Search results for: Reliability evaluation

Authors: Nipun Manirajan, Heeralal Gargama, Sushil Guhe, Manoj Prabhakaran

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In railway industry, train sets are designed based on contractual requirements (mission profile), where reliability targets are measured in terms of mean distance between failures (MDBF). However, during the beginning of revenue services, trains do not achieve the designed mission profile distance (mileage) within the timeframe due to infrastructure constraints, scarcity of commuters or other operational challenges thereby not respecting the original design inputs. Since trains do not run sufficiently and do not achieve the designed mileage within the specified time, car builder has a risk of not achieving the contractual MDBF target. This paper proposes a constant failure rate based model to deal with the situations where mileage accumulation is not a part of the design mission profile. The model provides appropriate MDBF target to be demonstrated based on actual accumulated mileage. A case study of rolling stock running in the field is undertaken to analyze the failure data and MDBF target demonstration during low mileage accumulation. The results of case study prove that with the proposed method, reliability targets are achieved under low mileage accumulation.

Keywords: Mean distance between failures, mileage based reliability, reliability target normalization, rolling stock reliability.

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Authors: Hasan Keshavarzian, Tayebeh Nesari

Abstract:

Bolted rail joint is one of the most vulnerable areas in railway track. A comprehensive approach was developed for studying the reliability of fatigue crack initiation of railroad bolt hole under random axle loads and random material properties. The operation condition was also considered as stochastic variables. In order to obtain the comprehensive probability model of fatigue crack initiation life prediction in railroad bolt hole, we used FEM, response surface method (RSM), and reliability analysis. Combined energy-density based and critical plane based fatigue concept is used for the fatigue crack prediction. The dynamic loads were calculated according to the axle load, speed, and track properties. The results show that axle load is most sensitive parameter compared to Poisson’s ratio in fatigue crack initiation life. Also, the reliability index decreases slowly due to high cycle fatigue regime in this area.

Keywords: Rail-wheel tribology, rolling contact mechanic, finite element modeling, reliability analysis.

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Authors: M. Bouguerra, I. Habi

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The continuity in the electric supply of the electric installations is becoming one of the main requirements of the electric supply network (generation, transmission, and distribution of the electric energy). The achievement of this requirement depends from one side on the structure of the electric network and on the other side on the avaibility of the reserve source provided to maintain the supply in case of failure of the principal one. The avaibility of supply does not only depends on the reliability parameters of the both sources (principal and reserve) but it also depends on the reliability of the circuit breaker which plays the role of interlocking the reserve source in case of failure of the principal one. In addition, the principal source being under operation, its control can be ideal and sure, however, for the reserve source being in stop, a preventive maintenances which proceed on time intervals (periodicity) and for well defined lengths of time are envisaged, so that this source will always available in case of the principal source failure. The choice of the periodicity of preventive maintenance of the source of reserve influences directly the reliability of the electric feeder system In this work and on the basis of the semi- markovian's processes, the influence of the time of interlocking the reserve source upon the reliability of an industrial electric network is studied and is given the optimal time of interlocking the reserve source in case of failure the principal one, also the influence of the periodicity of the preventive maintenance of the source of reserve is studied and is given the optimal periodicity.

Keywords: Semi-Markovians processes, reliability, optimization, industrial electric network.

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Authors: Yong-Jun Kim, Jae-Hyun Ro, Chang-Bin Ha, Hyoung-Kyu Song

Abstract:

Because current wireless communication requires high reliability in a limited bandwidth environment, this paper proposes the variable modulation scheme based on the codebook. The variable modulation scheme adjusts transmission power using the codebook in accordance with channel state. Also, if the codebook is composed of many bits, the reliability is more improved by the proposed scheme. The simulation results show that the performance of proposed scheme has better reliability than the the performance of conventional scheme.

Keywords: MIMO-OFDM, variable modulation, codebook, channel state.

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Authors: Aleš Florian, Lenka Ševelová, Jaroslav Žák

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Formation of tensile cracks in concrete slabs of rigid pavement can be (among others) the initiation point of the other, more serious failures which can ultimately lead to complete degradation of the concrete slab and thus the whole pavement. Two measures can be used for reliability assessment of this phenomenon - the probability of failure and/or the reliability index. Different methods can be used for their calculation. The simple ones are called moment methods and simulation techniques. Two methods - FOSM Method and Simple Random Sampling Method - are verified and their comparison is performed. The influence of information about the probability distribution and the statistical parameters of input variables as well as of the limit state function on the calculated reliability index and failure probability are studied in three points on the lower surface of concrete slabs of the older type of rigid pavement formerly used in the Czech Republic.

Keywords: Failure, pavement, probability, reliability index, simulation, tensile crack.

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Authors: Perumal Nallagownden, Ravindra N. Mukerjee, Syafrudin Masri

Abstract:

In a competitive energy market, system reliability should be maintained at all times. Power system operation being of online in nature, the energy balance requirements must be satisfied to ensure reliable operation the system. To achieve this, information regarding the expected status of the system, the scheduled transactions and the relevant inputs necessary to make either a transaction contract or a transmission contract operational, have to be made available in real time. The real time procedure proposed, facilitates this. This paper proposes a quadratic curve learning procedure, which enables a generator-s contribution to the retailer demand, power loss of transaction in a line at the retail end and its associated losses for an oncoming operating scenario to be predicted. Matlab program was used to test in on a 24-bus IEE Reliability Test System, and the results are found to be acceptable.

Keywords: Deregulation, learning coefficients, reliability, prediction, competitive energy market.

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Authors: V. V. Singh, Yusuf Ibrahim Gwanda, Rajesh Prasad

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In this paper, we focus on the reliability and performance analysis of Computer Centre (CC) at Yobe State University, Damaturu, Nigeria. The CC consists of three servers: one database mail server, one redundant and one for sharing with the client computers in the CC (called as a local server). Observing the different possibilities of the functioning of the CC, the analysis has been done to evaluate the various popular measures of reliability such as availability, reliability, mean time to failure (MTTF), profit analysis due to the operation of the system. The system can ultimately fail due to the failure of router, redundant server before repairing the mail server and switch failure. The system can also partially fail when a local server fails. The failed devices have restored according to Least Recently Used (LRU) techniques. The system can also fail entirely due to a cooling failure of the server, electricity failure or some natural calamity like earthquake, fire tsunami, etc. All the failure rates are assumed to be constant and follow exponential time distribution, while the repair follows two types of distributions: i.e. general and Gumbel-Hougaard family copula distribution.

Keywords: Reliability, availability Gumbel-Hougaard family copula, MTTF, internet data center.

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Authors: Mohd Azman Abdul Latif, Erwan Basiron

Abstract:

A flaw or drift from expected operational performance in one component (NAND, PMIC, controller, DRAM, etc.) may affect the reliability of the entire Solid State Drive (SSD) system. Therefore, it is important to ensure the required quality of each individual component through qualification testing specified using standards or user requirements. Qualification testing is time-consuming and comes at a substantial cost for product manufacturers. A highly technical team, from all the eminent stakeholders is embarking on reliability prediction from beginning of new product development, identify critical to reliability parameters, perform full-blown characterization to embed margin into product reliability and establish control to ensure the product reliability is sustainable in the mass production. The paper will discuss a comprehensive development framework, comprehending SSD end to end from design to assembly, in-line inspection, in-line testing and will be able to predict and to validate the product reliability at the early stage of new product development. During the design stage, the SSD will go through intense reliability margin investigation with focus on assembly process attributes, process equipment control, in-process metrology and also comprehending forward looking product roadmap. Once these pillars are completed, the next step is to perform process characterization and build up reliability prediction modeling. Next, for the design validation process, the reliability prediction specifically solder joint simulator will be established. The SSD will be stratified into Non-Operating and Operating tests with focus on solder joint reliability and connectivity/component latent failures by prevention through design intervention and containment through Temperature Cycle Test (TCT). Some of the SSDs will be subjected to the physical solder joint analysis called Dye and Pry (DP) and Cross Section analysis. The result will be feedbacked to the simulation team for any corrective actions required to further improve the design. Once the SSD is validated and is proven working, it will be subjected to implementation of the monitor phase whereby Design for Assembly (DFA) rules will be updated. At this stage, the design change, process and equipment parameters are in control. Predictable product reliability at early product development will enable on-time sample qualification delivery to customer and will optimize product development validation, effective development resource and will avoid forced late investment to bandage the end-of-life product failures. Understanding the critical to reliability parameters earlier will allow focus on increasing the product margin that will increase customer confidence to product reliability.

Keywords: e2e reliability prediction, SSD, TCT, Solder Joint Reliability, NUDD, connectivity issues, qualifications, characterization and control.

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Authors: Tomas Luneckas, Dainius Udris

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In this paper a simple terrain evaluation method for hexapod robot is introduced. This method is based on feet coordinate evaluation when all are on the ground. Depending on the feet coordinate differences the local terrain evaluation is possible. Terrain evaluation is necessary for right gait selection and/or body position correction. For terrain roughness evaluation three planes are plotted: two of them as definition points use opposite feet coordinates, third coincides with the robot body plane. The leaning angle of body plane is evaluated measuring gravity force using three-axis accelerometer. Terrain roughness evaluation method is based on angle estimation between normal vectors of these planes. Aim of this work is to present a simple method for embedded robot controller, allowing to find the best further movement settings.

Keywords: Hexapod robot, pose estimation, terrain evaluation, terrain roughness.

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Authors: Sui Xin, Li Chunsheng, Tian Di

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Short message integrated distributed monitoring systems (SM-DMS) are growing rapidly in wireless communication applications in various areas, such as electromagnetic field (EMF) management, wastewater monitoring, and air pollution supervision, etc. However, delay in short messages often makes the data embedded in SM-DMS transmit unreliably. Moreover, there are few regulations dealing with this problem in SMS transmission protocols. In this study, based on the analysis of the command and data requirements in the SM-DMS, we developed a processing model for the control center to solve the delay problem in data transmission. Three components of the model: the data transmission protocol, the receiving buffer pool method, and the timer mechanism were described in detail. Discussions on adjusting the threshold parameter in the timer mechanism were presented for the adaptive performance during the runtime of the SM-DMS. This model optimized the data transmission reliability in SM-DMS, and provided a supplement to the data transmission reliability protocols at the application level.

Keywords: Delay, SMS, reliability, distributed monitoringsystem (DMS), wireless communication.

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Authors: J. Menčík

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Actual load, material characteristics and other quantities often differ from the design values. This can cause worse function, shorter life or failure of a civil engineering structure, a machine, vehicle or another appliance. The paper shows main causes of the uncertainties and deviations and presents a systematic approach and efficient tools for their elimination or mitigation of consequences. Emphasis is put on the design stage, which is most important for reliability ensuring. Principles of robust design and important tools are explained, including FMEA, sensitivity analysis and probabilistic simulation methods. The lifetime prediction of long-life objects can be improved by long-term monitoring of the load response and damage accumulation in operation. The condition evaluation of engineering structures, such as bridges, is often based on visual inspection and verbal description. Here, methods based on fuzzy logic can reduce the subjective influences.

Keywords: Design, fuzzy methods, Monte Carlo, reliability, robust design, sensitivity analysis, simulation, uncertainties.

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Authors: B. Juhasova, I. Halenar, M. Juhas

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The wireless communication is one of the widely used methods of data transfer at the present days. The benefit of this communication method is the partial independence of the infrastructure and the possibility of mobility. In some special applications it is the only way how to connect. This paper presents some problems in the implementation of a sensor network connection for measuring environmental parameters in the area of manufacturing plants.

Keywords: Network, communication, reliability, sensors.

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Authors: Tirthankar Ghosh, Dilip Roy, Nimai Kumar Chandra

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Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

Keywords: Discretization, Reversed Hazard Rate, Exponential distribution, reliability approximation, engineering item.

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Authors: Rajasekhar Mamilla, Janardhana G., Anjan Babu G.

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The present research study analyses the students’ satisfaction with university performance regarding the reliability dimension, ability of professors and staff to perform the promised services with quality to students in the post-graduate courses offered by Sri Venkateswara University in India. The research is done with the notion that the student compares the perceived performance with prior expectations. Customer satisfaction is seen as the outcome of this comparison. The sample respondents were administered with schedule based on stratified random technique for this study. Statistical techniques such as factor analysis, t-test and correlation analysis were used to accomplish the respective objectives of the study.

Keywords: Satisfaction, Reliability, Service Quality.

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Authors: Raed A. Amro

Abstract:

Standard packaging and interconnection technologies of power devices have difficulties meeting the increasing thermal demands of new application fields of power electronics devices. Main restrictions are the decreasing reliability of bond-wires and solder layers with increasing junction temperature. In the last few years intensive efforts have been invested in developing new packaging and interconnection solutions which may open a path to future application of power devices. In this paper, the main failure mechanisms of power devices are described and principle of new packaging and interconnection concepts and their power cycling reliability are presented.

Keywords: Power electronics devices, Reliability, Power Cycling, Low-temperature joining technique (LTJT)

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Authors: Jeongim Kang, Moon Hee Kim, Seong Baeg Kim

Abstract:

This paper proposes a novel e-learning model that is  based on a dynamic formative evaluation. On evaluating the existing  format of e-learning, conditions regarding repetitive learning to  achieve mastery, causes issues for learners to lose tension and become  neglectful of learning. The dynamic formative evaluation proposed is  able to supplement limitation of the existing approaches. Since a  repetitive learning method does not provide a perfect feedback, this  paper puts an emphasis on the dynamic formative evaluation that is  able to maximize learning achievement. Through the dynamic  formative evaluation, the instructor is able to refer to the evaluation  result when making an estimation about the learner. To show the flow  chart of learning, based on the dynamic formative evaluation, the  model proves its effectiveness and validity.

 

Keywords: Online learning, dynamic formative evaluation, mastery learning, repetitive learning method, learning achievement.

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Authors: Tomas Duranik, Juraj Ruzbarsky, Markus Stopper

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CONWIP (constant work-in-process) as a pull production system have been widely studied by researchers to date. The CONWIP pull production system is an alternative to pure push and pure pull production systems. It lowers and controls inventory levels which make the throughput better, reduces production lead time, delivery reliability and utilization of work. In this article a CONWIP pull production system was simulated. It was simulated push and pull planning system. To compare these systems via a production planning system (PPS) game were adjusted parameters of each production planning system. The main target was to reduce the total WIP and achieve throughput and delivery reliability to minimum values. Data was recorded and evaluated. A future state was made for real production of plastic components and the setup of the two indicators with CONWIP pull production system which can greatly help the company to be more competitive on the market.

Keywords: CONWIP, constant work in process, delivery reliability, hybrid production planning, PPS.

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Authors: Ivayla Trifonova, Naoum Jamous, Holger Schrödl

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A good web design is a prerequisite for a successful business nowadays, especially since the internet is the most common way for people to inform themselves. Web design includes the optical composition, the structure, and the user guidance of websites. The importance of each website leads to the question if there is a way to measure its usefulness. The aim of this paper is to suggest a methodology for the evaluation of web design. The desired outcome is to have an evaluation that is concentrated on a specific website and its target group.

Keywords: Evaluation methodology, factor analysis, target group, web design.

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Authors: Zakari Yaou, Lirong Cui

Abstract:

In a product development process, understanding the functional behavior of the system, the role of components in achieving functions and failure modes if components/subsystem fails its required function will help develop appropriate design validation and verification program for reliability assessment. The integration of these three issues will help design and reliability engineers in identifying weak spots in design and planning future actions and testing program. This case study demonstrate the advantage of unascertained theory described in the subjective cognition uncertainty, and then applies blind number (BN) theory in describing the uncertainty of the mechanical system failure process and the same time used the same theory in bringing out another mechanical reliability system model. The practical calculations shows the BN Model embodied the characters of simply, small account of calculation but betterforecasting capability, which had the value of macroscopic discussion to some extent.

Keywords: Mechanical structure Design, time-dependent stochastic process, unascertained information, blind number theory.

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Authors: Amar Aliche, Hocine Hammoum, Karima Bouzelha, Arezki Ben Abderrahmane

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Traditionally, the dimensioning of storage tanks is conducted with a deterministic approach based on partial coefficients of safety. These coefficients are applied to take into account the uncertainties related to hazards on properties of materials used and applied loads. However, the use of these safety factors in the design process does not assure an optimal and reliable solution and can sometimes lead to a lack of robustness of the structure. The reliability theory based on a probabilistic formulation of constructions safety can respond in an adapted manner. It allows constructing a modelling in which uncertain data are represented by random variables, and therefore allows a better appreciation of safety margins with confidence indicators. The work presented in this paper consists of a mecano-reliability analysis of a concrete storage tank placed on ground. The classical method of Monte Carlo simulation is used to evaluate the failure probability of concrete tank by considering the seismic acceleration as random variable.

Keywords: Reliability approach, storage tanks, Monte Carlo simulation, seismic acceleration.

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Authors: Anujendra, Parag Kumar Guha Thakurta

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The data transmission between mobile hosts and base stations (BSs) in Mobile networks are often vulnerable to failure. So, efficient link connectivity, in terms of the services of both base stations and communication channels of the network, is required in wireless mobile networks to achieve highly reliable data transmission. In addition, it is observed that the number of blocked hosts is increased due to insufficient number of channels during heavy load in the network. Under such scenario, the channels are allocated accordingly to offer a reliable communication at any given time. Therefore, a reliability-based channel allocation model with acceptable system performance is proposed as a MOO problem in this paper. Two conflicting parameters known as Resource Reuse factor (RRF) and the number of blocked calls are optimized under reliability constraint in this problem. The solution to such MOO problem is obtained through NSGA-II (Non dominated Sorting Genetic Algorithm). The effectiveness of the proposed model in this work is shown with a set of experimental results.

Keywords: Base station, channel, GA, Pareto-optimal, reliability.

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Authors: Vijayalakshmy Periaswamy S., Kevin McDaid

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Testing accounts for the major percentage of technical contribution in the software development process. Typically, it consumes more than 50 percent of the total cost of developing a piece of software. The selection of software tests is a very important activity within this process to ensure the software reliability requirements are met. Generally tests are run to achieve maximum coverage of the software code and very little attention is given to the achieved reliability of the software. Using an existing methodology, this paper describes how to use Bayesian Belief Networks (BBNs) to select unit tests based on their contribution to the reliability of the module under consideration. In particular the work examines how the approach can enhance test-first development by assessing the quality of test suites resulting from this development methodology and providing insight into additional tests that can significantly reduce the achieved reliability. In this way the method can produce an optimal selection of inputs and the order in which the tests are executed to maximize the software reliability. To illustrate this approach, a belief network is constructed for a modern software system incorporating the expert opinion, expressed through probabilities of the relative quality of the elements of the software, and the potential effectiveness of the software tests. The steps involved in constructing the Bayesian Network are explained as is a method to allow for the test suite resulting from test-driven development.

Keywords: Software testing, Test Driven Development, Bayesian Belief Networks.

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Authors: Nicoletta Adamo-Villani

Abstract:

The object of this research is the design and evaluation of an immersive Virtual Learning Environment (VLE) for deaf children. Recently we have developed a prototype immersive VR game to teach sign language mathematics to deaf students age K- 4 [1] [2]. In this paper we describe a significant extension of the prototype application. The extension includes: (1) user-centered design and implementation of two additional interactive environments (a clock store and a bakery), and (2) user-centered evaluation including development of user tasks, expert panel-based evaluation, and formative evaluation. This paper is one of the few to focus on the importance of user-centered, iterative design in VR application development, and to describe a structured evaluation method.

Keywords: 3D Animation, Virtual Reality, Virtual Learning Environments, User-Centered Design, User-centered Evaluation.

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Authors: Eui-Hak Lee, Jae-Hyun Ro, Hyoung-Kyu Song

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In internet of things (IoT) system, the communication scheme with reliability and low power is required to connect a terminal. Cooperative communication can achieve reliability and lower power than multiple-input multiple-output (MIMO) system. Cooperative communication increases the reliability with low power, but decreases a throughput. It has a weak point that the communication throughput is decreased. In this paper, a novel scheme is proposed to increase the communication throughput. The novel scheme is a transmission structure that increases transmission rate. A decoding scheme according to the novel transmission structure is proposed. Simulation results show that the proposed scheme increases the throughput without bit error rate (BER) performance degradation.

Keywords: Cooperative communication, IoT, STBC, Transmission rate.

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Authors: Hye Lyeong Kim, Sang Yeong Choi

Abstract:

This paper discusses a discrete event simulation model for the availability analysis of weapon systems. This model incorporates missions, operational tasks and system reliability structures to analyze the availability of a weapon system. The proposed simulation model consists of 5 modules: Simulation Engine, Maintenance Organizations, System, its Mission Profile and RBD which are based on missions and operational tasks. Simulation Engine executes three kinds of discrete events in chronological order. The events are mission events generated by Mission Profile, failure events generated by System, and maintenance events executed by Maintenance Organization. Finally, this paper shows the case study of a system's availability analysis and mission reliability using the simulation model.

Keywords: MTBF (Mean Time Between Failure), MTTR (Mean Time To Repair), Availability, Reliability, RBD (Reliability Block Diagram)

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Authors: Shigeaki Sakurai, Makino Kyoko, Shigeru Matsumoto

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This paper proposes a method that predicts attractive evaluation objects. In the learning phase, the method inductively acquires trend rules from complex sequential data. The data is composed of two types of data. One is numerical sequential data. Each evaluation object has respective numerical sequential data. The other is text sequential data. Each evaluation object is described in texts. The trend rules represent changes of numerical values related to evaluation objects. In the prediction phase, the method applies new text sequential data to the trend rules and evaluates which evaluation objects are attractive. This paper verifies the effect of the proposed method by using stock price sequences and news headline sequences. In these sequences, each stock brand corresponds to an evaluation object. This paper discusses validity of predicted attractive evaluation objects, the process time of each phase, and the possibility of application tasks.

Keywords: Trend rule, frequent pattern, numerical sequential data, text sequential data, evaluation object.

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Authors: Shibesh Dutta, Sivaramakrishnan R., Sundar Gopalan, Balakrishnan Shankar

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MOSCAPs of various combinations of Hafnium oxide and Titanium oxide of varying thickness with Aluminum as gate electrode have been fabricated and electrically characterized. The effects of voltage stress on the I-V characteristics for prolonged time durations have been studied and compared. Results showed hard breakdown and negligible degradation of reliability under stress.

Keywords: breakdown, MOSCAP, voltage stress.

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Authors: R. Reka, R. S. D. Wahidabanu

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The aim of this paper is to propose a novel technique to guarantee Quality of Service (QoS) in a highly dynamic environment. The MANET changes its topology dynamically as the nodes are moved frequently. This will cause link failure between mobile nodes. MANET cannot ensure reliability without delay. The relay node is selected based on achieving QoS in previous transmission. It considers one more factor Connection Existence Period (CEP) to ensure reliability. CEP is to find out the period during that connection exists between the nodes. The node with highest CEP becomes a next relay node. The relay node is selected dynamically to avoid frequent failure. The bandwidth of each link changed dynamically based on service rate and request rate. This paper proposes Active bandwidth setting up algorithm to guarantee the QoS. The series of results obtained by using the Network Simulator (NS-2) demonstrate the viability of our proposed techniques.

Keywords: Bandwidth, Connection Existence Period (CEP), Mobile Adhoc Network (MANET), Quality of Service (QoS), Relay node.

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Authors: Omid A. Zargar

Abstract:

The simulated mass and spring method evaluation for subway or railways construction and installation systems have a wide application in rail industries. This kind of design should be optimizing all related parameters to reduce the amount of vibration in cities, homelands, historical zones and other critical locations. Finite element method could help us a lot to analysis such applications with an excellent accuracy but always developing some simple, fast and user friendly evaluation method required in subway industrial applications. In addition, process parameter optimization extremely required in railway industries to achieve some optimal design of railways with maximum safety, reliability and performance. Furthermore, it is important to reduce vibrations and further related maintenance costs as well as possible. In this paper a simple but useful simulated mass and spring evaluation system developed for Esfahan subway construction. Besides, some of related recent patent and innovations in rail world industries like Suspension mass tuned vibration reducer, short sleeper vibration attenuation fastener and Airtight track vibration-noise reducing fastener discussed in details.

Keywords: Subway construction engineering, natural frequency, operation frequency, vibration analysis, polyurethane layer.

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Authors: Yu-Cheng Chou, Po Ting Lin

Abstract:

The network of delivering commodities has been an important design problem in our daily lives and many transportation applications. The delivery performance is evaluated based on the system reliability of delivering commodities from a source node to a sink node in the network. The system reliability is thus maximized to find the optimal routing. However, the design problem is not simple because (1) each path segment has randomly distributed attributes; (2) there are multiple commodities that consume various path capacities; (3) the optimal routing must successfully complete the delivery process within the allowable time constraints. In this paper, we want to focus on the design optimization of the Multi-State Flow Network (MSFN) for multiple commodities. We propose an efficient approach to evaluate the system reliability in the MSFN with respect to randomly distributed path attributes and find the optimal routing subject to the allowable time constraints. The delivery rates, also known as delivery currents, of the path segments are evaluated and the minimal-current arcs are eliminated to reduce the complexity of the MSFN. Accordingly, the correct optimal routing is found and the worst-case reliability is evaluated. It has been shown that the reliability of the optimal routing is at least higher than worst-case measure. Two benchmark examples are utilized to demonstrate the proposed method. The comparisons between the original and the reduced networks show that the proposed method is very efficient.

Keywords: Multiple Commodities, Multi-State Flow Network (MSFN), Time Constraints, Worst-Case Reliability (WCR)

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