Reliability Analysis Of Multi-state Systems Research Articles

Reliability analysis of multi-state series systems with k-out-of-n: G subsystems considering performance sharing

Motivated by real-world engineering systems, this paper presents an in-depth exploration of a novel reliability model for a complex multi-state series system (MSSS) that incorporates a performance sharing mechanism. Specifically, the MSSS is composed of m distinct subsystems featuring a k-out-of-n: G structure. The ith subsystem consists of ni elements, such that a minimum of ki functioning elements is required for normal operation. Transmission devices (TDs) are present between adjacent subsystems to share surplus performance. Both element performance and subsystem demand are treated as random variables, and the performance of all elements in each subsystem is cumulated to meet its individual random demand. Subsystem failure can result from either an inability to meet performance demands or an insufficient number of functioning elements. The surplus performance of a subsystem can only be transferred to its adjacent subsystem via the TD. The entire MSSS will fail if at least one subsystem does not work properly by using performance sharing mechanism. To analyze the reliability indexes of the MSSS, a new algorithm based on the generalized universal generating function (GUGF) has been developed. Numerical examples are provided to illustrate the accuracy and effectiveness of the proposed model and method.

Reliability analysis of interval-valued multi-state sliding window system for sequential tasks

In industrial applications, an interval variable with both an upper and a lower bound is utilized to define the bounded or ranged performance of a system or its elements. This paper proposes a new interval-valued multi-state sliding window system for sequential tasks (IMSWS-ST). The proposed system consists of n circularly or linearly connected multi-state elements (MEs) with their performance states described as interval-valued variables. The system function is determined by the ability of any group of r consecutive MEs for completing predetermined sequential tasks with interval-valued demands. To describe and evaluate system reliability, a universal generating function technique is employed, considering the differences between linear and circular configurations. Additionally, we develop a state aggregation method to reduce the computational burden during reliability evaluation. Numerical experiments are then conducted to demonstrate the proposed system model and validate the suggested algorithms. Finally, we investigate the optimal sequencing problem for MEs within the IMSWS-ST to achieve higher system reliability.

Reliability analysis on energy storage system combining GO-FLOW methodology with GERT network

Energy storage systems are widely used in various industrial areas, playing a crucial role in improving system reliability. In the energy storage system, the batteries serve as standbys for generators and have an auxiliary regulation function, so the complex relationship between them is unable to be accurately described by the basic GO-FLOW operators. To address this issue, this paper proposes a new operator for simulating the energy storage system, employing the GERT network for modelling and calculation. In this approach, the energy storage system operator is created to represent the energy storage system with ‘n generators with l degradation states, m batteries’. Firstly, each degradation state of generators is determined. Secondly, each macro state of the energy storage system is determined by combining the states of the batteries. Finally, based on the relationships between these states, the steady-state availability of the energy storage system is obtained using the GERT algorithm. A numerical example of a repairable power supply system is employed to validate the feasibility and effectiveness of the model and algorithm. And this method holds great significance for the reliability analysis of multi-state complex systems.

Reliability analysis of multi-state balanced systems with standby components switching mechanism

An increasing attention has been paid to the reliability analysis of balanced system. In previous studies, there were three rebalancing strategies for balanced systems: forcing down the unbalanced pair of subsystems, restarting components that have been shut down, and dynamically adjusting the state of the working components. In this paper, a new rebalancing strategy is proposed by switching the standby components for a multi-state balanced system. The system consists of m subsystems, each with one working component and n-1 standby components. The system is balanced when the working components do not fail and the system's balanced degree doesn't exceed a threshold. Two cases of system balance conditions are considered: one is based on component states and the other is based on symmetric component states. If the system is imbalanced or fails, the system needs to adjust the state of the working component by switching switches to let the system operate normally. The switching rules for each case are given separately. In this paper, the finite Markov chain imbedding approach (FMCIA) is used to derive the system reliability. Finally, numerical examples and sensitivity analysis are given.

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.

Reliability analysis of repairable multistate phased mission systems with Markov approach based on states

PurposeThe purpose of this study is to find the reliability of the three-component three-phased mission system, which can be repaired by considering the exponential distribution for repair and failure rates in the transitions between the phases based on states with Markov approach. Also, multilevel-phased mission systems are calculated based on states for partially working states.Design/methodology/approachThe reliabilities of the repairable two-level and three-level three-component three-phased mission systems based on states are calculated with the Markov approach. The structure functions are obtained for each phase of the systems, and differential equations are created by the failure and repair of each working state component. These equations are solved using Laplace method.FindingsReliability values of two-level and three-level three-component three-phased systems with different failure, repair, and time intervals are calculated and compared. The intermediate states that multilevel systems handle differently from two-level systems provide a better investigation of the systems. So, these repairable systems offer transparent information in complex systems like transportation and energy, ensuring appropriate timing and cost for repair operations.Originality/valueThis study is original in terms of calculating the reliability of the repairable phased mission system based on the states using Markov method. It is also important in calculating the reliability of the repairable multilevel phased mission system based on states and making reliability comparisons according to different repair and failure rates, equal and different time intervals.

Reliability analysis of complex multi-state system based on universal generating function and Bayesian Network

In the complex multi-state system (MSS), reliability analysis is an important research content, both for equipment design, manufacturing, operation and maintenance. Universal Generating Function (UGF) is an essential method in reliability analysis, which efficiently obtains system reliability by a fast algebraic procedure. However, when structural relationships between subsystems or components are unclear or without explicit expressions, the UGF method is difficult to use or not applicable at all. Bayesian Network (BN) has a natural advantage in terms of reliability inference for the relationship without explicit expressions. When the number of components is extremely large, though, it has the defects of low efficiency. To overcome the respective shortcomings of UGF and BN, a novel reliability analysis method called UGF-BN is proposed for the complex MSS. In the UGF-BN framework, the UGF method is first used to analyze the bottom components with a large number. Then probability distributions obtained are taken as the input of BN. Finally, the reliability of the complex MSS is modeled by the BN method. This proposed method improves the computational efficiency, especially for the MSS with a large number of bottom components. Besides, the aircraft reliability-based design optimization based on the UGF-BN method is further studied with budget constraints on mass, power, and cost. Finally, two cases are used to demonstrate and verify the proposed method.

A novel approach based on fault tree analysis and Bayesian network for multi-state reliability analysis of complex equipment systems

Due to the complex structure of multi-state complex systems and the lack of data, information, and knowledge, the uncertainty of the logical relationship between the failure states of systems and components and the uncertainty of related failure data become the key issues in the reliability analysis of multi-state complex systems. In this paper, combined with multi-state fault tree (MSFT), a multi-state reliability assessment framework for complex systems considering uncertainty based on multi-source information fusion and multi-state Bayesian network (MSBN) is proposed. The multi-source information fusion method combines historical data and experts’ opinions to solve the uncertainty problem of multi-state failure data in complex equipment systems effectively. Based on the multi-source information fusion method, the calculation method of multi-state prior probability and the construction method of conditional probability are given. By constructing the conditional probability table (CPT), the uncertain logic relationship between the multi-state nodes is effectively expressed, which effectively improves the efficiency of CPT acquisition for MSBN and reduces the workload of experts scoring. Finally, a mud circulating system is taken as an example to prove the proposed method, and the specific calculation process, evaluation results, and some discussions are given. The results show that the proposed method is an effective multi-state reliability analysis method for complex uncertain multi-state systems.

Reliability Analysis of Multiperformance Multistate System Considering Performance Conversion Process

A large variety of real engineering systems operate with multiple performance measures that are multistate in nature. These systems are usually modeled as multiperformance multistate systems (MPMSSs). However, existing MPMSS models fail to consider an important aspect, i.e., the performance conversion process. For example, in a combined heat and power (CHP) generating unit, apart from the output heat and electricity, decision-makers are also interested in the unit's capacity to convert gas into electricity and heat. The latter is related to the performance conversion process. This article proposes a framework for the reliability evaluation of performance conversion-based MPMSS. In the proposed MPMSS model, the couplings among different types of performances inside the components are quantified into the multistate performance conversion matrix. The performance conversion structure functions are proposed to derive system performance conversion capability based on the conversion capabilities of the components. Two reliability evaluation methods considering the steady-state performance conversion process and the continuous-time performance conversion process are proposed, respectively. Numerical examples are given to demonstrate the developed methods.

Reliability analysis of multi-state systems with lag-dependent components

In a multi-state system (MSS) with dependent components, the performance distributions of low priority components (LPCs) depend on the states of high priority components (HPCs). However, the relationship between LPCs and HPCs is usually considered as the instantaneous dependency (instant-dependency). In practice, the dependency between them is lagging due to the electronic circuits, i.e, the performance distributions of LPCs would be changed after a certain transmission time when one state of HPCs transfers to another. In this paper, the lag-dependency between LPCs and HPCs in a MSS is considered. At the beginning of transfer of each state for HPCs, three kinds of lag threshold values are set to quantify the transmission time from HPCs to corresponding LPCs. Due to the lag-dependency, the sojourn time and probabilities of states of HPCs are reanalyzed. As an important method of reliability analysis, the universal generating function is utilized to analyze the reliability of a MSS with lag-dependent components. The effectiveness of the proposed methods is proved via a comparative analysis of MSSs with instant-dependent components and lag-dependent components. The results show that the reliability of MSS would be underestimated if the lag-dependency is not considered.

Mission aborting and system rescue for multi-state systems with arbitrary structure

Rescue procedures (RP), triggered either by the occurrence of the mission failure or by a certain undesired system state, are usually applied to survive a life-critical or safety-critical system mitigating or avoiding costly consequences. Existing works model either the mission failure-triggered RP or the system state-triggered RP, but not both. This paper makes contributions by co-modeling both types of RPs in the reliability analysis of multi-state systems with arbitrary structure and heterogeneous system elements. The system performs a primary mission (PM) with the specified time duration. System configuration (i.e., required subset of working elements and system functioning criteria) and reliability characteristics of system elements are different during PM and RP. A probabilistic modeling method is proposed to analyze reliability metrics of the considered system in forms of mission success probability (MSP) and system survival probability (SSP). Based on the MSP and SSP evaluation, two types of mission abort rules (performance constraint-based and system state subset-based) are investigated and compared. An example of an electrical heating system is provided to illustrate the proposed method and solutions to the optimal mission aborting policy that maximizes MSP subject to meeting a certain level of SSP.

Multi-State System Reliability Analysis with Two Types of Common Cause Shock Failures

Multi-State System Reliability Analysis with Two Types of Common Cause Shock Failures

A C++ class for multi-state algebraic reliability computations

We present the design and implementation of a C++ class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source CoCoALib library and provides functions to compute system reliability and bounds. The algorithms we present may be applied to general systems with independent components having identical or non-identical probability distributions.

Reliability Analysis of a Complex Multistate System Based on a Cloud Bayesian Network

This study focused on mixed uncertainty of the state information in each unit caused by a lack of data, complex structures, and insufficient understanding in a complex multistate system as well as common-cause failure between units. This study combined a cloud model, Bayesian network, and common-cause failure theory to expand a Bayesian network by incorporating cloud model theory. The cloud model and Bayesian network were combined to form a reliable cloud Bayesian network analysis method. First, the qualitative language for each unit state performance level in the multistate system was converted into quantitative values through the cloud, and cloud theory was then used to express the uncertainty of the probability of each state of the root node. Then, the β-factor method was used to analyze reliability digital characteristic values when there was common-cause failure between the system units and when each unit failed independently. The accuracy and feasibility of the method are demonstrated using an example of the steering hydraulic system of a pipelayer. This study solves the reliability analysis problem of mixed uncertainty in the state probability information of each unit in a multistate system under the condition of common-cause failure. The multistate system, mixed uncertainty of the state probability information of each unit, and common-cause failure between the units were integrated to provide new ideas and methods for reliability analysis to avoid large errors in engineering and provide guidance for actual engineering projects.

Reliability analysis of discrete multi-state systems based on survival signature

System signature has been widely utilized to facilitate reliability assessment of coherent systems and networks consisting of a single type of components, which enables us to separate aspects of components’ failure time and system structure. Recently, survival signature fulfils the similar work, extended to the implementation of systems with multiple types of components. However, when the system has several states, the relevant work is limited to complete the reliability assessment by the survival signature. This paper proposed a novel pattern of survival signature for the multi-state system with multiple types of components and the presented approach is executed to demonstrate the validity via a numerical case with 2-type and 3-state components.

Reliability Characterization of Binary-Imaged Multi-State Coherent Threshold Systems

A notable reliability model is the binary threshold system (also called the weighted-k-out-of-n system), which is a dichotomous system that is successful if and only if the weighted sum of its component successes exceeds or equals a particular threshold. The aim of this paper is to extend the utility of this model to the reliability analysis of a homogeneous binary-imaged multi-state coherent threshold system of (m+1) states, which is a non-repairable system with independent non-identical components. The paper characterizes such a system via switching-algebraic expressions of either system success or system failure at each non-zero level. These expressions are given either (a) as minimal sum-of-products formulas, or (b) as probability–ready expressions, which can be immediately converted, on a one-to-one basis, into probabilities or expected values. The various algebraic characterizations can be supplemented by a multitude of map representations, including a single multi-value Karnaugh map (MVKM) (giving a superfluous representation of the system structure function S), (m+1) maps of binary entries and multi-valued inputs representing the binary instances of S, or m maps, again of binary entries and multi-valued inputs, but now representing the success/failure at every non-zero level of the system. We demonstrate how to reduce these latter maps to conventional Karnaugh maps (CKMs) of much smaller sizes. Various characterizations are inter-related, and also related to pertinent concepts such as shellability of threshold systems, and also to characterizations via minimal upper vectors or via maximal lower vectors.

Enhanced reliability analysis method for multistate systems with epistemic uncertainty based on evidential network

AbstractEvidential network is considered to have superiority in conducting reliability analysis for complex engineering systems with epistemic uncertainty. However, existing methods tend to result in combinational explosion when multistate systems are involved in the reliability analysis, which means the reliability analysis cost increases exponentially with the number of components and that of functioning states. Therefore, an enhanced reliability analysis method is proposed in this paper for reliability analysis and performance evaluation of multistate systems with epistemic uncertainty, through which the combination explosion can be significantly alleviated. Firstly, the functioning states of each component are sequenced according to utility functions. Secondly, the basic belief assignment (BBA) of each component is reassigned in terms of commonality function, through which the BBA defined in the power set space is represented by two extreme BBA distributions defined in the frame of discernment. Thirdly, the reliability intervals of the system states are calculated through evidential network, and the system performance level is computed. Two multistate system numerical examples are investigated to demonstrate the effectiveness and efficiency of the proposed method.

Reliability Analysis of Common Cause Failure Multistate System Based on CUGF

This paper addresses the problem of mixed uncertainty in the reliability analysis of multistate systems under common cause failure conditions. Combining the cloud model theory, universal generation function (UGF) method, and common cause failure theory, the universal generation function method is extended based on a probabilistic cloud model, i.e., the cloud universal generation function (CUGF) analysis method. The cloud model represents the random and cognitive uncertainty of the state probability, i.e., mixed uncertainty. Next, through CUGF, according to the calculation rules of cloud operators, we provide steps to obtain the reliability of a multistate system under independent failure and common cause failure conditions and obtain cloud digital features for reliability. The accuracy and feasibility of the method are verified by a numerical example. This paper solves the problem of reliability analysis of multistate systems with mixed uncertainty in unit state probability information under common cause failure conditions. We integrate system multistate, information uncertainty, and common cause failure for reliability analysis to avoid large errors, more in line with a project’s actual situation. We propose new ideas and methods to process randomness and fuzzy information or data in multistate system reliability analysis.

Probabilistic model-checking based reliability analysis for failure correlation of multi-state systems

Many conventional reliability analysis methods for multi-state systems assume independence among the various subsystems. To avoid this, we propose a probabilistic model checking-based approach for failure correlation analysis of multi-state systems. First, an improved Apriori algorithm is used to determine the effect of a subsystem failure on the associated subsystems. Next, a copula function is applied to establish the relationship between failures of the associated subsystems. Finally, probabilistic model-checking is used to analyze the reliability of the entire system and all its subsystems. The effectiveness of the proposed method is verified using an application involving offshore wind turbines. The results show that the proposed method can be used flexibly and effectively for multi-state system reliability analysis. Moreover, the proposed method lays the foundation for system maintenance strategy formulation and other engineering applications.

Application of GO methodology in reliability analysis of aircraft flap hydraulic system

ABSTRACTThe Goal-Oriented methodology (GO methodology) is an effective method for the reliability analysis of complex systems. It is especially suitable for the reliability analysis of multi-state complex systems containing the actual logistics, such as current, airflow and liquid flow. In order to solve the limitation that the GO methodology is not suitable for the reliability analysis of the system with feedback loop, the Boolean algebra idea is introduced to construct the Boolean operation formula of the feedback loop. In this paper, a certain type of civil aircraft flap hydraulic system with feedback loop is taken as the research object. According to the structural schematic diagram of the flap hydraulic system, the GO model of the flap hydraulic system is established. Next, the GO calculation is carried out to obtain the reliability of the flap hydraulic system. The comparison between the system reliability without feedback loop and that with feedback loop proves that the GO methodology with feedback loop is more accurate. The reliability of the system is analyzed by using the fault tree analysis (FTA) method, and the GO methodology with feedback loop is compared with the FTA method to verify the availability and correctness of the GO methodology in the reliability analysis and safety evaluation of aircraft flap hydraulic system.