Universal Generating Function Technique Research Articles

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 for complex electromechanical multi-state systems utilizing universal generating function techniques

The large-scale adoption of complex electromechanical systems (CMESs) renders it challenging to perform reliability assessments for such systems. In terms of the reliability evaluation of CMESs, previous studies generally assume that only binary states exist within the systems. However, owing to the stochastic failures and various operating characteristics of the system components, not only the good/bad states but also the performance levels within the system should be taken into account when analyzing the reliability of CMESs. Hence, we abstract the CMES as a multi-layer and multi-state network in which minimum maintenance units (MMUs) and three types of connections constitute nodes and edges in different layers. Furthermore, multi-state models for different MMUs in the CMES are developed based on universal generating functions (UGFs). Aggregation operators are then utilized to aggregate these UGFs to obtain the multi-state models. Subsequently, a cascading failure model is introduced to incorporate MMUs into the system reliability assessment. Thus, the effects of the operating mechanism and topological attributes can be considered in the reliability evaluation of the CEMS. Finally, the CRHX high-speed train system is used as an example to demonstrate the applicability and effectiveness of the proposed method in the reliability assessment of the CMES.

Signature reliability scrutiny of domestic refrigerator

PurposeThe purpose of this paper is to evaluate the reliability and structure function of refrigeration complex system consisted of four components in complex manner.Design/methodology/approachAlthough, a variety of methodologies have been used to assess the refrigeration system's reliability function that has proven to be effective, the universal generating function approach is the basis of this research study, which is used in the calculation of a domestic refrigeration system with four separate components that are related in series and parallel with a corresponding sample to form a complex machine.FindingsIn this paper, signature reliability of the refrigeration system has been evaluated with the universal generating function technique. There are four components present in the proposed system in complex (series and parallel) manner. The tail signature, signature, Barlow–Proschan index, expected lifetime and expected cost of independent identically distributed are all computed.Originality/valueThis is the first study of domestic refrigeration system to examine the signature reliability with the help of universal generating function techniques with various measures. Refrigeration systems are an essential process in industries and home applications as they perform cooling or the maintain temperature at the desired value. A cycle of refrigeration consists of four main components such as, heat exchange, compression and expansion with a refrigerant flowing through the units within the cycle.

UGF-based signature reliability for solar panel k-out-of-n- multiplex systems

PurposeThe purpose of this paper is to evaluate the reliability and signature reliability of solar panel k-out-of-n-multiplex system with the help of universal generating function.Design/methodology/approachEnergy scarcity and global warming issues have become important concerns for humanity in recent decades. To solve these problems, various nations work for renewable energy sources (RESs), including sun, breeze, geothermal, wave, radioactive and biofuels. Solar energy is absorbed by solar panels, referred to as photovoltaic panels, which then transform it into electricity that can be used to power buildings or residences. Remote places can be supplied with electricity using these panels. Solar energy is often generated using a solar panel that is connected to an inverter for power supply. As a result, a converter reliability evaluation is frequently required. This paper presents a study on the reliability analysis of k-out-of-n systems with heterogeneous components. In this research, the universal generating function methodology is used to identify the reliability function and signature reliability of the solar array components. This method is commonly used to assess the tail signature and Barlow-Proschan index with independent and identically distributed components.FindingsThe Barlow-Proschan index, tail signature, signature, expected lifetime, expected cost and minimal signature of independent identically distributed are all computed.Originality/valueThis is the first study of solar panel k-out-of-n-multiplex systems to examine the signature reliability with the help of universal generating function techniques with various measures.

Reliability analysis and optimal generator allocation and protection strategy of a non-repairable power grid system

In a power grid system, generators may fail due to the internal structure and material degradation caused by stress levels or work conditions. However, power grid systems may also be subject to external impacts such as landslides and earthquakes. Protecting these systems can mitigate the external negative effects. In this research, we extend the general network reliability model with consideration of the individual generator protection and the overarching protection. The generators can be destroyed if and only if both the individual protection and the overarching protection are destroyed. A joint generator allocation and protection optimization problem is formulated to increase the system reliability. We propose an algorithm to evaluate the system reliability by extending the universal generating function technique. Numerical experiments show that determining the generator allocation and the protection strategy optimally can improve the system reliability.

Reliability analysis of m-out-of-r-within-k-out-of-n system

A binary-state m-out-of-r-within-k-out-of-n:G model is proposed and the reliability of the model is estimated with the help of Universal Generating Function (UGF). In the proposed system, the subsystems are connected in k-out-of-n:G type configuration. The subsystems are also a combination of m-out-of-r:G type. The elements of the subsystem consist of components connected in series. The components cannot be divided further and taken as an individual unit. The reliability function and absolute reliability of the proposed model are evaluated from the UGF technique.

Universal generating function -based narrow reliability bounds to evaluate reliability of project completion time

Project completion time is one of the important indicators for managing/scheduling construction projects. This paper proposes a method for evaluating the reliability of project completion time by using the Universal Generating Function technique. The proposed method is used to overcome the limitations of existing project reliability evaluation methods by providing accurate results while requiring low computational burden. Also, unlike many of the methods revealed in the literature, in the proposed method, the activity duration does not need to follow any specific distribution. Our methodology consists of five main parts: 1) determining the u-function of the activity durations 2) modeling the stochastic project network as a parallel-series multi-state system, 3) determining the u-function of the project network paths to determine the probability of failure in each path, 4) determining the probability of simultaneous failure of each pair of paths, and 5) computing reliability bounds for project completion time by integrating the NRB and UGF methods. Results of the proposed method were compared with those of the Monte Carlo simulation method indicating that the reliability level obtained from both methods are indifferent at 0.01 significance level, while the computation time of the proposed method is significantly lower.

Analysis of signature reliability of ring-shaped network system

PurposeThe purpose of this paper is to design a ring network topology system and alter it into a series–parallel type framework. Then, reliability of the framework is analysed and authors also discussed the signature to analyse the most sensitive component.Design/methodology/approachThis study presents a ring-shaped network system where this type of topology forms a single continuous pathway for signals through every node. In this study, a system consists of ring network topology is generalized in the series–parallel mixed configuration and reliability characteristics are evaluated with the assistance of universal generating function (UGF) technique. The system consists of wires, repeaters, components or computers and power supply. The wires and repeaters are in series, so, if they fail the whole system will fail and the signals will not go further. The components or computers are connected to each other in parallel configuration. So, the whole system will not fail until the last computer is working. There is also a two-unit power supply system which has one unit in a standby mode. On the failure of first power supply, the second one will start functioning and the whole system fails on the failure of both power supply.FindingsBy the assistance of UGF technique, reliability function of the framework is evaluated. Also, Barlow–Proschan index and expected lifetime for the designed system is estimated by considering a numerical example for the general ring-shaped network system.Originality/valueUGF technique is very effective for estimating the reliability of a system with complex structure and having two performance rates, i.e. completely failed and perfectly working, or more than two, i.e. multi-state performance. This technique enables to estimate every components contribution in the working and failure of the whole system. A general model of ring-shaped network system is taken and generalized algorithm is drawn for the system. Then a particular numerical example is solved for illustrating the use of this technique.

Mixed shock model for multi-state weighted k-out-of-n: F systems with degraded resistance against shocks

In previous studies of shock models, the probability of shocks causing damage to the system during operation is always constant. However, it is more practical for the system to become more vulnerable to shocks under a severe condition and the probabilities of subsequent shocks causing damage to the system increase. Furthermore, few studies have focused on the shock environment of weighted k-out-of-n: F systems. To fill these research gaps, this paper proposes a novel mixed shock model for a multi-state weighted k-out-of-n: F system with a consideration of its resistance against shocks. The components in the system operate in a two-stage process and different weights are taken for their different states. The system has multiple states determined by the total system weight/performance. System failure results from the competing failure criteria of insufficient system weight/performance and from reaching the critical number of failed components. A combination of finite Markov chain imbedding approach, universal generating function technique and phase-type distribution is adopted to analyze the probabilistic indices of the components and entire system. Numerical illustrations based on a power-generating plant are presented to demonstrate the applicability of new shock model and the effectiveness of proposed method.

Reliability assessment of multi-state performance sharing systems with transmission loss and random shocks

In this article, a performance sharing system with transmission loss and a shock operation environment is studied. Such systems are widely found in power distribution systems, distributed computing systems, data transmission systems, communication systems, and so on. The system consists of n components and each of them works to satisfy its demand and shares its performance surplus with others through a common bus. When the system operates, it may suffer a variety of stresses from its operating environment, which can be regarded as random external shocks, and the transmission loss is also wildly seen in engineering systems. Therefore, the random shocks and transmission loss are considered in this article. The performance level of a component is affected by three types of random external shocks – invalid shocks, valid shocks and extreme shocks. The system fails if at least one component cannot satisfy its demand. A finite Markov chain imbedding approach and phase-type distributions are used to estimate the performance level for each component and the universal generating function technique is applied to analyze system reliability. Analysis of a power distribution system is given to show the application of the model under study and the effectiveness of the proposed method.

Redundancy optimization for multi-state series-parallel systems using ordinal optimization-based-genetic algorithm

Multi-state series-parallel systems (MSSPSs) are widely-used for representing engineering systems. In real-life cases, engineers need to design an optimal MSSPS structure by combining different versions and number of redundant components. The objective of the design is to ensure reliability requirements using the least costs, which could be formulated as a redundancy optimization problem under reliability constraints. The genetic algorithm is one of the most frequently used method for solving redundancy optimization problems. In traditional genetic algorithms, the population size needs to be determined based on the experience of the modeler. Often, this ends up creating a large number of unnecessary samples. As a result, the computational burden can be huge, especially for large-scale MSSPS structures. To solve these problems, this paper proposes an optimal structure designing method named as redundancy ordinal optimization. The universal generating function technique is applied to evaluate the reliabilities of the MSSPSs. Based on the reliabilities, an ordinal optimization algorithm is adapted to update the parent populations and the stopping criterion of genetic algorithm, so that the unnecessary structure designs can be eliminated. Numerical examples show that the proposed method improves the computational efficiency while remaining satisfactorily accurate.

Redundancy Optimization for Multi-Performance Multi-State Series-Parallel Systems Considering Reliability Requirements

Various engineering systems operating with multiple performance measures are multi-state in nature. These systems are usually modelled as multi-performance multi-state series-parallel systems (MPS). In real-life cases, engineers need to design an optimal MPS structure by combining different versions and number of redundant multi-performance components. Moreover, to design a reliable structure, reliability evaluation is inevitable. However, the conventional redundancy optimization measured by single performance is difficult to model the optimal MPS structure. Furthermore, as the most frequently used method, randomly sizing of parent populations and stopping criterion of traditional genetic algorithm (GA) may lead to massive unnecessary structures. The computational burden may be huge for the redundancy optimization considering multi-performance measures. This paper proposes a redundancy optimization model considering multi-performance measuring systems. The optimization objective and the reliability constraints are described by multiple performance measures. The universal generating function technique is applied to evaluate the reliability. Based on the reliability, the efficient optimization method combining with ordinal optimization and genetic algorithms is proposed to design the optimal MPS structure. The ordinal optimization algorithm is employed to modify both the parent populations and stopping criterion of genetic algorithm. Finally, the proposed model and method are illustrated by numerical examples.

Reliability modeling and optimization of a two-dimensional sliding window system

Existing research on the reliability of multi-state systems concentrated on one-dimensional systems. However, many two-dimensional systems widely exist in real-world applications such as collaborative robot supported matrix production systems and touch panel systems. Motivated by these practical systems, this research studies a two-dimensional sliding window system consisting of multi-state components which fails if the cumulative performance of any sliding window cannot meet a predetermined demand. The system reliability is evaluated by extending the universal generating function technique. In order to improve the system availability, the joint optimization problem of component maintenance and allocation is further studied. A case study on a collaborative robots supported matrix automotive assembly system is presented to illustrate the proposed model and algorithm.

Reliability analysis of performance-based balanced systems with common bus performance sharing

In this paper, a performance-based balanced system with common bus performance sharing is established. The system consists of n components connected by a common bus. Each component has its individual performance which can be shared among all components via the common bus. The system is balanced if the performance of each component is the same and it can be rebalanced by redistributing performances among all components via the common bus if the system is out of balance. The system fails when the system is out of balance after performance sharing or the total performance of the system is less than a predetermined value, whichever occurs first. A Markov process is employed to describe the performance variation of each component and the universal generating function technique is applied to obtain analytical solution of the system reliability. A specific analysis of battery balancing of lithium battery pack is given to show the application of the proposed model and effectiveness of the proposed method.

Reliability and Economic Evaluation of Offshore Wind Power DC Collection Systems

One key directive to realize the global transition towards net-zero emission goals is to integrate more renewable energy resources into the generation mix. Due to higher and more consistent wind speeds, offshore wind farms (OWFs) have the potential to generate more energy at a steadier rate than their onshore counterpart. However, at the collection system level, all the OWFs use alternating current (AC) technology at present. Nonetheless, with an increasing capacity of the single wind turbine (WT) and larger distances to the shore, the use of direct current (DC) technology at the collection system level is beneficial. To select a suitable DC collection system topology, this paper proposes a comprehensive analytical reliability evaluation method, based on the Universal Generating Function technique, together with associated economic factors. Four candidates DC collection system options were evaluated with different WT capacities for a 400 MW OWF. The availability indices such as Generation Ratio Availability and Expected Energy Not Supplied were used to assess their reliability levels. The results show that the radial topology with a single platform DC/DC converter is more reliable and economical than the other candidate options.

Pareto-based grouping meta-heuristic algorithm for humanitarian relief logistics with multistate network reliability

This article considers a biobjective location-routing problem to deliver relief resources to the victims affected by a disaster under uncertainty in demand, transportation infrastructure, and travel time. Since transportation networks are exposed to a considerable level of uncertainty, choosing the reliable path for relief goods to be transmitted to the affected areas ensures the arrival of these supplies. For the first time, route reliability is calculated based on the multistate theory, and the universal generating function technique is used for network reliability assessment. The problem is formulated as a multiperiod robust biobjective mixed-integer programming model. Two objective functions are considered: (a) decreasing the sum of arrival times of relief vehicles at the demand nodes for delivering aids to the affected areas, and (b) increasing the minimum route reliability for all the serving vehicles. A novel multiobjective grouping algorithm is proposed to obtain the Pareto-optimal solutions of the problem. Then, its performance is compared with two other multiobjective grouping algorithms. To evaluate the solution method, the algorithms are implemented on various test problems and compared statistically. A case study is presented to illustrate the potential applicability of our model. Additionally, to determine the effect of the changes in the main parameters of the problem on the value of objective functions, the sensitivity analyses are performed and the managerial insights are given.

Reliability of integrated electricity and gas supply system with performance substitution and sharing mechanisms

The reliability of a system that shares a single type of resource with others has been studied in the literature. In reality, a system may require different types of resources. For example, a building service system may be powered by electricity (for lighting) and gas (for heating). However, in the literature, research in this area is scarce. This paper therefore investigates the reliability of a system with multiple nodes. Each node has demand requirement for two types of resources, which can be shared among the system nodes subject to their bandwidths, respectively. In addition, the resources may be able to substitute each other. This paper considers both unidirectional and bidirectional substitutions. The system is said failed if either resource supply in a node is smaller than its demand even after performance substitution and sharing. A universal generating function technique is proposed to evaluate the system reliability. Numerical examples are presented to illustrate the applicability of the model. The influences of bandwidths and substitution rates on system reliability are also discussed.

Reliability evaluation of consecutive-k-out-of-n: F systems with two performance sharing groups

From previous studies on performance sharing systems, the system structure is considered to be either series, or series-parallel, or k-out-of-n structure. To enrich the research and extend application on performance sharing systems, the consecutive-k-out-of-n: F system with two performance sharing groups is investigated in this paper. Such systems consist of n units and two common buses, and each unit has a random performance to satisfy its random demand. Units connected by the same common bus make up one performance sharing group. If a unit has surplus performance, the surplus performance can be transmitted to the units which are experiencing performance deficiency and belonging to the same performance sharing group via the common bus. If the demand of one unit is not satisfied, the unit has to be shut down. The system fails due to at least k consecutive shut-down units. The universal generating function technique is used to analyze the system reliability. Analytical and numerical examples of the heating system are presented to demonstrate the new model under study.

Multi-State System Reliability Evaluation and Component Allocation Optimization Under Multi-Level Performance Sharing

With the development of science and technology, the structure of engineering system has become increasingly large and complex. In order to ensure the safety and stability of the system in operation, the reliability evaluation of complex system has become an important research field. However, previous studies on the reliability of multi-state systems did not take into account the multi-level performance sharing in the system, and it has been unable to accurately assess the reliability of such complex systems. Therefore, based on the actual engineering system, this paper proposes a multi-state system with multi-level performance sharing mechanism. On this basis, we established a system reliability evaluation model using universal generating function technique. Through numerical examples, the application of the model and analyze the influence of different parameters on system reliability are demonstrated. In addition, we also use genetic algorithm to optimize the allocation of components in the system, so as to improve the reliability of the system. Different from the previous studies on system reliability with common bus performance sharing, the system proposed in this study is more general.

Signature reliability evaluation of renewable energy system

In this paper, a real-life renewable energy-based system is considered and the reliability function of this system is evaluated with the help of Universal Generating Function technique.The renewable energy-based system is considered from the project in Germany where the wind turbine and hydro power plant are combined. In this project the wind turbines are the world?s tallest wind turbines of about 584 feet and one reservoir have the capacity of 1.6 million gallons of water. The wind turbines are set at the top of the hills and the reservoirs are allowed to be filled with river water. This paper presents a renewable energy-based system where the wind turbine and hydro power plant are combined together to produce electricity in bulk. Universal generating function technique is used to obtain the reliability function of the proposed system. Also tail signature, signature, expected cost rate, expected lifetime, and Barlow-Proschan Index are estimated.