Multi-state System Model Research Articles

Reliability of consecutive-[formula omitted]-out-of-[formula omitted]: F systems with shared components under non-homogeneous Markov dependence

Multi-state system models are more practical and valuable when describing complex engineering structures than binary-state system models. Modelling of linear consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence is discussed in this work. The proposed model is an extension of both “consecutive-k-out-of-n: F system” and “consecutive-k-out-of-n: F system with shared components between adjacent subsystems”. All the components in the system are assumed to have three states and are non-homogeneous Markov-dependent. Using the method of sum of disjoint products (SDP), the system reliability formula is derived by summing the reliability values for all disjoint cases. The well-known finite Markov chain imbedding approach (FMCIA) is used for deriving the reliability formula for each disjoint case. For the special cases of systems with homogeneous Markov-dependent or independent components, the corresponding results are deduced. Finally, some numerical examples are presented to illustrate all the results developed here.

Performance reliability analysis of multi-state degraded system with improved Lz transform

Universal Generating Functions and Lz transformations have been widely used in the reliability modeling of multi-state systems. In order to solve the problem of complex calculations due to the dense random combination of multi-state performance parameters in the Lz transformation, a screening function is defined before the Lz transformation, and the screening function is combined with the performance threshold to screening the state performance parameters in advance, and the process is simplified through the screen matrix and the screen block diagram, effectively reduce the combined dimensions and quantity, improve the efficiency of reliability analysis, and combine with specific examples for application verification.

Definitions and Reliability Evaluation of Multi-state Systems Considering State Transition Process and its Application for Gas Systems

Multi-state system (MSS) models have been widely used to represent the reliability of engineering systems that have a finite number of performance levels. The previous studies related to the reliability evaluation of the MSSs generally follow the assumption that the transition among different performance states is instantaneous with no time delay. However, there exist several engineering systems that transit slowly between different states, such as gas supply systems and heating distribution systems. When evaluating the operating reliability of such an engineering system, the neglect of the non-instant state transition process may lead to inaccurate or insufficient evaluation results. To fill the research gap, the traditional MSS model is extended to handle the situation where the non-instant state transition features should be considered. The concepts and features of multi-state systems considering state transition process (MSS-STP) are innovatively proposed. Considering the non-instant state transition process, the traditional reliability evaluation framework for the MSSs is extended to evaluate the operating reliability of MSS-STP. The procedure of transition curve discretization is innovatively proposed to divide the dynamic transition process into a series of discrete states. The developed general MSS-TSP model is applied to the natural gas system (NGS) to demonstrate the effectiveness of the proposed reliability evaluation framework. The proposed technique can provide a useful tool for system operators to accurately evaluate the operating reliability of MSS-STP

BIRNBAUM CRITICALITY AND IMPORTANCE MEASURES FOR MULTISTATE SYSTEMS WITH REPAIRABLE COMPONENTS

We suggest four new measures of importance for repairable multistate systems based on the classical Birnbaum measure. Periodic component life cycles and general semi-Markov processes are considered. Similar to the Birnbaum measure, the proposed measures are generic in the sense that they only depend on the probabilistic properties of the components and the system structure. The multistate system model encodes physical properties of the components and the system directly into the structure function. As a result, calculating importance is easy, especially in the asymptotic case. Moreover, the proposed measures are composite measures, combining importance for all component states into a unified quantity. This simplifies ranking of the components with respect to importance. The proposed measures can be characterized with respect to two features: forward-looking versus backward-looking and with respect to how criticality is measured. Forward-looking importance measures focus on the next component states, while backward-looking importance measures focus on the previous component states. Two approaches to measuring criticality are considered: probability of criticality versus expected impact. Examples show that the different importance measures may result in unequal rankings.

Multi-State System Modeling and Reliability Assessment for Groups of High-speed Train Wheels

The polygonization of high-speed train wheels is commonly considered as a serious threat to reliability of high-speed trains all over the world. Traditional studies in polygonization of wheels focus on modeling its mechanism via physics-based models. However, to the knowledge of the authors, the polygonization process has not been fully explained by existing studies due to the complex degradation mechanism and varying operation environment which is difficult to monitor and measure. In this article, the data-driven multi-state system (MSS) models are developed for the reliability assessment of high-speed train wheels based on the analysis of actual operation data. The results can be used to support practical maintenance decision making. Another contribution of this paper is to prove that the environmental factors exert significant impacts on the reliability of Chinese high-speed train wheels. This finding has been included in the development of the MSS models. The results by these models are used to suggest a more reasonable maintenance schedule for Chinese high-speed train wheels. The obtained maintenance intervals are expected to assist the railway companies to reduce the operational risk as well as improve the maintenance efficiency.

A state–behavior–function model for functional modeling of multi-state systems

Since functional modeling can be very useful in conceptual design, it has received considerable attention from engineering design community. However, existing functional models still cannot effectively assist designers in analyzing the functionalities of multi-state systems during conceptual design. As a result, designers often have to manually carry out functionality analysis according to their experiences, which are not only tedious, but also error-prone. Therefore, this paper proposes a state–behavior–function model for functional modeling of multi-state systems, which can provide designers with automated functional analysis support. The approach involves not only a state–behavior–function model for representing components, but also a model for representing the functionalities of multi-state systems. A prototype software is then developed for demonstrating the proposed model, with the functional modeling of a peeler centrifuge as an example to illustrate the proposed functional modeling approach.

On sensitivity analysis of aging multi-state system by using LZ-transform

The paper considers a sensitivity evaluation for an aging multi-state system (MSS) under minimal repair. Investigation of an impact of changing different failure/repair rates of different elements in MSS is important for practical reliability engineering. In practical reliability engineering a "curse of dimensionality" (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for sensitivity assessment. Straightforward Markov Method applied to solve this problem requires building a model with numerous numbers of states and solving a corresponding system of differential equations. In order to solve this problem, the paper proposes to use a new method based on an LZ-transform of the discrete-state continuous-time Markov process, and on Ushakov's Universal Generating Operator. New sensitivity measures useful for aging MSS reliability analysis were introduced. It was shown that the proposed method drastically reduces a computational burden. A numerical example is presented in order to illustrate the approach.

A universal generating function-based multi-state system performance model subject to correlated failures

Multi-state system (MSS) reliability modeling is a paradigm that allows both systems and components to exhibit more than two performance levels. While several researchers have introduced correlation or dependence into MSS models to assess its negative influence on performance and associated measures, these methods exhibit complexity that is exponential or worse in the worst case. To overcome this limitation, this paper proposes an extension to the discrete universal generating function approach for MSS to allow correlation between the elements comprising a multi-state component. We subsequently generalize to the continuous case and allow failures to follow any life distribution. The approach possesses an analytical form and therefore enables efficient performance and reliability assessment as well as sensitivity analysis on the impact of correlation. This sensitivity analysis can be applied to a wide range of measures including performance, reliability, the density function, hazard rate, mean time to failure, availability, and mean residual life. The approach is illustrated through a series of examples, demonstrating the efficiency of the approach to assess performance and reliability as well as to conduct sensitivity analysis. The results indicate that the approach can identify the impact of correlation on performance, reliability, and the many measures of interest.

Multi-state systems reliability with composite importance measures of fuzzy petri nets

A fuzzy petri nets method for modelling and analysing the reliability of a multi-state software system is proposed here. This new method is based on fuzzy parameter of the FPN, which depends on the state probability which is learned by the enhanced fuzzy reasoning algorithm. First, the multi-state system model of fuzzy petri nets was proposed. Second, fuzzy petri nets adaptive learning algorithms were proposed, and the state probability is drawn to the optimal value. Then the reliability of the multi-state system was determined. Finally, with respect to the different Type 1 importance measures, according to the state probability, multi-state system, the reliability of the state with fuzzy petri nets (FPN) composite importance measures (CIM) was estimated and the comparison results table between the CIM and the FPN CIM was produced. From the experiment, multi-state system reliability with composite importance measures of fuzzy petri nets in this paper shows that the variances are consistently low, and the measures can be considered to be robust. This makes the system more reliable and accuracy from the user's perspective, the method becomes more efficient.

Multi-state systems reliability with composite importance measures of fuzzy petri nets

A fuzzy petri nets method for modelling and analysing the reliability of a multi-state software system is proposed here. This new method is based on fuzzy parameter of the FPN, which depends on the state probability which is learned by the enhanced fuzzy reasoning algorithm. First, the multi-state system model of fuzzy petri nets was proposed. Second, fuzzy petri nets adaptive learning algorithms were proposed, and the state probability is drawn to the optimal value. Then the reliability of the multi-state system was determined. Finally, with respect to the different Type 1 importance measures, according to the state probability, multi-state system, the reliability of the state with fuzzy petri nets (FPN) composite importance measures (CIM) was estimated and the comparison results table between the CIM and the FPN CIM was produced. From the experiment, multi-state system reliability with composite importance measures of fuzzy petri nets in this paper shows that the variances are consistently low, and the measures can be considered to be robust. This makes the system more reliable and accuracy from the user's perspective, the method becomes more efficient.

On Birnbaum importance assessment for aging multi-state system under minimal repair by using the Lz-transform method

This paper considers a reliability importance evaluation for components in an aging multi-state system. In practical reliability engineering a “curse of dimensionality” (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for importance assessment. In order to challenge the problem, this paper proposes a new method that is based on an LZ-transform of the discrete-state continuous-time Markov process and on Ushakov׳s Universal Generating Operator. The paper shows that the proposed method can drastically reduce a computational burden. In order to illustrate the method, a solution of a real world problem is presented as a numerical example.

Bayesian Networks Application in Multi-State System Reliability Analysis

Aiming at the limitations of traditional reliability analysis theory in multi-state system, a method for reliability modeling and assessment of a multi-state system based on Bayesian Network (BN) is proposed with the advantages of uncertain reasoning and describing multi-state of event. Through the case of cell production line system, in this paper we will discuss how to establish and construct a multi-state system model based on Bayesian network, and how to apply the prior probability and posterior probability to do the bidirectional inference analysis, and directly calculate the reliability indices of the system by means of prior probability and Conditional Probability Table (CPT) . Thereby we can do the qualitative and quantitative analysis of the multi-state system reliability, identify the weak links of the system, and achieve assessment of system reliability.

Decision Diagram Based Methods and Complexity Analysis for Multi-State Systems

Decision diagrams are graphical structures based on Shannon's decomposition. They have been extensively used for representing and manipulating logic functions in areas such as circuit verification, compact Markov chain representation, and symbolic model checking. However, their applicability in reliability modeling and analysis has only been recently studied. Moreover, the study had been mostly restricted to binary-state systems in which both the system and its components are either operational, or failed. Nevertheless, many practical systems are multi-state systems (MSS) in which both the system and its components may reside at multiple (more than two) performance levels (or states), varying from perfect operation to complete failure. This paper presents three forms of decision diagrams for the modeling and analysis of MSS: binary decision diagrams, logarithmically encoded binary decision diagrams, and multi-valued decision diagrams. We present both separated, and shared methods based on these decision diagrams. Comprehensive complexity analysis, and performance comparisons among these methods, are conducted with both mathematical, and empirical approaches.

Performance assessment of multi-state systems with critical failure modes: Application to the flotation metallic arsenic circuit

This paper considers a number of alternative measures of multi-state systems with two failure modes. Almost all of them are based on a probabilistic model and the extent to which the multi-state system performance analysis may typically lead. The conventional multi-state theory is used to assess the fundamental problems of the performance of complex systems. In real life, it may be difficult to obtain sufficient data to estimate the precise values of the performance levels of modern engineering systems. This paper suggests reliability measures for multi-state systems with two failure modes, and presents a procedure for evaluating these measures. Generalized assumptions of multiple factors that may affect the reliability of such systems are introduced by developing multi-state operators that obey the commutative and the associative laws. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Mathematical problems raised by applications of multi-state system model in system failure engineering are addressed. Engineering case study of the flotation circuit of mineral processing plant is modeled as a homogeneous coherent multi-state system composed of homogeneous coherent multi-state subsystems, and its reliability is calculated.

Fuzzy Multi-State Systems: General Definitions, and Performance Assessment

Compared with a binary system model, a multi-state system model provides a more flexible tool for representing engineering systems in real life. In conventional multi-state theory, it is assumed that the exact probability and performance level of each component state are given. However, it may be difficult to obtain sufficient data to estimate the precise values of these probabilities and performance levels in many highly reliable modern engineering systems. New techniques are needed to solve these fundamental problems. A general fuzzy multi-state system model is proposed in this article to overcome these deficiencies. The basic definitions and assumptions of such systems are introduced. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Future research directions include performance evaluation algorithms for the defined fuzzy multi-state systems.

Performance Evaluation of Generalized Multi-State<tex>$k$</tex>-Out-of-<tex>$n$</tex>Systems

The generalized multi-state k-out-of-n:G system model defined by Huang provides more flexibilities for modeling of multi-state systems. However, the performance evaluation algorithm they proposed for such systems is not efficient, and it is applicable only when the k/sub i/ values follow a monotonic pattern. In this paper, we defined the concept of generalized multi-state k-out-of-n:F systems. There is an equivalent generalized multi-state k-out-of-n:G system with respect to each generalized multi-state k-out-of-n:F system, and vice versa. The form of minimal cut vector for generalized multi-state k-out-of-n:F systems is presented. An efficient recursive algorithm based on minimal cut vectors is developed to evaluate the state distributions of a generalized multi-state k-out-of-n:F system. Thus, a generalized multi-state k-out-of-n:G system can first be transformed to the equivalent generalized multi-state k-out-of-n:F system, and then be evaluated using the proposed recursive algorithm. Numerical examples are given to illustrate the effectiveness and efficiencies of the proposed recursive algorithms.

A multi-state system model

This paper presents a Markov model with one successful mode and three mutually exclusive failure modes. Three extra system states are introduced at the repair stage. The state probability equations are developed to obtain system availability and mean time to system failure.

A multi-state system model : Balbir S. Dhillon. Microelectron. Reliab.16, 55 (1977)

A multi-state system model : Balbir S. Dhillon. Microelectron. Reliab.16, 55 (1977)