Multi-state System Reliability Research Articles

Survival signature-based structural importance analysis of multi-state system with binary-state components

Abstract System reliability analysis aims to identify a system's weaknesses or critical components and quantify their failures' impact. Analyzing the influence of system components on system failure is a common problem in reliability engineering, known as the importance analysis of a system. Reliability analysis uses two main models: the binary-state system (BSS) and the multi-state system (MSS). To evaluate the reliability of MSS with binary-state components, computing methods of survival signature are studied. The structural functions of MSS and the survival signature allow for various mathematical approaches, including logical differential calculus (LDC). LDC can be employed to identify situations where a change in the number of functioning components leads to a change in the system's state, known as the structural importance measure. This paper presents a technique for calculating structural importance measures of MSS with binary-state components. The technique uses the survival signature of MSS instead of the structure function. It is based on logical differential calculus, specifically direct partial logical derivatives (DPLD). Numerical and application examples are provided to demonstrate and validate the technique, exhibiting its superiority and potential for real engineering use.

Evaluation and Management of Sustainable Supply Chain Systems with Carbon Emissions and Transport Damage Based on Multi-state System Reliability Assessment

Evaluation and Management of Sustainable Supply Chain Systems with Carbon Emissions and Transport Damage Based on Multi-state System Reliability Assessment

Reliability analysis of (r,s)-out-of-n multi-state systems using copulas

PurposeThis study evaluates the reliability of a multi-state system (MSS) with n components, each having two s-dependent components via copulas.Design/methodology/approachThe study employs copula functions to model dependencies between components in an MSS. Specifically, it analyzes a (1,1)-out-of-n three-state system using Frank and Clayton copulas for reliability evaluation. A simulation-based case study of a micro-inverter solar panel system is also conducted using the Farlie–Gumbel–Morgenstern (FGM) copula.FindingsThe study finds that incorporating component dependencies significantly impacts the reliability of multi-state systems. Using Frank and Clayton copulas, the analysis shows how dependency structures alter system performance compared to independent models. The case study on a micro-inverter solar panel system, using the FGM copula, demonstrates that real-world systems with dependent components exhibit different performances. Also some effects of dependence parameters on the performance characteristics of the system such as mean residual lifetime and mean past lifetime are also examined.Originality/valueThis study is original in its use of copula functions to evaluate the performance of multi-state systems, particularly focusing on a (1,1)-out-of-n three-state system with dependent components. By applying Frank and Clayton copulas, the research advances reliability analysis by considering component dependencies, often overlooked in traditional models. Additionally, a case study on a micro-inverter solar panel system using the FGM copula highlights the practical application of these methods.

Reliability modeling of multi-state phased mission systems with random phase durations and dynamic combined phases

Random phase durations and dynamic combined phases challenge the application of existing reliability models in the reliability analysis of multistate-phased mission systems (MS-PMSs). To this end, this paper presents a new reliability modeling method for multi-state phased mission systems with random phase durations and dynamic combined phases. Initially, a multi-state multi-valued decision diagram-based (MMDD-based) reliability modeling method is created to efficiently map random phase durations and the dynamic combined phase nature of MS-PMSs into the reliability model. To solve the MMDD-based reliability model, a path probability evaluation method is subsequently constructed with the assistance of the Markov regenerative function. The effectiveness and the superior performance of the proposed MMDD-based reliability model and its solving algorithm are validated by the application to the reliability modeling and analysis of an attitude and orbit control system with multiple modes. Overall, this paper provides the reliability sector with a new reliability model and its solving algorithm to enhance the reliability and safety of multi-state phased mission systems.

Multi-state system reliability: An emerging paradigm for sophisticated engineered systems

Multi-state system reliability: An emerging paradigm for sophisticated engineered systems

A Novel Multi-state Bogie System Reliability Evaluation Approach by Extended d-MC Model for High Speed Train

Abstract Bogie is a pivotal system and plays a critical part in the safety and reliability management of high speed rail. However, the available bogie system reliability analysis methods lack the consideration of multi-state characteristics, and the common multi-state reliability analysis methods, being an NP-hard problem, lead to a low efficiency. In order to overcome the mentioned drawbacks, this paper proposes a novel multi-state rail train bogie system reliability analysis approach based on the extended d-MC model. Three different function interactions within the bogie system are considered to build the multi-state bogie system flow network model. Meanwhile, an extended d-MC model is established to remove unnecessary d-MC candidates and duplicates, which greatly enhances the computing efficiency. The bogie system reliability is calculated, and the examples are provided. Numerical experiments are carried out for the different operational conditions of the bogie system and are used to testify the practicability of the method projected in this article, and is is found that the proposed method outperforms a newly developed method in solving the multi-state reliability problems.

Research on three-state reliability evaluation method of high reliability system based on multi-source prior information.

A high reliability system has the characteristics of complexity, modularization, high cost and small sample size. Throughout the entire lifecycle of system development, storage and use, the high reliability requirements and the risk analysis form a direct contradiction with the testing expenses. In order to ensure the system, module or component maintains good reliability status and effectively reduces the cost of sampling tests, it is necessary to make full use of multi-source prior information to evaluate its reliability. Therefore, in order to evaluate the reliability of highly reliable equipment under the condition of a small sample size correctly, the equipment reliability evaluation model should be built based on multi-source prior information and form scientific computing methods to meet the needs of condition evaluation and fund assurance of high reliability system. In engineering practice, high reliability system or module gradually develops from normal state to failure state, generally going through three working states of "safety-potential failure-functional failure". Firstly, the historical test data under the three states can be used for the data source for the reliability evaluation of the system at the current stage, which supplements the deficiency of the field data; secondly, due to the lack of accurate judgment on the working state of a high reliability system or modules and analysis of the health status, the unnecessary maintenance may aggravate the evolution speed from potential failure to functional failure; thirdly, when high reliability system or module operates under overload or harsh conditions, the potential failure will be worsened to a certain extent. Aiming at the difficulty of multi-state system reliability evaluation, a reliability evaluation method based on non-information prior distribution is proposed by fusing multi-source prior information, which provides ideas and methods for reliability evaluation and optimization analysis of high reliability system or module. The results show that the three-state reliability evaluation method proposed in this article is consistent with the actual engineering situation, providing a scientific theoretical basis for preventive maintenance of high reliability system. At the same time, the research method not only helps evaluate the reliability state of a high reliability system accurately, but also achieves the goal of effectively reducing test costs with good economic benefits and engineering application value.

Joint optimization of fleet-level sequential selective maintenance and repairpersons assignment for multi-state manufacturing systems

Due to limited maintenance resources, the joint optimization of fleet-level selective maintenance and repairpersons assignment aims to determine the optimal subset of maintenance actions for each repairperson to ensure that manufacturing systems in the fleet complete subsequent missions. However, related studies ignore the uncertain maintenance duration and flow dependency (a stochastic dependency caused by dynamic material flow) resulting in overestimation of system reliability and total profit. Therefore, this paper proposes a novel joint optimization model of fleet-level sequential selective maintenance and repairpersons assignment under flow dependency and uncertain maintenance duration. The model requires identifying a subset of maintenance actions, assigning the selected maintenance actions to repairpersons, and planning sequence of maintenance actions executed by each repairperson. Moreover, the degradation model of multi-state machines under flow dependency is established by analyzing dynamic characteristics of production processes. Further, the reliability of multi-state manufacturing systems considering the interaction among repairpersons, flow dependency, and uncertain maintenance duration is incorporated into the optimization model. The objective is to maximize the total profit under predetermined system reliability thresholds. Then, the optimization problem is solved by a tailored genetic algorithm with segment-based evolution strategy. Finally, numerical examples are given to verify the effectiveness of the proposed method.

Multi-state balance system reliability research considering load influence

Multi-state balance system reliability research considering load influence

Fusing Conflicting Multisource Imprecise Information for Reliability Assessment of Multistate Systems: A Two-Stage Optimization Approach

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

Warship Mission Reliability Modeling and Simulation from the Perspective of Equipment Support Resource

To address the complex role of equipment support resource allocation on mission reliability during warship missions, this study establishes a warship mission reliability simulation system by using agent-based modeling to simulate warship task flow, equipment reliability structures, fault rules, and equipment support resource allocation schemes. The simulation system has the characteristics of multielement, modular, flexible configuration and easy operation. The key metrics relevant to different task conditions, such as the mission reliability of multistage and multistate systems, and the number of recommended allocations of equipment support resources, can be calculated by the system. In addition, sensitivity analyses of task parameters, equipment reliability structure, and the number of spare parts is carried out, and the effects on task reliability are discussed. The influencing factors considered in the modeling and calculation of mission reliability are expanded in this study, which can provide technical support for the optimal allocation of shipboard equipment support resources during the use phase of a warship, and the supportability design of warship equipment during the development phase.

Reliability and importance analysis of multi-state system considering common cause failures

In this paper, a reliability and importance analysis method for common cause failure (CCF) of multi-state system (MSS) based on multi-valued decision diagram (MDD) is proposed. The MDD model mapped from the reliability block diagram (RBD) decomposes components into the collection of components influenced by the CCF and others with different component state probability vectors. An improved variable sorting heuristic algorithm is proposed to minimize the size of the MDD model by considering the number of component states and causality of common cause groups (CCGs). Through the composite importance measures (CIM), the possible state levels and state probabilities are incorporated into the calculation of MSS component importance. Finally, a case study is illustrated to verify the effectiveness and feasibility of the proposed method.

Measuring Conflicts of Multisource Imprecise Information in Multistate System Reliability Assessment

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

A generic physics-informed neural network-based framework for reliability assessment of multi-state systems

In this paper, we develop a generic physics-informed neural network (PINN)-based framework to assess the reliability of multi-state systems (MSSs). The proposed framework follows a two-step procedure. In the first step, we recast the reliability assessment of MSS as a machine learning problem using the framework of PINN. A feedforward neural network with two individual loss groups is constructed to encode the initial condition and the state transitions governed by ordinary differential equations in MSS, respectively. Next, we tackle the problem of high imbalance in the magnitudes of back-propagated gradients from a multi-task learning perspective and establish a continuous latent function for system reliability assessment. Particularly, we regard each element of the loss function as an individual learning task and project a task’s gradient onto the norm plane of any other task with a conflicting gradient by taking the projecting conflicting gradients (PCGrad) method. We demonstrate the applications of the proposed framework for MSS reliability assessment in a variety of scenarios, including time-independent or dependent state transitions, where system scales increase from small to medium. The computational results indicate that PINN-based framework reveals a promising performance in MSS reliability assessment and incorporation of PCGrad into PINN substantially improves the solution quality and convergence speed of the algorithm.

Angular Control Charts: A new perspective for monitoring reliability of multi-state systems

Control charts, as had been used traditionally for quality monitoring, were applied alternatively to monitor systems’ reliability. In other words, they can be applied to detect changes in the failure behavior of systems. Such purpose imposed modifying traditional control charts in addition to developing charts that are more compatible with reliability monitoring. The latter developed category is known as probability limits control charts. The existing reliability monitoring control charts were only dedicated to binary-state systems, and they cannot be used to monitor several states simultaneously. Therefore, this paper develops a design of control charts that accommodates multi-state systems, called here as the Angular Control Chart, which represents a new version of the probability limits control charts. This design is able to monitor state transitions simultaneously and individually in addition. Illustrative system examples are implemented to explore the monitoring procedure of the new design and to demonstrate its efficiency, effectiveness, and limitations.

Inference for stress–strength reliability of multi-state system with dependent stresses and strengths using improved generalized survival signature

Multi-state systems are widely used in engineering field, which usually contain complex internal structures and variable external environmental stresses. Discussing the reliability of such system has theoretical significance and application values. In this paper, a new stress–strength model for multi-state system consisting of multi-type multi-state components is introduced. Each type of components has two dependent strengths, which is suffered from two dependent stresses in working environment, while the strengths and stresses are independent. We discuss inferential procedures for stress–strength reliability of the multi-state system using the proposed improved generalized survival signature in the case of all types of components exposed to common pair of dependent stresses. Based on the assumption that strength variables follow Weibull and exponential distributions, as well as the stress variables, the expressions of stress–strength reliability of such multi-state system in different states are derived by using Gumbel and Clayton copulas. The pseudo maximum likelihood estimation is employed to estimate the dependence parameters and maximum likelihood estimation, asymptotic confidence interval, parametric bootstrap confidence interval and transformation-based confidence interval to make inference for stress–strength reliability. Monte Carlo simulations are carried out to compare the performances of the proposed estimation methods. Finally, a real data analysis is presented to illustrate the developed model and inferential procedures.

Analysis of a Stochastic Model with Rework System

The demand in the present global industrial system, requires the challenge to meet the growing consumer capabilities and requirements constantly. So, there is always a need to improve different parameters, one of them being different types of failures involved in the working of different engineering systems related to communication systems, manufacturing goods, nuclear and hydro power plants, automobiles and many others. Human error occurring in the working of various systems has always been the challenge to the researchers and is being constantly worked upon by the researchers in the analysis and improvement of reliability and availability of different complex and multistate systems. In the present paper, there is a three-unit system consisting of the unit A with two subunits in parallel and other units B and C are connected in series with A. The authors have investigated and analysed different reliability measures like availability, MTTF and sensitivity taking into account the human failure and carrying out rework system. This research work aims at the study of reliability and availability measures of a multi-state system incorporating human error so as to increase the efficiency of industrial systems by taking maintenance and rework measures to enhance the availability factors. This would help to understand and estimate the reliability measures of any such systems in the field of telecommunication, any electronic devices like that in small power plants, robot systems and such others. Also, a comparison has been made between the availability and reliability estimates in the presence and in the absence of human error. The techniques used are Markov process, Laplace transformation and supplementary variable technique.

Evaluating multi-state systems reliability with a new improved method

The computation of network reliability for a system with many states is an NP-hard issue. Finding all the minimum path vectors (d-MPs) lower boundary points for each level d is one of the few approaches for computing such dependability. This research proposed enhancements to the technique described in Chen's "Searching for d-MPs with rapid enumeration" paper. We propose additional adjustments to the method that creates the flow vector F in this enhancement. This decreases the number of required steps and the temporal complexity of the method. Comparing the newly suggested approach to the old algorithm reveals that the adjustment has increased the enumeration's efficiency and degree of complexity.

Three-parameter interval number theory and its application in power system reliability evaluation

With the increasing integration of renewable energy in the power system, its strong volatility and randomness will greatly affect the planning and operation of the power system. In this situation, compared to the traditional point-value-based reliability assessment results, system operators prefer the results which can give the most likely recommended values and their possible ranges. To this end, in this paper, we present a novel framework to evaluate the reliability of multi-state power systems that incorporates three-parameter interval number theory and improved universal generating function method. In particular, we first improve the three-parameter interval number theory by proposing a similarity-based indicator to describe the distance (or closeness-degree) between two three-parameter interval numbers and redefine the probability that one three-parameter interval number is greater or less than another one. Secondly, we extended the traditional universal generating function to a three-parameter interval number-based universal generating function. Moreover, the three-parameter interval number-based universal generating functions of conventional generators, renewable energy generators and load demand are further established to describe their multi-state characteristics. At last, a three-parameter interval number-based loss of load expectation metric is presented for reliability evaluation. Compared with the existing methods, the proposed framework can well evaluate the reliability of multi-state power systems, and can describe the uncertainty of reliability evaluation results through the three-parameter interval number, thus providing the most likely value of the evaluation result and its fluctuation range at the same time. In the numerical simulation part, a comparison of five different scenarios is performed on an IEEE Reliability Test System. The results show that the proposed method is suitable for the reliability assessment of power systems with high penetration of renewable energy, which can describe the fluctuation range and indicate the most possible value of reliability simultaneously.

Multistate Reliability Analysis of Recessive Fault of Mechanical Meta-Action Unit Based on Markov Process

In order to clearly express the reliability dynamic change process of mechanical meta-action units with recessive fault on continuous time series, this paper proposes a reliability analysis method for multistate systems with recessive failures of mechanical meta-action units based on the fusion of vibration signal analysis and Markov process. By analyzing the vibration signal, five major recessive fault types of mechanical meta-action units are determined. By analyzing the experimental data and based on the average time of the first occurrence of five major recessive faults, a performance level state representation model of mechanical meta-action unit based on fault importance weight is established. Then, based on the repairable characteristics of the mechanical element action unit, the two-way state transition model and state probability differential equation of mechanical meta-action units are established, and the state probability of each state is obtained. Next, under the condition of determining the initial state, the change process curves of the instantaneous availability, instantaneous average performance, and instantaneous average performance deficit of the mechanical meta-action unit are obtained by solving the reliability index calculation formula. Finally, this paper takes the worm rotation meta-action unit as an example to verify the law and probability of the state transition of the mechanical meta-action unit, and the performance level change accompanying the state transition process, by analyzing the failure modes and causes of recessive faults, the corresponding reliability control measures are formulated, and the control effects before and after reliability control are analyzed. The research results show that this method can effectively improve the accuracy of the state probability when calculating the state probability of each state, and compared with the discrete Markov model, when studying the reliability of complex multistate systems, this method can dynamically describe the change process of state probability, instantaneous availability, instantaneous average performance, and instantaneous average performance deficit in real time under the condition of continuous time-dependent variables. It has certain guiding significance for the reliability analysis of mechanical element action units in the long-term range.