Reliability Evaluation Of Multi-state Systems Research Articles

Combinatorial Reliability Evaluation of Multi-State System with Epistemic Uncertainty

Multi-state systems (MSSs) are common in real-word applications, in which a system and/or its components exhibit multiple stochastically-dependent states or performance levels. Such characteristic poses challenges to the reliability evaluation of MSSs. Multi-valued decision diagrams (MDDs) have been developed to address the reliability analysis of MSSs under the assumption that the failure-time parameters of system components are deterministic. However, due to epistemic uncertainty, it is often difficult or impossible to obtain the determinate values of the component parameters. Therefore, this paper aims to address the MDD-based reliability evaluation of MSSs with epistemic uncertainty by incorporating the interval theory and fuzzy set theory. The proposed methods are verified through a detailed case study of a high-speed train bogie system. The results show that the proposed methods can obtain practical reliability evaluation results reflecting the condition of epistemic uncertainty.

Reliability Evaluation of Multi-State Systems With Common Bus Performance Sharing Considering Performance Excess

In a multi-state system with common bus performance sharing, the residual performance of any sub-unit can be shared to other sub-units with insufficient performance by the common bus with stochastic sharing capacity. This study extends the reliability evaluation model by considering both the minimum and maximum requirements of elements, which should not only meet the random minimum requirements of each single element, but also require that there should be no excess performance. The reliability of the multi-state system (MSS) is estimated by using the Universal Generating Function (UGF) technique. Illustrative example is presented to illustrate the procedures. In addition, the genetic operator is used to obtain the optimal location of the components with maximum reliability.

Survival signature for reliability evaluation of a multi-state system with multi-state components

Survival signature technology has recently attracted increasing attention for its merits on quantifying reliability of systems with multiple types of components. In order to implement reliability evaluation of multi-state system (MSS), computing methods of survival signature are studied for reliability analysis of several different systems in this paper. For an MSS consisting of multi-state components, its survival signature can be developed based on the different state definition of system. For the binary-state system with multi-state components, its survival signature is based on the generalization of survival signature for multi-state components. For a real life engineering MSS consisting of subsystems, the computing method of survival signature of system has also been derived based on the survival signature of subsystems and mapping of subsystems’ states to system's states. This enables consecutive application of the new method to substantial realistic MSS, with no theoretical limit on the size of the systems. Examples illustrate the applicability of the analysis approach for systems reliability.

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

Mission Reliability Evaluation for Fuzzy Multistate Manufacturing System Based on an Extended Stochastic Flow Network

Due to the artificial division of a machine performance state and unpredictable external working conditions, the performance and state transition strength of multistate machines (that is, their fuzzy multistate characteristic) cannot be accurately identified. Moreover, existing research on the reliability evaluation of multistate systems does not consider the operating mechanism of a manufacturing system. Therefore, this article proposes a mission reliability evaluation method for fuzzy multistate manufacturing systems based on an extended stochastic flow network (ESFN). First, from the relationship between the production task execution state, production machine degradation state, and produced product quality state, the operation mechanism of a fuzzy multistate manufacturing system is proposed, and the connotation of mission reliability is further defined. Second, an ESFN model of the multistate manufacturing system based on the operating mechanism of a fuzzy multistate manufacturing system is established. Third, on the basis of a fuzzy Markov model, the mission reliability evaluation method of the fuzzy multistate manufacturing system is proposed. Finally, a case study of the manufacturing system for producing a ferrite phase shifting unit is presented to verify the proposed approach, and a sensitivity analysis is conducted to analyze the impacts of the parameters in the proposed model.

Reliability Assessment for Uncertain Multi-state Systems: An Extension of Fuzzy Universal Generating Function

Universal generating function (UGF) technology is the basic approach to reliability evaluation of multi-state systems. For products with high reliability and long lifetime in practical engineering, their system structure is usually uncertain and the external working condition is extremely complex. Thus, accurate failure or degradation data of components are difficult to define. Data are often characterized by types of randomness, probability, grey, fuzzy and other uncertain numbers. Based on interval grey number, the concept of generalized uncertain number is proposed. In this paper, we first unify arbitrary type of uncertain numbers, propose the definition of generalized standard uncertain number and study algorithm such as addition, subtraction, multiplication and division between them. Based on generalized standard uncertain number, generalized universal generating function, which is an extension of fuzzy UGF, is proposed. Several commonly used generalized universal generating operators are discussed with system connection structure between components. According to the relationship between output performance and system demand level, reliability indexes such as availability, expected output performance and mean performance deficiency are evaluated. Comparisons in a real case show the effectiveness of the proposed approach. Therefore, relevant results can strengthen the theoretical research depth of uncertain reliability and definitely expand the application scope of fuzzy universal generating function.

Reliability Evaluation and Selection in Multi-State System

The multi-state system is an essential tool to present engineering system and previous researches have been focusing on the reliability evaluation of multi-state system recently. The Analytical algorithm and Monte Carlo simulation are the major reliability evaluation methods. However, it is inefficient to apply these algorithms to find the optimal multi-state system with greatest reliability in numbers of systems, whose computational time may last for hours. Hence, this paper proposes a new method based on ordinal optimization algorithm and Monte Carlo simulation applied in reliability evaluation. Calculation methods concerning the characteristics of system are defined, which can dramatically and effectively shorten the computational time. An effective and convenient precision and efficiency verification according to the proposed method is illustrated.

A stochastic approach for the reliability evaluation of multi-state systems with dependent components

A multi-state system (MSS) employs more than two discrete states to indicate different performance rates. Methods using a universal generating function (UGF) and Monte Carlo (MC) simulation are primary approaches for the reliability analysis of an MSS. However, these approaches incur a large computational overhead because the number of system states increases significantly with the number of components in an MSS. In this paper, stochastic multi-valued (SMV) models are proposed for evaluating the reliability of an MSS with dependent multi-state components (MSCs). The performance rates and their corresponding probabilities of the MSCs are simultaneously encoded in multi-valued non-Bernoulli sequences using permutations of fixed numbers of 1 s and 0 s. The sequences are then processed by logic gates. The effectiveness of the proposed approach is demonstrated via a comparative evaluation of a multi-state system consisting of dependent components with steady and time-varying state probabilities.

A new efficient algorithm for finding all d-minimal cuts in multi-state networks

Reliability evaluation of multi-state systems gives a reasonable demonstration of system performance, and thus is of great importance to their planning, designing and operation. One of the common methods for reliability evaluation is using d-minimal cuts (d-MCs). This paper proposes a new method to solve the d-MC problem. Specifically, several efforts have been devoted to searching for all d-MCs from two aspects: (i) A new technique is developed to calculate lower capacity bounds of edges which are appropriately used to determine some real d-MCs without any verification, and further to reduce the number of d-MC candidates; (ii) A new approach is put forward to correctly and effectively detect duplicate d-MCs, and the approach brings important insights into the underlying reason why a d-MC derived from one MC can be generated from another MC once again. A simple example and a real case study of the LCD monitor delivery are provided to illustrate the solution procedure, and the utility of the proposed algorithm, respectively. In addition, numerical experiments conducted on four benchmark networks show that the proposed algorithm outperforms a newly developed method in the literature.

Reliability evaluation of multi-state systems under cost consideration

A more practical and desirable performance index of multi-state systems is the two-terminal reliability for level (d,c) (2TRd,c), defined as the probability that d units of flow can be transmitted from the source node to the sink node with the total cost less than or equal to c. In this article, a simple algorithm is developed to calculate 2TRd,c in terms of (d,c)-MPs. Two major advantages of the proposed algorithm include: (1) as of now, it is the only algorithm that searches for (d,c)-MPs without requiring all minimal paths (MPs) and the procedure of transforming feasible solutions; (2) it is more practical and efficient in solving (d,c)-MP problem in contrast to the best-known method. An example is provided to illustrate the generation of (d,c)-MPs by using the presented algorithm, and 2TRd,c is thus evaluated. Furthermore, the computational experiments are conducted to verify the performance of the presented algorithm.

Reliability evaluation of multistate systems with multistate components : Terje Aven. IEEE Trans. Reliab.R-34(5), 473 (1985)

Reliability evaluation of multistate systems with multistate components : Terje Aven. IEEE Trans. Reliab.R-34(5), 473 (1985)

Reliability Evaluation of Multistate Systems with Multistate Components

This paper presents two efficient algorithms for reliability evaluation of monotone multistate systems with s-independent multistate components. The algorithms are based on the Doulliez & Jamoulle decomposition method. Algorithm 1 requires the minimal paths to be known; Algorithm 2 requires the minimal cuts to be known (the state of the system need not be specified for each vector of component states). Computer programs for implementing the algorithms are given. Computational-times are presented, and compared with the ``Inclusion-Exclusion Method'' and the ``State Enumeration Method''. The results demonstrate clearly the superiority of the algorithms to the two other methods.