Multi-state System Reliability Research Articles

Reliability of multi-state systems with a performance sharing group of limited size

Previous research in series systems assumes that each element must satisfy its own demand individually. However, the surplus performance from some elements can be transmitted to other deficient elements in some practical systems such as power generating systems and collaborative computing systems. In this paper, we consider a series system with a performance sharing group of limited size, i.e., the number of elements that can be connected into the performance sharing group is limited. It is assumed that the elements connected into the performance sharing group can change dynamically when the state of the system changes in order to minimize the possible performance deficiency of the system. A reliability evaluation algorithm is proposed for the suggested system and the optimal connection strategy is discussed. Numerical experiments are conducted to illustrate the applications.

A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation

Structural complexity of systems, coupled with their multi-state characteristics, renders their reliability and availability evaluation difficult. Notwithstanding the emergence of various techniques dedicated to complex multi-state system analysis, simulation remains the only approach applicable to realistic systems. However, most simulation algorithms are either system specific or limited to simple systems since they require enumerating all possible system states, defining the cut-sets associated with each state and monitoring their occurrence. In addition to being extremely tedious for large complex systems, state enumeration and cut-set definition require a detailed understanding of the system׳s failure mechanism. In this paper, a simple and generally applicable simulation approach, enhanced for multi-state systems of any topology is presented. Here, each component is defined as a Semi-Markov stochastic process and via discrete-event simulation, the operation of the system is mimicked. The principles of flow conservation are invoked to determine flow across the system for every performance level change of its components using the interior-point algorithm. This eliminates the need for cut-set definition and overcomes the limitations of existing techniques. The methodology can also be exploited to account for effects of transmission efficiency and loading restrictions of components on system reliability and performance. The principles and algorithms developed are applied to two numerical examples to demonstrate their applicability.

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.

Multi-state System Reliability Modeling and Optimization with Considering Dynamic Load Distribution Mechanism

Multi-state System Reliability Modeling and Optimization with Considering Dynamic Load Distribution Mechanism

Reliability analysis of excavator rectifier feedback system with multi-state components based on belief universal generating function method

In view of the complexity and uncertainty of system, both the state performances and state probabilities of multi-state components can be expressed by interval numbers. The belief function theory is used to characterize the uncertainty caused by various factors. A modified Markov model is proposed to obtain the state probabilities of components at any given moment and subsequently the mass function is used to represent the precise belief degree of state probabilities. Based on the primary studies of universal generating function (UGF) method, a belief UGF (BUGF) method is utilized to analyze the reliability and the uncertainty of excavator rectifier feedback system. This paper provides an available method to evaluate the reliability of multi-state systems (MSSs) with interval state performances and state probabilities, and also avoid the interval expansion problem.

New method for multi-state system reliability analysis based on linear algebraic representation

Multi-state system is a certain complex system with failure criteria that are not limited to “normal or failure.” During the life cycle, both the system and each component inside have different states at any time point. State transition of the whole system depends on the structure function while that of any component has a certain mechanism. To directly express state transition processes of the whole system and all components, we develop a linear algebraic representation method. Based on this method, dynamic transition can be expressed by mathematic equations, in which information of both system structure function and components transition mechanism is embedded. Furthermore, the extended multi-state dynamic fault tree is introduced to multi-state system modeling. By means of the proposed linear algebraic representation, standard operating rules for both static and dynamic gates are generated by introducing two variables that are used to determine whether the transition occurs and which state the output would convert into, respectively. Then, a Monte Carlo simulation coupled with the multi-state dynamic fault tree method is proposed to calculate the reliability indices of a multi-state system. The proposed method is then validated with a dynamic fault tree problem from a literature. Finally, the servo turret system is taken as an example for the application of the proposed method.

Bayesian Reliability and Performance Assessment for Multi-State Systems

This paper develops a Bayesian framework to assess the reliability and performance of multi-state systems (MSSs). An MSS consists of multiple multi-state components of which the degradation follows a Markov process. Due to the lack of sufficient data, and only vague knowledge from experts, the transition intensities of multi-state components between any pair of states and the state probabilities cannot be precisely estimated. The proposed Bayesian method can merge prior knowledge from experts' judgments with continuous and discontinuous inspection data to obtain posterior distributions of transition intensities. A simulation method embedded with the universal generating function (UGF) is developed to estimate the posterior state probabilities, the reliability, and the performance of the entire MSS. Two numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Reliability Optimization for Multi-State Series-Parallel System Design Using Ant Colony Algorithm

In this paper, an algorithm based ant colony approach (ACA) is designed to find the optimal configuration for redundancy apportionment problem (RAP) of series-parallel multi-state system (MSS). In order to achieve maximum system reliability under cost and performance constraints, the algorithm takes advantage of ACA’s combinatorial optimization, uses heuristic information about reliability to arrange components from available choice. Different from traditional nominal performance and reliability system, universal generating function (UGF) is introduced and used to estimate the multi-state system reliability. Finally the experiment has shown that the presented algorithm can provide optimal and near optimal solutions, and have efficient and convenient calculation performance.

A model for reliability analysis of multi-state manufacturing systems

Purpose – The purpose of this paper is to investigate the reliability analysis of a multi-state manufacturing system with different performance levels. In, fact, reliability assessment of manufacturing systems gives a reasonable demonstration of system performance. Design/methodology/approach – This research utilizes a multi-state system reliability analysis to develop a new metric for evaluating production systems. Findings – The proposed model provides a sensible measure to assess the system situation against the best-case scenario of a production line. Originality/value – The proposed model incorporates not only failures that stop production but also deals with partial failures where the system continues to operate at reduced performance rates. The analyses are represented in a best-case vs worst-case situation. Each of these cases provides insight for managers with respect to planning operation and maintenance activities.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods

In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed universal generation function (UGF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. This research deals with evaluating non-repairable three-state systems reliability and proposes a novel method based on a Markov process for which an appropriate state definition is provided. It is shown that solving the derived differential equations significantly reduces the computational time compared to the UGF and the recursive algorithm.

Coloured stochastic Petri nets modelling for the reliability and maintenance analysis of multi-state multi-unit systems

Purpose – The purpose of this paper is to introduce a method for modelling the multi-state repairable systems subject to stochastic degradation processes by using the coloured stochastic Petri nets (CSPN). The method is a compact and flexible Petri nets model for multi-state repairable systems and offers an alternative to the combinatory of Markov graphs. Design/methodology/approach – The method is grounded on specific theorems used to design an algorithm for systematic construction of multi-state repairable systems models, whatever is their size. Findings – Stop and constraint functions were derived from these theorems and allow to considering k-out-of-n structure systems and to identifying the minimal cut sets, useful to monitoring the states evolution of the system. Research limitations/implications – The properties of this model will be studied, and new investigations will help to demonstrate the feasibility of the approach in real world, and more complex structure will be considered. Practical implications – The simulation models based on CSPN can be used as a tool by maintenance decision makers, for prediction of the effectiveness of maintenance strategies. Originality/value – The proposed approach and model provide an efficient tool for advanced investigations on the development and implementation of maintenance policies and strategies in real life.

Random Fuzzy Extension of the Universal Generating Function Approach for the Reliability Assessment of Multi-State Systems Under Aleatory and Epistemic Uncertainties

Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties. First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle. Finally, an efficient algorithm is designed to extract probability boxes ( p-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system availability and reliability estimation. The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.

Reliability of Series-Parallel Systems With Random Failure Propagation Time

This paper presents an algorithm for evaluating the reliability and performance distribution of complex non-repairable series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originating from different elements can cause failures of different subsets of system elements. The failure propagation time is assumed to be a random value with a given distribution. The suggested algorithm is based on the universal generating function approach, and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The evaluation procedure is repeated for each combination of elements affected by the common cause failures. Illustrative examples are provided.

Probabilistic production simulation of a power system with wind power penetration based on improved UGF techniques

Universal Generating Function (UGF) techniques have been applied to Multi-State System (MSS) reliability analysis, such as long term reserve expansion of power systems with high wind power penetration. However, using simple steady-state distribution models for wind power and large generating units in reliability assessment can yield pessimistic appraisals. To more accurately assess the power system reliability, UGF techniques are extended to dynamic probabilistic simulation analysis on two aspects of modelling improvement. Firstly, a principal component analysis (PCA) combined with a hierarchal clustering algorithm is used to achieve the salient and time-varying patterns of wind power, then a sequential UGF equivalent model of wind power output is established by an apportioning method. Secondly, other than the traditional two-state models, the conventional generator UGF equivalent model is established as a four discrete-state continuous-time Markov model by Lz-transform. In the construction process of such a UGF model, the state values are transformed into the integral multiples of one common factor by choosing proper common factors, thus effectively restraining the exponential growth of its state number and alleviating the explosion thereof. The method is suitable for reliability assessment with dynamic probabilistic distributed random variables. In addition, by acquiring the clustering information of wind power, the system reliability indices, such as fuel cost and CO2 emissions through different seasons and on different workdays, are calculated. Finally, the effectiveness of the method is verified by a modified IEEE-RTS 79 system integrated with several wind farms of historical hourly wind power data of Zhangbei wind farm in North China.

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.

Multiple-Valued Logic mathematical approaches for multi-state system reliability analysis

A mathematical description of an examined system such as Multi-State System (MSS) permits the system reliability to be analyzed in more detail, because the MSS defines some performance levels (more than only working and failure). The structure function is one of the basic definitions and representations of MSS. But the dimension of the structure function increases critically depending on the number of system components. Therefore, the development of methods for examination and quantification of such a function is an actual problem in MSS reliability analysis. In this paper, a method for the analysis of the MSS structure function of high dimension is proposed. The principal point of this method is the interpretation of the MSS structure function as a Multiple-Valued Logic function. It allows effective and approved mathematical methods of Multiple-Valued Logic to be used for analysis and quantification of the MSS structure function. We propose to use two mathematical approaches of Multiple-Valued Logic for the MSS. One of them is a representation of the MSS structure function by a Multiple-Valued Decision Diagram. It is an effective approach for analysis and estimation of the function of high dimension in Multiple-Valued Logic. The other approach is Logic Differential Calculus. Logic Differential Calculus is a useful approach for analysis of the MSS state changes.

An extension of Universal Generating Function in Multi-State Systems Considering Epistemic Uncertainties

Many practical methods and different approaches have been proposed to assess Multi-State Systems (MSS) reliability measures. The universal generating function (UGF) method, introduced in 1986, is known to be a very efficient way of evaluating the availability of different types of MSSs. In this paper, we propose an extension of the UGF method considering epistemic uncertainties. This extended method allows one to model ill-known probabilities and transition rates, or to model both aleatory and epistemic uncertainty in a single model. It is based on the use of belief functions which are general models of uncertainty. We also compare this extension with UGF methods based on interval arithmetic operations performed on probabilistic bounds.