Minimal Path Sets Research Articles

Precise Modeling and Analysis of Aviation Power System Reliability via the Aviation Power System Reliability Probability Network Model

This study addresses the challenges of accurately analyzing the reliability of aviation power systems (APS) using traditional models by introducing the Aviation Power System Reliability Probability Network Model (APS-RPNM). The model directly transforms the system architecture into an equivalent probability network, aiming to develop a precise reliability model that captures system functions and fault logic. By classifying APS components into five distinct structural patterns and mapping them to corresponding nodes in the APS-RPNM, the model is successfully constructed. Specifically, None-Input-to-Multiple-Output components are transformed into two-state nodes, while Multiple-Input-to-None-Output, Single-Input-to-Multiple-Output, and Multiple-Input-to-Single-Output components are mapped to three-state nodes. For Multiple-Input-to-Multiple-Output components, a novel approach employing multiple two-state sub-nodes is adopted to capture their complex functional logic. A case study comparing the performance of the APS-RPNM with the traditional minimal path set method in reliability analysis was conducted. The results demonstrate that the APS-RPNM not only simplifies the model construction process and eliminates errors stemming from subjective engineering judgments but also enables the efficient computation of power supply reliability for all load points in a single inference by integrating all of the components. This significantly improves computational efficiency and system dependency analysis capabilities, highlighting the APS-RPNM’s tremendous potential in optimizing the reliability design of APS.

Risk assessment of fire and explosion accidents in oil-hydrogen fueling station based on fault tree analysis

Owing to the coexistence of gasoline, diesel, and hydrogen, a specific and thorough risk assessment approach must be promptly implemented for oil-hydrogen fueling stations. Consequently, this study makes innovations in considering the safety issues of the joint construction of gas station and hydrogen refueling station, and undertaking the modeling and analysis of fire and explosion incidents at oil-hydrogen fueling stations based on fault tree analysis. The findings reveal that the risk level for fire and explosion at oil-hydrogen fueling stations is categorized as grade III. In our fault tree analysis model, there are 3240 minimum cut sets and 194 minimum path sets. The probability of fire and explosion incidents occurring at oil-hydrogen fueling stations is calculated to be 0.000265. This indicates that while the possibility of such accidents is low, their potential severity is exceedingly high. Ultimately, it is recommended that the safety of oil-hydrogen fueling stations be enhanced through the reinforcement of emergency management, customer safety education, and electrostatic discharge devices.

Determining reliability signature by minimal cut method for complex-parallel network

The process of counting minimal cut sets (MCS) in a network is typically more difficult than finding minimal path sets (MPS). The first aim of this work is to provide a precise and effective method for counting the (MCS) of directed networks. The second aim is to calculate the effectiveness of a complex-parallel network using the (MCM) to evaluate the reliability of a complex-parallel network. The (MCM) has been applied for predicting network reliability, minimal (MS), tails signatures (TS), signatures, and Barlow-Brochan indexes.

A flow-directed minimal path sets method for success path planning and performance analysis

Emergency operation plans are indispensable elements for effective process safety management especially when unanticipated events occur under extreme situations. In the paper, a synthesis framework is proposed for the integration success path planning and performance analysis. Within the synthesis framework, success path planning is implemented through flow-directed signal tracing, renaming and reconstruction from a complete collection of Minimal Path Sets (MPSs) that are obtained using graph traversal search on GO-FLOW model diagram. The performance of success paths is then evaluated and prioritized according to the task complexity and probability calculation of MPSs for optimum action plans identification. Finally, an Auxiliary Feed Water System of Pressurized Water Reactor (PWR-AFWS) is taken as an example system to demonstrate the flow-directed MPSs search method for success path planning and performance analysis. It is concluded that the synthesis framework is capable of providing procedural guidance for emergency response and safety management with optimal success path planning under extreme situations.

Criticality-based allocation of active redundancies for asymmetric components in coherent systems

The active redundancy technique is widely used in reliability engineering to enhance the performance of reliability systems. In this paper, we utilize the criticality ordering to study optimal allocations of active redundancies in coherent systems comprising independent components. Firstly, we establish optimal allocation strategies for two heterogeneous active redundancies for components ranked by the criticality ordering, which is characterized by the structure relationships induced from the associated minimal cut sets. Our findings demonstrate that, under certain conditions where the criticality ordering (and reliability performances) between any two original components is required, the stronger redundancy should be allocated to the more critical component. Secondly, we investigate the best allocation policies for a batch of homogeneous active spares for different components while preserving the criticality ordering. It is shown that allocating more active redundancies to the more critical component results in a more reliable coherent system. Additionally, we prove that under certain conditions, an imbalance in the numbers of allocated spares leads to even greater reliability in the system. Thirdly, we study optimal allocations for any two components in coherent systems when their locations are quantified by minimal path sets. The optimal allocation policies are further derived, most of which are similar to those obtained by applying minimal cut sets. Numerical examples are provided to illustrate the main findings, and we apply our findings to a real-world scenario in an airplane cockpit system to enhance its reliability.

Research of Risk Identification and Prevention of Underground Pressure Pipelines Damage Caused by External Disturbance

External disturbance is an important cause of underground pressure pipeline damage, which leads to accidents, and it is crucial to study the risk of damage caused by external disturbance and come up with proper prevention and control measures. We reviewed literature on risk identification of underground pressure pipelines damage due to external disturbance was conducted, and a list of risk factors was formed. Based on the list of risk factors, fault tree analysis was carried out on underground pressure pipelines damage caused by external disturbances, and risk prevention and control measures were proposed through the calculation of minimum cut sets, minimum path sets, and structural importance, in hopes of providing reference for the normal operation of underground pressure pipelines.

On the status of component failures in a working coherent system when the lifetimes are DNID random variables

In this paper, we investigate the number of failed components in a coherent system with possibly dependent and not necessarily identically distributed component lifetimes. Based on two different partial information about the status of component failures, obtained either with a single inspection or under double monitoring of the system, we compute the probability of the given number of failures in a working coherent system. In the computations, we use the concept of minimal path sets of the system. These results enable us to establish explicit expressions for survival functions of two types of residual lifetimes of a used system. For illustration, we provide numerical examples of coherent systems composed of discretely or continuously distributed component lifetimes.

Simple method to extract minimal cut sets of a direct network

System planning, design, and control, network reliability validation, and evaluation are critical. The enumeration of minimal cut sets (MCs) in a network is usually more complicated than the search for minimal path sets (MPs). The purpose of this research is to offer an efficient accurate approach for enumerating directed networks’ MCs. The method is concerned with determining the MCs depending on the set of minimal path nodes.

Reliability Calculation Method of Shipborne Vehicles' Sortie Mission for Dynamic Network Structure.

To provide decision support to the commander, it is necessary to calculate shipborne vehicles' sortie mission reliability during the formulation of the layout plan. Therefore, this paper presents the sortie mission network model and reliability calculation method for shipborne vehicles. Firstly, the shipborne vehicle layout and sortie task characteristics are used to establish the sortie mission network model. The shipborne vehicles' sortie mission reliability problem is transformed into a two-terminal network reliability problem. Secondly, the minimal path set method is used to calculate the two-terminal network reliability. An improved tabu search algorithm based on a strategy of breaking up the whole into parts is proposed to search for the minimal path set that matches the length. Finally, the sum of disjoint products is used to process the minimal path set to obtain the shipborne vehicles' sortie mission reliability calculation formula. A numerical analysis of two simplified shipborne vehicles' layouts is given to illustrate the calculation process of the method. This study provides a new evaluation index and an effective quantitative basis for the evaluation system of shipborne vehicles' layout. It also provides theoretical support for the development of decision-making related to the sortie mission of shipborne vehicles.

Efficient Minimum Flow Decomposition via Integer Linear Programming.

Minimum flow decomposition (MFD) is an NP-hard problem asking to decompose a network flow into a minimum set of paths (together with associated weights). Variants of it are powerful models in multiassembly problems in Bioinformatics, such as RNA assembly. Owing to its hardness, practical multiassembly tools either use heuristics or solve simpler, polynomial time-solvable versions of the problem, which may yield solutions that are not minimal or do not perfectly decompose the flow. Here, we provide the first fast and exact solver for MFD on acyclic flow networks, based on Integer Linear Programming (ILP). Key to our approach is an encoding of all the exponentially many solution paths using only a quadratic number of variables. We also extend our ILP formulation to many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors. On both simulated and real-flow splicing graphs, our approach solves any instance in <13 seconds. We hope that our formulations can lie at the core of future practical RNA assembly tools. Our implementations are freely available on Github.

Influencing factors of agricultural machinery accidents based on fuzzy fault tree analysis

Safety is an important indicator to the design of agricultural machinery products. In order to grasp the risk source of agricultural machinery accidents accurately, explore the causes and laws of agricultural machinery accidents, and prevent the occurrence of various accidents in the process of agricultural machinery products effectively. This study constructs a fuzzy fault tree model by combining the fault tree analysis method with the triangular fuzzy number, and analyzes the factors which cause agricultural machinery accidents. The results are as follows: 1) Through fault tree analysis, 23 known and potential causes of agricultural machinery accidents were deduced, and 57 minimum cut sets and 3 minimum path sets were solved; 2) The probabilities of 23 basic events were fuzzed by triangular fuzzy number theory, and the fuzzy probability value of each basic event was obtained; 3) Sorting fuzzy importance of 23 basic events has clarified the degree of influence of each basic event on the top event. Factors such as, Machine without safety protection device (X1), Personnel not wearing safety protective equipment (X2), Long Working Hours (X16), Unreasonable control device (X15), Speeding and overloading (X7), are ranked top among the 23 factors. The analysis result shows that these factors have a great impact on the occurrence of agricultural machinery accidents which should be given priority in the formulation of preventative measurements to agricultural machinery accidents.

Study on the Covering Problem in Network Reliability for Precision Business Management

A new research area namely, precision business management, is quietly blooming through network theory. In precision business management, several new management tools can be developed to precisely adjust the behavior of the entities in the company to satisfy the management requirement. This paper deals with the situation when specific business process pattern should be recognized, and the related entities in the process have to be identified. It is referred to a kind of covering problem in network reliability. Minimal path set can be considered as a set of flow combinations. However, in some cases, a subset of the flow combination may be required for applications. Therefore, techniques for dealing such cases are needed. This paper proposes a heuristic approach to solve the covering problem in network reliability. Some numerical examples are presented for explanation. The results show that the cases are interesting in the discussion.

Reliability Uncertainty Analysis Method for Aircraft Electrical Power System Design Based on Variance Decomposition

As a safety critical system, affected by cognitive uncertainty and flight environment variability, aircraft electrical power system proves highly uncertain in its failure occurrence and consequences. However, there are few studies on how to reduce the uncertainty in the system design stage, which is of great significance for shortening the development cycle and ensuring flight safety during the operation phrase. For this reason, based on the variance decomposition theory, this paper proposes an importance measure index of the influence of component failure rate uncertainty on the uncertainty of power supply reliability (system reliability). Furthermore, an algorithm to calculate the measure index is proposed by combining with the minimum path set and Monte Carlo simulation method. Finally, the proposed method is applied to a typical series-parallel system and an aircraft electrical power system, and a criteria named as “quantity and degree optimization criteria” is drawn from the case study. Results demonstrate that the proposed method indeed realizes the measurement of the contribution degree of component failure rate uncertainty to system reliability uncertainty, and combined with the criteria, proper solutions can be quickly determined to reduce system reliability uncertainty, which can be a theoretical guidance for aircraft electrical power system reliability design.

Hardware Reliability Analysis of a Coal Mine Gas Monitoring System Based on Fuzzy-FTA

The hardware reliability of a gas monitoring system was investigated using the fuzzy fault tree analysis method. A fault tree was developed considering the hardware failure of the gas monitoring system as a top event. Two minimum path sets were achieved through qualitative analysis using the ascending method. The concept of fuzzy number of the fuzzy set theory was applied to describe the probability of basic event occurrence in the fault tree, and the fuzzy failure probabilities of the middle and top events were calculated using fuzzy AND and OR operators. The results show that the proposed fuzzy fault tree is an effective method of reliability analysis for gas monitoring systems. Results of calculations using this method are more reasonable than those obtained with the conventional fault tree method.

A modified technique to compute the minimal path sets for the reliability of complex network

Consider a complex network whose components either work or fail, there probabilities are known. Our paper study two methods for the exact computation of the reliability network, the first one is a decomposition method which may be used even after the community can go through no further modular decomposition, is based on a partition the vertices of network into sets that can be analyzed them sequentially. This method involves choosing one component as a key and then calculate the reliability network twice the first when the key work and the other if the key failed. These two probabilities are then combined to obtain the reliability network. The second method is inclusion-exclusion method which is one of the earliest techniques to compute complex network reliability expressions using the probability laws. We get the same polynomial by using two methods. In both methods, we need to calculate all of the minimum paths so we calculated them by use the adjacency matrix.

Research on reliability evaluation method of protection system based on Kaplan-Meier and GO method

In the reliability analysis of the traditional substation protection system, methods such as minimum path set method, fault tree method and Markov method are mostly used. These three methods have disadvantages such as large amount of calculation and strong subjectivity in the application process. Based on the shortcomings of traditional reliability analysis methods, this paper proposes a protection system reliability evaluation method based on survival analysis plus GO method. In view of the problem of timing truncation of the failure data of the protection system and the different time of operation of the protection device, the survival analysis (Kaplan-Meier) method is used to estimate the reliability of the equipment in different time periods, and the GO method is combined to obtain the GO graph of the protection system and GO operation, and then get the reliability of the entire protection system. The results show that the method can quantitatively calculate the reliability of the relay protection system, has the advantages of simplicity, intuitiveness, and easy computer programming. It can be used to analyse the reliability of the relay protection system and guide the design, operation and maintenance of the substation.

An Improved Multiobjective Shortest Path Algorithm

We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra’s algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude.

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

A flexible optimization algorithm for GO-FLOW methodology to deal with shared signals

In this paper, we propose an optimized GO-FLOW algorithm for time-dependent system reliability analysis. The optimized GO-FLOW algorithm is implemented based on recursive calculation of the complete set of minimum path sets. The algorithm is augmented with a cut-off criterion for probabilistic models to offer a much more flexible approach to achieve the trade-off between computational complexity and accuracy. The optimization method and algorithm are tested with an example case study of reliability analysis of auxiliary feedwater system in nuclear power plants. The verification results show that the retrofitting GO-FLOW method is capable of efficient processing of the shared signals and providing accuracy solutions at high speed.

On the isometric path partition problem

The isometric path cover (partition) problem of a graph is to find a minimum set of isometric paths which cover (partition) the vertex set of the graph. The isometric path cover (partition) number of a graph is the cardinality a minimum isometric path cover (partition). We prove that the isometric path partition problem and the isometric $k$-path partition problem for $k\geq 3$ are NP-complete on general graphs. Fisher and Fitzpatrick \cite{FiFi01} have shown that the isometric path cover number of $(r\times r)$-dimensional grid is $\lceil 2r/3\rceil$. We show that the isometric path cover (partition) number of $(r\times s)$-dimensional grid is $s$ when $r \geq s(s-1)$. We establish that the isometric path cover (partition) number of $(r\times r)$-dimensional torus is $r$ when $r$ is even and is either $r$ or $r+1$ when $r$ is odd. Then, we demonstrate that the isometric path cover (partition) number of an $r$-dimensional Benes network is $2^r$. In addition, we provide partial solutions for the isometric path cover (partition) problems for cylinder and multi-dimensional grids.