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2018 | Book

Reliability of a Network with Heterogeneous Components Read chapter Read first chapter

Recent Advances in Multi-state Systems Reliability

Theory and Applications

Editors: Dr. Anatoly Lisnianski, Dr. Ilia Frenkel, Dr. Alex Karagrigoriou

Publisher: Springer International Publishing

Book Series : Springer Series in Reliability Engineering

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book addresses a modern topic in reliability: multi-state and continuous-state system reliability, which has been intensively developed in recent years. It offers an up-to-date overview of the latest developments in reliability theory for multi-state systems, engineering applications to a variety of technical problems, and case studies that will be of interest to reliability engineers and industrial managers. It also covers corresponding theoretical issues, as well as case studies illustrating the applications of the corresponding theoretical advances.

The book is divided into two parts: Modern Mathematical Methods for Multi-state System Reliability Analysis (Part 1), and Applications and Case Studies (Part 2), which examines real-world multi-state systems. It will greatly benefit scientists and researchers working in reliability, as well as practitioners and managers with an interest in reliability and performability analysis. It can also be used as a textbook or

as a supporting text for postgraduate courses in Industrial Engineering, Electrical Engineering, Mechanical Engineering, Applied Mathematics, and Operations Research.

Table of Contents

Frontmatter

Modern Mathematical Methods for Multi-state System Reliability Analysis

Frontmatter
Reliability of a Network with Heterogeneous Components
Abstract
We investigate reliability of network-type systems under the assumption that the network has \(K>1\) types of i.i.d. components. Our method is an extension the D-spectra method to K dimensions. It is based on Monte Carlo simulation for estimating the number of system failure sets having \(k_i\) components of i-th type, \(i=1,2,\ldots ,K\). We demonstrate our approach on a Barabasi-Albert network with 68 edges and 34 nodes and terminal connectivity as an operational criterion, for \(K=2\) types of nodes or edges as the components subject to failure.
Ilya B. Gertsbakh, Yoseph Shpungin, Radislav Vaisman
Reliability Analysis of Complex Multi-state System with Common Cause Failure Based on DS Evidence Theory and Bayesian Network
Abstract
With the increasing complexity and larger size of modern advanced engineering systems, the traditional reliability theory cannot characterize and quantify the complex characteristics of complex systems, such as multi-state properties, epistemic uncertainties, common cause failures (CCFs), etc. This chapter focuses on the reliability analysis of complex multi-state system (MSS) with epistemic uncertainty and CCFs. Based on the Bayesian network (BN) method for reliability analysis of MSS, the DS evidence theory is used to express the epistemic uncertainty in system through the state space reconstruction of MSS. An uncertain state, which used to express the epistemic uncertainty is introduced in the new state space. The integration of evidence theory with BN is achieved by updating the conditional probability tables. When the multiple CCF groups (CCFGs) are considered in complex redundant systems, a modified factor parametric model is introduced to model the CCF in systems. An evidence theory based BN method is proposed for the reliability analysis and evaluation of complex MSSs in this chapter. The reliability analysis of servo feeding control system for CNC heavy-duty horizontal lathes (HDHLs) by this proposed method has shown that the presented method has high computational efficiency and strong practical value.
Jinhua Mi, Yan-Feng Li, Weiwen Peng, Hong-Zhong Huang
A D-MMAP to Model a Complex Multi-state System with Loss of Units
Abstract
A complex multi-state system subject to different types of failures and preventive maintenance, with loss of units, is modelled by considering a discrete marked Markovian arrival process. The system is composed of K units, one online and the rest in cold standby. The online unit is submitted to different types of failures and when a non-repairable failure occurs the corresponding unit is removed. Several internal degradation states are considered which are observed when a random inspection occurs. This unit is subject to internal repairable failure, external shocks and preventive maintenance. If one internal repairable failure occurs, the unit goes to the repair facility for corrective repair, if a major degradation level is observed by inspection, the unit goes to preventive maintenance and when one external shock happens, this one may produce an aggravation of the internal degradation level, cumulative external damage or external extreme failure (non-repairable failure). Preventive maintenance and corrective repair times follow different distributions. The system is modelled in transient regime and relevant performance measures are obtained. All results are expressed in algorithmic and computational form and they have been implemented computationally with MATLAB and R. A numerical example shows the versatility of the model.
Juan Eloy Ruiz-Castro
Modeling and Inference for Multi-state Systems
Abstract
In this work we are focused on multi-state systems modeled by means of a special type of semi-Markov processes. The sojourn times are seen to be independent not necessarily identically distributed random variables and assumed to belong to a general class of distributions closed under extrema that includes, in addition to some discrete distributions, several typical reliability distributions like the exponential, Weibull, and Pareto. A special parametrization is proposed for the parameters describing the system, taking thus into account various types of dependencies of the parameters on the the states of the system. We obtain maximum likelihood estimators of the parameters and plug-in type estimators are furnished for the basic quantities describing the semi-Markov system under study.
Vlad Stefan Barbu, Alex Karagrigoriou
Optimizing Availability and Performance of a Two-Unit Redundant Multi-state Deteriorating System
Abstract
The most of the contemporary large scale technological systems are functioning under multiple stages of degradation, from their perfect state to their total failure. The study of the performance and the availability of multi-stage systems is of great importance since their deterioration and/or failure may lead to important losses. Under a proper inspection and maintenance policy, it is feasible the operation of the system to be improved significantly. Our main goal is to model multi-state systems with redundancy and to identify the optimal maintenance policies. The system is inspected periodically. Depending on the condition of the system, either no action takes place or maintenance is carried out, either minimal or major. The proposed model takes also into account the scenario of imperfect and failed maintenance. The asymptotic behaviour of the system is studied and optimization problems for the asymptotic availability, the downtime cost and the expected cost due to maintenance and unavailability, with respect to inspection intervals, are formulated and solved.
Sonia Malefaki, Vasilis P. Koutras, Agapios N. Platis
Phase-Type Models and Their Extension to Competing Risks
Abstract
We present an extension of the phase-type methodology for modeling of lifetime distributions to include the case of competing risks. This is done by considering finite state Markov chains in continuous time with more than one absorbing state, letting each absorbing state correspond to a particular risk. The special structure of Coxian phase-type models is considered in particular. The chapter emphasizes the use of phase-type models in statistical modeling and inference for survival and competing risks data.
Bo Henry Lindqvist, Susanne Hodneland Kjølen
A Study on Repairable Series Systems with Markov Repairable Units
Abstract
Consider a repairable series system consisting of n units and each of them follows a Markov process with finite state and continuous time. Under independence assumption among units, the repairable series system has been widely studied by using the Markov process method and Lz-transform method. However, both methods have faced the problem of state exploration although some approximation methods have been used. Thus, it is still an interesting and significant problem to be explored. In this chapter, we investigate repairable series systems by using matrix method which has been widely used in aggregated stochastic processes especially in ion channel modeling and aggregated repairable systems. The formulas for reliability, instantaneous and interval availabilities are given in matrix form for four kinds of repairable series systems, general repairable series system, general repairable series system with neglected failures, phased-mission repairable series system and phased-mission repairable series system with neglected failures, respectively. Numerical examples are shown to illustrate the results for the four kinds of systems and present how matrix method is used to solve the problem of state exploration in the Lz-transform method. Finally, the conclusions and some future possible applications are given.
He Yi, Lirong Cui
Dynamic Performance of Series Parallel Multi-state Systems with Standby Subsystems or Repairable Binary Elements
Abstract
This chapter presents a method for evaluating dynamic performance of multi-state systems with a general series parallel structure. The system components can be either repairable binary elements with given time-to-failure and repair time distributions, or 1-out-of-N warm standby configurations of heterogeneous binary elements characterized by different performances and time-to-failure distributions. The entire system needs to satisfy a random demand defined by a time-dependent distribution. Iterative algorithms are presented for determining performance stochastic processes of individual components. A universal generating function technique is implemented for evaluating the dynamic system performance indices. Examples are provided to demonstrate applications of the proposed methodology.
Gregory Levitin, Liudong Xing
Optimal Imperfect Maintenance in a Multi-state System
Abstract
In this research, we are concerned with the modeling of optimal maintenance actions in multi-state systems. Most of the imperfect maintenance models that have been investigated in literature use either imperfect preventive maintenance actions or imperfect corrective maintenance actions. In this paper we consider a model with both imperfect preventive and imperfect corrective maintenance actions. A sequential failure limit preventive maintenance (PM) policy with infinite planning horizon and with imperfect preventive and imperfect corrective maintenance actions is used to formulate a cost optimization problem. Different cost functions for PM actions, as well as several discrete lifetime distributions are introduced. The solution of the cost optimization problem is illustrated by an example.
Stephanie Dietrich, Waltraud Kahle
Reliability Evaluation of Non-repairable Multi-state Systems Considering Survival-Death Markov Processes
Abstract
Multi-state system (MSS) models have been extensively studied in recent years, because of their accuracy and flexibility for reliability evaluation of complex systems. One of the most important multi-state systems is the non-repairable multi-state system, which cannot be repaired during its operating time or whose repair is not economical. The “death” Markov process provides a basis for reliability analysis of the non-repairable multi-state system. It does not consider, however, the impact of start–up failures of components on system reliability. In this chapter, two models of modified “death” Markov processes considering component start–up failures are proposed. They are referred to as “survival-death” Markov processes and they differ in that the first model considers not only completely successful and failed start up but also partially successful start-up, whereas the second model only considers completely successful or failed start up. In such processes, the analytic expressions of the time-dependent transition probabilities can be obtained by using the Laplace-Stieltjes transform and the inverse Laplace-Stieltjes transform. The stochastic processes are combined with the Lz-transform technique for evaluating dynamic reliability of non-repairable MSS.
Yan Yuan, Yi Ding, Chuanxin Guo, Yuanzhang Sun
Reliability Assessment of Systems with Dependent Degradation Processes Based on Piecewise-Deterministic Markov Process
Abstract
This chapter presents a reliability assessment framework for multi-component systems whose degradation processes are modeled by multi-state and physics-based models. The piecewise-deterministic Markov process modeling approach is employed to treat dependencies between the degradation processes within one component or/and among components. The proposed method can handle the dependencies between physics-based models, between multi-state models and between these two types of models. A Monte Carlo simulation algorithm is designed to compute the systems reliability. A case study on one subsystem of the residual heat removal system of a nuclear power plant is illustrated as exemplification of the proposed modeling framework.
Yan-Hui Lin, Yan-Fu Li, Enrico Zio
Trade-Off Between Redundancy, Protection, and Imperfect False Targets in Defending Parallel Systems
Abstract
A substantial amount of research over the past decades has studied the reliability of different systems, but most of them are restricted to systems with only internal failures. In practice, systems may fail due to unintentional impacts or intentional attacks. In this chapter, we first provide a comprehensive review of the research on improving system reliability. The survey shows that, for systems subject to intentional attacks, providing redundant system elements, protecting genuine elements, and deploying false targets are the three important measures to increase the system survivability. The trade-off between protecting genuine elements and deployment of imperfect false targets has been studied before, however, subject to a fixed number of genuine elements in the system. This chapter studies the trade-off between building redundant genuine elements, protection of genuine elements and deploying imperfect false targets in the defense of a capacitated parallel system. Numerical examples are carried out to illustrate the applications.
Hui Xiao, Rui Peng
Optimal Testing Resources Allocation for Improving Reliability Assessment of Non-repairable Multi-state Systems
Abstract
Due to limited reliability testing resources (e.g., budget, time, and manpower etc.), the reliability of a sophisticated system may not be able to accurately estimated by insufficient reliability testing data. The book chapter explores the reliability testing resources allocation problem for multi-state systems, so as to improve the accuracy of reliability estimation of an entire system. The Bayesian reliability assessment method is used to infer the unknown parameters of multi-state components by merging subjective information and continuous/discontinuous inspection data. The performance of each candidate testing resources allocation scheme is evaluated by the proposed uncertainty quantification metrics. By introducing the surrogate model, i.e., kriging model, the computational burden in seeking the optimal testing resources allocation scheme can be greatly reduced. The effectiveness and efficiency of the proposed method are exemplified via two illustrative case.
Yu Liu, Tao Jiang, Peng Lin
Topological Analysis of Multi-state Systems Based on Direct Partial Logic Derivatives
Abstract
Topological analysis deals with evaluation of influence of the system components on system operation. Such evaluation is usually performed by identification and quantification of situations in which degradation/improvement of a given system component results in system degradation/improvement. These situations can be revealed using Direct Partial Logic Derivatives (DPLDs). One of the open problems is how to compute DPLDs efficiently for large systems. In this paper, we develop a new method for their computation for systems that can be decomposed into disjoint modules. The method is based on the chain rule that is derived in this paper.
Miroslav Kvassay, Elena Zaitseva

Applications and Case Studies

Frontmatter
Short-Term Reliability Analysis of Power Plants with Several Combined Cycle Units
Abstract
This chapter presents a method for a short-term reliability analysis of power plants consisting of a number combined cycle generating units. A multi-state Markov model represents each generating unit with several states. Using a straightforward Markov method for reliability assessment is leading to explosion of number of states that should be analyzed. The chapter proposes a method for the estimation of important power system indices such as the availability for specified demand level, the loss of load probability, the expected energy not supplied to consumers etc. This method is based on Lz-transform of discrete-state continuous-time Markov process. The proposed approach is useful for a short-term reliability analysis of power system and operative decisions making. A numerical example is presented as an illustration of the proposed approach.
Anatoly Lisnianski, David Laredo, Hanoch Ben Haim
Reliability Analysis of a Modified IEEE 6BUS RBTS Multi-state System
Abstract
In this chapter, we attempt to develop a stochastic model based on a modification of a standard energy system. Aiming to achieve a high level of reliability in the system, it is necessary to implement specific modifications that are necessary to improve the structure of the system, in order to meet the demanded requirements. This improvement is actually a restructuring of an IEEE 6 BUS RBTS system by using an alternative combination of its generation units that presents the lowest possible failure rates using the same kind of generators and maintaining the level of output specifications according to the minimum reliability requirements. Using Multi-state systems and Semi-Markov modeling, the final result is a modified system that presents more flexibility and operates in less uncertainty environment, leading to a better level of reliability.
Thomas Markopoulos, Agapios N. Platis
Lz-Transform Approach for Fault Tolerance Assessment of Various Traction Drives Topologies of Hybrid-Electric Helicopter
Abstract
This chapter presents a preliminary analysis of fault tolerance, availability and performance assessment of the two promising options of the hybrid-electric traction drive version for the helicopter, which can be treated as multi-state system, where components and entire system in general case have an arbitrary finite number of states corresponding to the different performance rates. The performance rate (output nominal power) of the system at any time instant is interpreted as a discrete-state continuous-time stochastic process. In the present chapter, the Lz-transform is applied to a real multi-state hybrid-electric traction drive version for the helicopter system that is functioning under various stochastic demands and its availability and performance is analyzed. It is shown that Lz-transform application drastically simplifies the availability computation for such a system compared with the straightforward Markov method.
Ilia Frenkel, Igor Bolvashenkov, Hans-Georg Herzog, Lev Khvatskin
Patient Diagnostic State Evolution During Hospitalization: Developing a Model for Measuring Clinical Diagnostic Dynamics
Abstract
Patient health is represented by a set of diagnoses, which determines personal health status. Each set corresponds to a certain health state and so, can be treated as an individual performance in this state and individual health can be considered as a corresponding multi-state system. Appropriate metrics for measuring patient’s state diagnosis changes during hospitalization are proposed. The first metric determines the dissimilarity between two single diagnoses, each of which is based on internationally recognized classification scheme. The second metric is aimed to compare between two sets of diagnoses with respect to the same patient and is based on the first metric, but uses additional, recently proposed, ideas of measuring heterogeneity/segregation between sets of categorical data. A numerical example and a real world illustration of the above measures are provided. The ultimate goal is the analysis of multistate health status data in order to improve the accuracy and quality of medical diagnostics.
Yariv N. Marmor, Emil Bashkansky
Automated Development of the Markovian Chains to Assess the Availability and Performance of Multi-state Multiprocessor System
Abstract
Reliability design, availability and performance assessment of multi-state multiprocessor system with structural redundancy involves solving number of issues. This paper outlines a cutting-age technology of the analytical modelling of the discrete-continuous stochastic systems for automated development the Markovian chains to assess the availability and Performance of multi-state multiprocessor system, which shows the algorithm for reliability behaviour. For various configurations of the multi-state multiprocessor system, the use of the proposed model and problem-oriented software, ASNA represents the ability to automate constructed the Markovian chains after developed the structural-automated model. This model includes a number of settings: numbers of processor in the main sub-system; numbers of processor in the diverse sub-system; number of processor in hot standby; number of processor in cold standby; failure rate of the processor; mean time of sub-system repair; the structure of the system’s and reliability behaviours. The proposed structural-automated model for the automated development the Markovian chains are subject to structure adaptation of the multi-state multiprocessor system and/or the algorithms of reliability behaviour. This allows us to obtain a new model and the feasibility to automate development of the Markovian chains.
Bogdan Volochiy, Oleksandr Mulyak, Vyacheslav Kharchenko
Metadata
Title
Recent Advances in Multi-state Systems Reliability
Editors
Dr. Anatoly Lisnianski
Dr. Ilia Frenkel
Dr. Alex Karagrigoriou
Copyright Year
2018
Electronic ISBN
978-3-319-63423-4
Print ISBN
978-3-319-63422-7
DOI
https://doi.org/10.1007/978-3-319-63423-4