Search results for: key failure paths

Authors: Mehmet Karaata

Abstract:

Given two distinct vertices (nodes) source s and target t of a graph G = (V, E), the two node-disjoint paths problem is to identify two node-disjoint paths between s ∈ V and t ∈ V . Two paths are node-disjoint if they have no common intermediate vertices. In this paper, we present an algorithm with O(m)-time complexity for finding two node-disjoint paths between s and t in arbitrary graphs where m is the number of edges. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.

Keywords: disjoint paths, distributed systems, fault-tolerance, network routing, security

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Authors: Li-Zhi Liao

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The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

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Authors: Mei-Fang Wu, Shu-Li Wang, Feng-Tsung Cheng

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Highly developed technology and highly competitive global market highlight the important role of competitive advantages and operation performances in sustainable company operation. Activity-Based Costing (ABC) provides accurate operation cost and operation performance information. Rich literature provide relevant research with cases study on Activity-Based Costing application, and yet, there is no research studying on cause relationship between key success factors of applying Activity-Based Costing and its specific outcomes, such as profitability or share market. These relationships provide the ways to handle the key success factors to achieve the specific outcomes for ensuring to promote the competitive advantages and operation performances. The main purposes of this research are exploring the key success paths by Key Success Paths approach which will lead the ways to apply Activity-Base Costing. The Key Success Paths is the innovative method which is exploring the cause relationships and explaining what are the effects of key success factors to specific outcomes of Activity-Based Costing implementation. The cause relationships between key success factors and successful specific outcomes are Key Success Paths (KSPs). KSPs are the guidelines to lead the cost management strategies to achieve the goals of competitive advantages and operation performances. The research findings indicate that good management system design may impact the good outcomes of Activity-Based Costing application and achieve to outstanding competitive advantage, operating performance and profitability as well by KSPs exploration.

Keywords: activity-based costing, key success factors, key success paths approach, key success paths, key failure paths

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Authors: C. P. Autry, A. W. Roscoe, Mykhailo Magal

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We discuss the theoretical model underlying 2BPA (two-band peer authentication), a practical alternative to conventional authentication of entities and data in IoT. In essence, this involves assembling a virtual map of authentication assets in the network, typically leading to many paths of confirmation between any pair of entities. This map is continuously updated, confirmed, and evaluated. The value of authentication along multiple disjoint paths becomes very clear, and we require analogues of triangulation to extend authentication along extended paths and deliver it along all possible paths. We discover that if an attacker wants to make an honest node falsely believe she has authenticated another, then the length of the authentication paths is of little importance. This is because optimal attack strategies correspond to minimal cuts in the authentication graph and do not contain multiple edges on the same path. The authentication provided by disjoint paths normally is additive (in entropy).

Keywords: authentication, edge computing, industrial IoT, post-quantum resistance

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Authors: Stephen V. Crowder, Jonathan W. Lane

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With short production development times, there is an increased need to demonstrate product reliability relatively quickly with minimal testing. In such cases there may be few if any observed failures. Thus it may be difficult to assess reliability using the traditional reliability test plans that measure only time (or cycles) to failure. For many components, degradation measures will contain important information about performance and reliability. These measures can be used to design a minimal test plan, in terms of number of units placed on test and duration of the test, necessary to demonstrate a reliability goal. In this work we present a case study involving an electronic component subject to degradation. The data, consisting of 42 degradation paths of cycles to failure, are first used to estimate a reliability function. Bootstrapping techniques are then used to perform power studies and develop a minimal reliability test plan for future production of this component.

Keywords: degradation measure, time to failure distribution, bootstrap, computational science

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Authors: J. H. Lv, W. Z. Wang, S.W. Liu

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The major concern in the aviation industry is the flight safety. Although great effort has been put onto the development of material and system reliability, the failure cases of fatal accidents still occur nowadays. Due to the complexity of the aviation system, and the interaction among the failure components, the failure analysis of the related equipment is a little difficult. This study focuses on surveying the failure cases in aviation, which are extracted from failure analysis journals, including Engineering Failure Analysis and Case studies in Engineering Failure Analysis, in order to obtain the failure sensitive factors or failure sensitive parts. The analytical results show that, among the failure cases, fatigue failure is the largest in number of occurrence. The most failed components are the disk, blade, landing gear, bearing, and fastener. The frequently failed materials consist of steel, aluminum alloy, superalloy, and titanium alloy. Therefore, in order to assure the safety in aviation, more attention should be paid to the fatigue failures.

Keywords: aerospace, disk, failure analysis, fatigue

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Authors: Lei Chen, Jian Jiao, Tingdi Zhao

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Failures of automotive electric/electronic systems, which are universally considered to be safety-critical and software-intensive, may cause catastrophic accidents. Analysis and verification of failures in these kinds of systems is a big challenge with increasing system complexity. Model-checking is often employed to allow formal verification by ensuring that the system model conforms to specified safety properties. The system-level effects of failures are established, and the effects on system behavior are observed through the formal verification. A hazard analysis technique, called Systems-Theoretic Process Analysis, is capable of identifying design flaws which may cause potential failure hazardous, including software and system design errors and unsafe interactions among multiple system components. This paper provides a concept on how to use model-checking integrated with Systems-Theoretic Process Analysis to perform failure analysis and verification of automotive electric/electronic systems. As a result, safety requirements are optimized, and failure propagation paths are found. Finally, an automotive electric/electronic system case study is used to verify the effectiveness and practicability of the method.

Keywords: failure analysis and verification, model checking, system-theoretic process analysis, automotive electric/electronic system

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Authors: Ahmed R. Ismail, Hatem A. El Tawil, Nevin G. Rezk

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Historic paths in today's cities are facing the pressure of the urban development due to the rapid urban growth. Every new development is tearing the old urban fabric and the socio-economic character of the historic paths. Furthermore, in some cases historic paths suffer from negligence and decay. Kom El Dekka historic path was one of those deteriorated paths in the city of Alexandria, Egypt, in spite of its high heritage and socio-economic value. Therefore, there was a need to develop urban regeneration strategies as a part of a wider sustainable development vision, to handle the situation and revitalize the path as a livable space in the heart of the city. This study aims to develop a comprehensive assessment methodology to evaluate the different values of the path and to create community-oriented and economic-based analysis methodology for its socio-economic values. These analysis and assessments provide strategies for any regeneration action plan for Kom El Dekka historic path.

Keywords: community-oriented, economic-based, syntactical analysis, urban regeneration

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Authors: Manas Tripathi, Arunabha Mukhopadhyay

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In Cloud computing environment, cloud servers, sometimes may crash after receiving huge amount of request and cloud services may stop which can create huge loss to users of that cloud services. This situation is called Denial of Service (DoS) attack. In Distributed Denial of Service (DDoS) attack, an attacker targets multiple network paths by compromising various vulnerable systems (zombies) and floods the victim with huge amount of request through these zombies. There are many solutions to mitigate this challenge but most of the methods allows the attack traffic to arrive at Cloud Service Provider (CSP) and then only takes actions against mitigation. Here in this paper we are rather focusing on preventive mechanism to deal with these attacks. We analyze network topology and find most vulnerable paths beforehand without waiting for the traffic to arrive at CSP. We have used Dijkstra's and Yen’s algorithm. Finally, risk assessment of these paths can be done by multiplying the probabilities of attack for these paths with the potential loss.

Keywords: cloud computing, DDoS, Dijkstra, Yen’s k-shortest path, network security

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Authors: Tarek Ninouh, Ahmed Rouili

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The Roman paths or roads offer a very interesting archaeological material, because they allow us to understand the history of human settlement and are also factors that increase territorial identity. Roman roads are one of the hallmarks of the Roman empire, which extends to North Africa. The objective of this investigation is to attract the attention of researchers to the importance of Roman roads and paths, which are found in Algeria, according to the quality of the materials and techniques used in this period of our history, and to encourage other decision makers to protect and enhance these routes because the current urbanization, intensive agricultural practices, or simply forgotten, decreases the sustainability of this important historical heritage.

Keywords: Roman paths, quality of materials, property, valuation

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Authors: Yiqiang Ni, Xuanlong Chen, Enliang Li, Linting Zheng, Shizheng Yang

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Bipolar ICs are playing an important role in military applications, mainly used in logic gates, such as inverter and NAND gate. The defect of metal break located on the step is one of the main failure mechanisms of bipolar ICs, resulting in open-circuit or functional failure. In this situation, general failure localization methods like optical beam-induced resistance change (OBIRCH) and photon emission microscopy (PEM) might not be fully effective. However, active voltage contrast (AVC) can be used as a voltage probe, which may pinpoint the incorrect potential and thus locate the failure position. Two case studies will be present in this paper on how to implement AVC for failure localization, and the detailed failure mechanism will be discussed.

Keywords: bipolar IC, failure localization, metal break, open failure, voltage contrast

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Authors: Konja Knüppel, Gerrit Meyer, Peter Nyhuis

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The increasing interconnectedness and complexity of production processes raise the susceptibility of production systems to failure. Therefore, the ability to respond quickly to failures is increasingly becoming a competitive factor. The research project "Sustainable failure management in manufacturing SMEs" is developing a methodology to identify failures in the production and select preventive and reactive measures in order to correct failures and to establish sustainable failure management systems.

Keywords: failure categorization, failure management, logistic performance, production optimization

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Authors: Gaoyang Meng, Philip Harrison

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When manufacturing composite laminates, the fibre directions within the laminate are never perfectly straight and inevitably contain some degree of stochastic in-plane waviness or ‘meandering’. In this work we aim to understand the relationship between the degree of meandering of the fibre paths, and the resulting uncertainty in the laminate’s final mechanical properties. To do this, a numerical tool is developed to automatically generate meandering fibre paths in each of the laminate's 8 plies (using Matlab) and after mapping this information into finite element simulations (using Abaqus), the statistical variability of the tensile mechanical properties of a [45°/90°/-45°/0°]s carbon/epoxy (IM7/8552) laminate is predicted. The stiffness, first ply failure strength and ultimate failure strength are obtained. Results are generated by inputting the degree of variability in the fibre paths and the laminate is then examined in all directions (from 0° to 359° in increments of 1°). The resulting predictions are output as flower (polar) plots for convenient analysis. The average fibre orientation of each ply in a given laminate is determined by the laminate layup code [45°/90°/-45°/0°]s. However, in each case, the plies contain increasingly large amounts of in-plane waviness (quantified by the standard deviation of the fibre direction in each ply across the laminate. Four different amounts of variability in the fibre direction are tested (2°, 4°, 6° and 8°). Results show that both the average tensile stiffness and the average tensile strength decrease, while the standard deviations increase, with an increasing degree of fibre meander. The variability in stiffness is found to be relatively insensitive to the rotation angle, but the variability in strength is sensitive. Specifically, the uncertainty in laminate strength is relatively low at orientations centred around multiples of 45° rotation angle, and relatively high between these rotation angles. To concisely represent all the information contained in the various polar plots, rotation-angle dependent Weibull distribution equations are fitted to the data. The resulting equations can be used to quickly estimate the size of the errors bars for the different mechanical properties, resulting from the amount of fibre directional variability contained within the laminate. A longer term goal is to use these equations to quickly introduce realistic variability at the component level.

Keywords: advanced composite laminates, FE simulation, in-plane waviness, tensile properties, uncertainty quantification

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Authors: Roham Rafiee, Hadi Hesamsadat

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In this study, a parametric finite element modeling is developed to analyze failure modes of FRP pipes subjected to internal pressure. First-ply failure pressure and functional failure pressure was determined by a progressive damage modeling and then it is validated using experimental observations. The influence of both winding angle and fiber volume fraction is studied on the functional failure of FRP pipes and it corresponding pressure. It is observed that despite the fact that increasing fiber volume fraction will enhance the mechanical properties, it will be resulted in lower values for functional failure pressure. This shortcoming can be compensated by modifying the winding angle in angle plies of pipe wall structure.

Keywords: composite pipe, functional failure, progressive modeling, winding angle

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Authors: Chae Hoon Park, Jong Kang Park, Jong Tae Kim

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Electrical characteristics of capacitive touchscreen need to be accurately analyzed to result in better performance for multi-channel capacitance sensing. In this paper, we extracted the panel resistances and capacitances of the touchscreen by comparing measurement data and model data. By employing a lumped RC model for driver-to-receiver paths in touchscreen, we estimated resistance and capacitance values according to the physical lengths of channel paths which are proportional to the RC model. As a result, we obtained the model having 95.54% accuracy of the measurement data.

Keywords: electrical characteristics of capacitive touchscreen, iterative extraction, lumped RC model, physical lengths of channel paths

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Authors: Sam S. Hashemi

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The breakage of bonding between sand particles and their dislodgment from the borehole wall are among the main factors resulting in a borehole failure in poorly cemented granular formations. The grain debonding usually precedes the borehole failure and it can be considered as a sign that the onset of the borehole collapse is imminent. Detecting the bonding breakage point and introducing an appropriate failure criterion will play an important role in borehole stability analysis. To study the influence of different factors on the initiation of sand bonding breakage at the borehole wall, a series of laboratory tests was designed and conducted on poorly cemented sand samples. The total absorbed strain energy per volume of material up to the point of the observed particle debonding was computed. The results indicated that the particle bonding breakage point at the borehole wall was reached both before and after the peak strength of the thick-walled hollow cylinder specimens depending on the stress path and cement content. Three different cement contents and two borehole sizes were investigated to study the influence of the bonding strength and scale on the particle dislodgment. Test results showed that the stress path has a significant influence on the onset of the sand bonding breakage. It was shown that for various stress paths, there is a near linear relationship between the absorbed energy and the normal effective mean stress.

Keywords: borehole stability, experimental studies, poorly cemented sands, total absorbed strain energy

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Authors: S. W. Liu, J. H. Lv, W. Z. Wang

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In recent years, the failure accidents in petrochemical industry have been frequent, and have posed great security problems in personnel and property. The improvement of petrochemical safety is highly requested in order to prevent re-occurrence of severe accident. This study focuses on surveying the failure cases occurred in petrochemical field, which were extracted from journals of engineering failure, including engineering failure analysis and case studies in engineering failure analysis. The relation of failure mode, failure mechanism, type of components, and type of materials was analyzed in this study. And the analytical results showed that failures occurred more frequently in vessels and piping among the petrochemical equipment. Moreover, equipment made of carbon steel and stainless steel accounts for the majority of failures compared to other materials. This may be related to the application of the equipment and the performance of the material. In addition, corrosion failures were the largest in number of occurrence in the failure of petrochemical equipment, in which stress corrosion cracking accounts for a large proportion. This may have a lot to do with the service environment of the petrochemical equipment. Therefore, it can be concluded that the corrosion prevention of petrochemical equipment is particularly important.

Keywords: cases analysis, corrosion, failure, petrochemical industry

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Authors: V. V. Singh

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We have studied the reliability measures of a system, which consists of two subsystems i.e. subsystem-1 and subsystem-2 in series configuration under different types of failure. The subsystem-1 has three identical units in parallel configuration and operating under 2-out-of-3: G policy and connected to subsystem-2 in series configuration. Each subsystem has different types of failure and repair rates. An important cause for failure of system is unsuitability of the environmental conditions, like overheating, weather conditions, heavy rainfall, storm etc. The environmental failure is taken into account in the proposed repairable system. Supplementary variable technique is used to study of system and some traditional measures such as; availability, reliability, MTTF and profit function are obtained for different values of parameters. In the proposed model, some particular cases of failure rates are explicitly studied.

Keywords: environmental failure, human failure, availability, MTTF, reliability, profit analysis, Gumbel-Hougaard family copula

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Authors: Altoumi Alndalusi

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High-temperature hydrogen attack (HTHA) failure is the common phenomena at elevated temperature in hydrogen environment in oil and gas field. The failure occurred once after four years at the internal surface of Platforming elbow. Both visual and microscopic examinations revealed that the failure was initiated due to blistering forming followed by large cracking at the inner surface. Crack morphology showed that the crack depth was about 50% of material wall thickness and its behavior generally was intergranular. This study concluded that the main reason led to failure due to incorrect material selection comparing to the platforming conditions.

Keywords: decarburization, failure, heat affected zone, morphology, partial pressure, plate form

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Authors: Aydin Azizi, Ahmed Al. Azizi

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Mechanical seals are essential components in centrifugal pumps since they help in controlling leaking out of the liquid that is pumped under pressure. Unlike the common types of packaging, mechanical seals are highly efficient and they reduce leakage by a great extent. However, all multiphase mechanical seals leak and they are subject to failure. Some of the factors that have been recognized to their failure include excessive heating, open seal faces, as well as environment related factors that trigger failure of the materials used to manufacture seals. The proposed research study will explore the failure of multiphase mechanical seal in centrifugal pumps. The objective of the study includes how to reduce the failure in multiphase mechanical seals and to make them more efficient.

Keywords: mechanical seals, centrifugal pumps, multi phase failure, excessive heating

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

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This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution

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Authors: V. V. Singh

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In this paper we have focused on the study of a Linux operating system connected in a LAN (local area network). We have considered two different topologies STAR topology (subsystem-1) and BUS topology (subsystem-2) which are placed at two different places and connected to a server through a hub. In both topologies BUS topology and STAR topology, we have assumed 'n' clients. The system has two types of failure partial failure and complete failure. Further the partial failure has been categorized as minor partial failure and major partial failure. It is assumed that minor partial failure degrades the subsystem and the major partial failure brings the subsystem to break down mode. The system can completely failed due to failure of server hacking and blocking etc. The system is studied by supplementary variable technique and Laplace transform by taking different types of failure and two types of repairs. The various measures of reliability like availability of system, MTTF, profit function for different parametric values has been discussed.

Keywords: star topology, bus topology, hacking, blocking, linux operating system, Gumbel-Hougaard family copula, supplementary variable

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Faten Khanfir, Mohamed Tlili, Ali Medeb Hamrouni, Raki Selmi, M. S. Khalfi, Faten Ben Amor

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Introduction: dental implant failure is a major concern for the clinician and the patient. Objectives: The aim of our study is to investigate the way in which 100 Tunisian dentists carried implant treatment for their patients from the early phase of planning and selection of patients to the placement of the implant in order to look for the implant failure factors. Results: significant correlations were found between failure rates > 5 and their corresponding factors as the number of implants placed (p = 0.001<0, 05), smoking (0.046 <0.05), unbalanced diabetes (0.03<0.05), aseptic protocol (= 0.004< 0.05) and the drilling speed (0,002<0.05) Conclusion: It seems that the number of implant placed, smoking, diabetes, aseptic protocol, and the drilling speed may contribute to dental implant failure.

Keywords: failure, implants, survey, risk, osseointegration

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Authors: Jehnming Lin

Abstract:

In the laser cleavage of glass, the laser is mostly adopted as a heat source to generate a thermal stress state on the substrates. The crack propagation of the soda-lime glass in the laser thermal cleavage with the straight-turning paths was investigated in this study experimentally and numerically. The crack propagation was visualized by a high speed camera with the off-line examination on the micro-crack propagation. The temperature and stress distributions induced by the laser heat source were calculated by ANSYS software based on the finite element method (FEM). With the cutting paths in various turning directions, the experimental and numerical results were in comparison and verified. The fracture modes due to the normal and shear stresses were verified at the turning point of the laser cleavage path. It shows a significant variation of the stress profiles along the straight-turning paths and causes a change on the fracture modes.

Keywords: laser cleavage, glass, fracture, stress analysis

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Authors: Mehmet Hakan Karaata, Ali Hamdan, Omer Yusuf Adam Mohamed

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Consider a distributed system that delivers messages from a process to another. Such a system is often required to deliver each message to its destination regardless of whether or not the system components experience arbitrary forms of faults. In addition, each message received by the destination must be a message sent by a system process. In this paper, we first identify the necessary and sufficient conditions to detect some restricted form of Byzantine faults referred to as modifying Byzantine faults. An observable form of a Byzantine fault whose effect is limited to the modification of a message metadata or content, timing and omission faults, and message replay is referred to as a modifying Byzantine fault. We then present a distributed protocol to detect modifying Byzantine faults using optimal number of messages over node-disjoint paths.

Keywords: Byzantine faults, distributed systems, fault detection, network pro- tocols, node-disjoint paths

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Authors: Vijay Vir Singh

Abstract:

This work is focused studying the Linux operating system connected in a LAN (local area network). The STAR topology (to be called subsystem-1) and BUS topology (to be called subsystem-2) are taken into account, which are placed at two different locations and connected to a server through a hub. In the both topologies BUS topology and STAR topology, we have assumed n clients. The system has two types of failures i.e. partial failure and complete failure. Further, the partial failure has been categorized as minor and major partial failure. It is assumed that the minor partial failure degrades the sub-systems and the major partial failure make the subsystem break down mode. The system may completely fail due to failure of server hacking and blocking etc. The system is studied using supplementary variable technique and Laplace transform by using different types of failure and two types of repair. The various measures of reliability for example, availability of system, reliability of system, MTTF, profit function for different parametric values have been discussed.

Keywords: star topology, bus topology, blocking, hacking, Linux operating system, Gumbel-Hougaard family copula, supplementary variable

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Authors: Dongqin Cheng

Abstract:

The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.

Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges

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Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

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In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: cause of failure, linear degradation path, reliability function, expectation-maximization algorithm, intensity, masked data

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