms considering wind speed correlation and WTG outage

Wind speed correlation and wind turbine generator (WTG) outage are two factors affecting the reliability model of wind farms, but they are not addressed simultaneously in the existing literature. Meanwhile, WTG outage is reported to be dependent with wind speed to some extent. Therefore, the extended reliability models of wind farms incorporating both of these two factors and the dependency between WTG outage and wind speed are proposed in this paper. To consider the uncertainties and dependencies of wind speed and WTG failure, Copula method is applied to simulate correlated random variables representing for wind speed and the number of failed WTG units. Moreover, the linear apportioning technique is used to create multistate reliability models of wind farms from hourly wind power models. A number of sensitivity analyses on the modified IEEE RTS with wind power are conducted to validate the proposed reliability models for generation adequacy assessment. Case studies show that the generation adequacy indices increase with the correlation of wind speed and WTG forced outage rate (FOR). It is meaningful to point out that the effect of dependency between wind speed and WTG FOR on generation adequacy is minimal when WTG outages are independent, but it will be substantially larger when WTG outages are highly dependent. The proposed multistate reliability models of wind farms provide foundation for the reliability assessment of power systems with wind power integrated.

Reliability Modeling of Run-of-the-River Power Plants in Power System Adequacy Studies

Deployment of renewable energies for the electricity generation is on the rise around the world, among which is the run-of-the-river (ROR) power plant whose output power is variable throughout the year depending on the water flow of the respective river. The inherent uncertainty associated with renewable energy resources calls for new stochastic modeling approaches to measure the impacts of using these energies on the power system performance. This paper develops an analytical reliability model for ROR power plants. The model is based on the state-space analysis and is devised with the intention of being used in adequacy studies of power systems. Failure of related components and the intermittent nature of water flow are concurrently accommodated in the proposed model. The well-known technique of fuzzy c-means clustering is employed to find the optimal states of the resultant multistate reliability model. Two reliability test systems, i.e., Roy Billinton Test System (RBTS) and IEEE Reliability Test System (IEEE-RTS), are examined to demonstrate the effectiveness of the proposed reliability model. The water-flow data of Sheshpir River in Pars province of Iran are used.

Reliability Analysis and Optimization of Constant Current Remote Power Feeding System of Seafloor Observatory Network

Study on the deterioration of the constant current remote feeding system throughout the life of the structure is always one of the most important issues in seafloor observatory network reliability engineering. Relationship between current-to-current convertor subsystem and amount of loads in branch line is described by introducing failure rate factor. Multistate reliability model of remote power feeding system has been set up and solved by genetic algorithms. Simulation results show that as the load configuration in trunk line and branch line changing, there exists best combination maximizes the system reliability, besides, appropriate increasing amount of loads in branch line can optimize the preventive strategy.

Social network analysis via multi-state reliability and conditional influence models

This paper incorporates multi-state reliability measures into the assessment of a social network in which influence is treated as a multi-state commodity that flows through the network. The reliability of the network is defined as the probability that at least a certain level of influence reaches an intended target. We consider an individual's influence level as a function of the influence levels received from preceding actors in the network. We define several communication functions which describe the level of influence a particular actor will pass along to other actors within the network. Illustrative examples are presented, and the network reliability under the various communication influence levels is computed using exhaustive enumeration for a small example and Monte Carlo simulation for larger, more realistic sized examples.

Multi-State System Reliability: A New and Systematic Review

Reliability analysis considering multiple possible states is known as multi-state (MS) reliability analysis. Multi-state system reliability models allow both the system and its components to assume more than two levels of performance. Through multi-state reliability models provide more realistic and more precise representations of engineering systems, they are much more complex and present major difficulties in system definition and performance evaluation. MSS reliability has received a substantial amount of attention in the past four decades. This article presents a new and systematic review about multi-state system reliability. A timely review is an effective work related to improving the development of MSS theory. The review about the latest studies and advances about multi-state system reliability evaluation, multi-state systems optimization and multi-state systems maintenance is summarized in this paper.

A Multi-state Reliability Model for a Gas Fueled Cogenerated Power Plant

Cogeneration plant consists of many equipment and distinguished by their structural complexity. Failure of a component can cause failure of a sub-system or the entire system with various adverse consequences such as loss of power may result in loss of production, in damage of production equipment and it may cause accidents. In such cases, the system failure can direct to reduce ability to carry out the particular task, but not to complete failure. Moreover, each system element can also perform its task with some various levels. For example, the generating unit in power system has its maximum generating capacity, which is fully obtainable if there are no failures. Some types of failure can cause complete unit outage, whereas other types of failure can cause a unit to work with reduced capacity. Therefore, reliability and availability have to be considered in the operation of power systems using multi-state system theory. Cogeneration power plant can have an arbitrary finite number of different states (task performance levels) the system is termed a multi-state system (MSS). This paper assesses the reliability and availability of cogeneration power plant using Markov model associated with universal generating function takes into account multistate models for all system components.

Multi-state Reliability Modeling and Analysis of Reconfigurable Manufacturing Systems

To solve the problem that there is combination problem when multi-state system reliability model is formulated by traditional methods,the multi-state reliability model of Reconfigurable manufacturing system(RMS) is built based on the stochastic process and the universal generating function(UGF) technique.In order to get all the steady-state probability,the Markov process model of reconfigurable machine tool(RMT) with the characteristic of non-adjacent state transition is established.Through defining the buffer states and analysing the influence of buffer states on the machine availability,both the buffer availability and the actual steady-state probability are obtained.According to the characteristics of RMS and RMT,UGF technique is perfected,and by which generating functions of machine level and system level are expressed followed by the establishment of multi-state reliability model of repairable RMS for multi-parts family.Furthermore,the performance indexes of RMS are also discussed.A parallel-serial hybrid machining system with four stages for double-parts family composed of cylinder heads is taken as an example to verify the effectiveness of the model and the validity of the analysis method.

Multi-state reliability and message time delay in wireless sensor networks

Reliability is an important parameter to measure the function of a wireless sensor network (WSN). In this paper, we consider a multi-state reliability model and message time delay problems in WSNs. The message time delay between target nodes and the sink node is an important factor to measure the reliability of WSNs. By defining the expected time delay for the message transmission, we further consider the multi-state reliability as the probability that there is at least one message which can be received by the sink node within the time period ?. Furthermore, an integer programming method is used to compute the multi-state reliability. Finally, examples are used to show the effectiveness of the proposed method.

Customer-Centered Multi-State System Reliability and Repair Models

This paper proposes a decision model for when to repair a multi-state system from the collective viewpoint of the system designer/engineer as well as the system users (customers). Most systems normally deteriorate stochastically over time, and have several levels of performance. This degradation of performance causes the utility loss for customers and forces them to consider repairing/restoring the system before it reaches the state total failure. The decision model proposed in this paper is a dynamic model that incorporates the stochastic degradation process of a system’s performance and a customer’s objective and subjective factors related to repair costs and utility derived from the system.

An Algorithm for Lower Reliability Bounds of Multistate Two-Terminal Networks

Network reliability is extensively used to measure the degree of stability of the quality of infrastructure services. The performance of an infrastructure network and its components degrades over time in real situations. Multi-state reliability modeling that allows a finite number of different states for the performance of the network and its components is more appropriate for the reliability assessment, and provides a more realistic view of the network performance than the traditional binary reliability modeling. Due to the computational complexity of the enumerative methods in evaluating the multi-state reliability, the problem can be reduced to searching lower boundary points, and using them to evaluate reliability. Lower boundary points can be used to compute the exact reliability value and reliability bounds. We present an algorithm to search for lower boundary points. The proposed algorithm has considerable improvement in terms of computational efficiency by significantly reducing the number of iterations to obtain lower reliability bounds.

Multistate coherent systems of order k

Recently the theory of multistate reliability models has been developed to cope with many real-life situations. The present paper introduces multistate coherent systems of order k, where k refers to the number of levels for which the underlying components of the system are relevant. It is shown that many multistate systems introduced earlier by different authors are included in the class of multistate coherent systems of order k. The dual class, k-parallel and k-series systems are introduced and studied. The main structural properties of this class, which are analogous to the well-known results for coherent systems, are established.

Comment on: "Component relevancy in multistate reliability models"

The author comments on the paper by A.M. Abouammoh and M.A. Al-Kadi (see ibid., vol.40, p.370-4, 1991) which discusses various notions of component relevancy for multistate systems and suggests a unified form of relevancy. The paper contains many misprints, some wrong examples, and several results that need clarification. The most important are mentioned.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

DYNAMIC RELIABILITY MEASURES AND LIFE DISTRIBUTION MODELS FOR MULTISTATE SYSTEMS

This paper generalizes the dynamic binary state reliability parameters R(t), F(t), λ(t) and MTBF to corresponding dynamic multistate reliability parameter vectors R(t), F(t), λ(t) and M. Then, probability models for system lifetime used on binary state reliability models, such as exponential, Weibull, and other distributions are generalized for multistate models. Continuous time Markov process and Semi-Markov process are used to model the lifetime distribution for multistate system. Multistate reliability measures, such as R(t), F(t), λ(t), M are derived for those multistate reliability models.

Component relevancy in multistate reliability models : A. M. Abouammoh and M. A. Al-Kadi. IEEE Trans. Reliab.40(3), 370 (1991)

Component relevancy in multistate reliability models : A. M. Abouammoh and M. A. Al-Kadi. IEEE Trans. Reliab.40(3), 370 (1991)

Component relevancy in multistate reliability models

The concept of relevancy for components in multistate reliability models is the main condition for the underlying models to be coherent. The authors review existing component relevancy conditions and their structure functions, investigate their interrelationships and introduce a unified relevancy condition. They discuss the mathematical formulation of these relevancy conditions and their interrelationships. They introduce a unified criterion for defining the relevancy conditions shown to be special cases of the unified form. The effect of these relevancy conditions on the well known principle used by design engineers, that redundancy at the component level is preferable to redundancy at the system level is studied. Some counter-examples for the inverse implications between relevancies are given. >

Maximum flow in planar networks with exponentially distributed arc capacities

Abstract : This paper develops methods for the exact computation of the distribution of the maximum flow and related quantities in a planar network with independent and exponentially distributed arc capacities. A continuous time Markov chain (CTMC) with upper triangular rate matrix and single absorbing state is equal to the value of maximum flow in the network. Recursive algorithms are developed for computing the distribution and moments of the maximum flow. Algorithms are also presented to compute the probability that a given cut is the minimum capacity cut in the network. The algorithms are efficient and computationally stable. Distribution of the maximum flow, given a minimum cut, is studied. Keywords include: Maximum flow; Stochastic networks; Multi-state reliability modeling; Markov chains.