Search results for: system failure

Authors: V. V. Singh

Abstract:

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: V. V. Singh

Abstract:

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: 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: 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: Akram Khaleghei, Ghosheh Balagh, Viliam Makis

Abstract:

In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, residual life prediction

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Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

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In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed and illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, multivariate Bayesian control

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Authors: Chur Hee Lee, Jae in Lee, Minh Chau Diah, Jong Su Yoon, Seung Wan Kim

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This paper deals with Real Time Digital Simulator (RTDS) analysis about effects of transmission lines failure in power system equipped with Thyristor Controlled Series Capacitance (TCSC) in Korea. The TCSC is firstly applied in Korea to compensate real power in case of 765 kV line faults. Therefore, It is important to analyze with TCSC replica using RTDS. In this test, all systems in Korea, other than those near TCSC, were abbreviated to Thevenin equivalent. The replica was tested in the case of a line failure near the TCSC, a generator failure, and a 765-kV line failure. The effects of conventional operated STATCOM, SVC and TCSC were also analyzed. The test results will be used for the actual TCSC operational impact analysis.

Keywords: failure analysis, power system, RTDS, TCSC

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Authors: Min-Tsai Lai, Taqwa Hariguna

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This paper presents a periodical replacement model for a system, considering the concept of single and cumulative repair cost limits simultaneously. The failures are divided into two types. Minor failure can be corrected by minimal repair and serious failure makes the system breakdown completely. When a minor failure occurs, if the repair cost is less than a single repair cost limit L1 and the accumulated repair cost is less than a cumulative repair cost limit L2, then minimal repair is executed, otherwise, the system is preventively replaced. The system is also replaced at time T or at serious failure. The optimal period T minimizing the long-run expected cost per unit time is verified to be finite and unique under some specific conditions.

Keywords: repair-cost limit, cumulative repair-cost limit, minimal repair, periodical replacement policy

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Authors: Vijay Vir Singh

Abstract:

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 local server). Observing the different possibilities of functioning of the CC, analysis has been done to evaluate the various reliability characteristics of the system. The system can completely fail due to failure of router, redundant server before repairing the mail server, and switch failure. The system can also partially fail when local server fails. The system can also fail completely due to a cooling failure, electricity failure or some natural calamity like earthquake, fire etc. All the failure rates are assumed to be constant while repair follows two types of distributions: general and Gumbel-Hougaard family copula.

Keywords: reliability, availability Gumbel-Hougaard family copula, MTTF, internet data centre

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Authors: Lei Chen, Jian Jiao, Tingdi Zhao

Abstract:

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: Viriyavudh Sim, WooYoung Jung

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Window system in high rise building is occasionally subjected to an excessive wind intensity, particularly during typhoon. The failure of window system did not affect overall safety of structural performance; however, it could endanger the safety of the residents. In this paper, comparison of fragility curves for window system of two residential buildings was studied. The probability of failure for individual window was determined with Monte Carlo Simulation method. Then, lognormal cumulative distribution function was used to represent the fragility. The results showed that windows located on the edge of leeward wall were more susceptible to wind load and the probability of failure for each window panel increased at higher floors.

Keywords: wind fragility, window system, high rise building, wind disaster

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Authors: B. Lee, B. H. Choi

Abstract:

The loss of safety for reservoirs brought about by climate change and facility aging leads to reservoir failures, which results in the loss of lives and property damage in downstream areas. Therefore, it is necessary to provide a reservoir failure alert system for downstream residents to detect the early signs of failure (with sensors) in real-time and perform safety management to prevent and minimize possible damage. 10 case studies were carried out to verify the water level management criteria of four levels (attention, caution, alert, serious). Peak changes in water level data were analysed. The results showed that ‘Caution’ and ‘Alert’ were closed to 33% and 66% of difference in level between flood water level and full water level. Therefore, it is adequate to use initial water level management criteria of reservoir failure alert system for the first year. Acknowledgment: This research was supported by a grant (2017-MPSS31-002) from 'Supporting Technology Development Program for Disaster Management' funded by the Ministry of the Interior and Safety(MOIS)

Keywords: alert system, management criteria, reservoir failure, sensor

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Authors: Royia Soliman, Salma ElAnsary, Akram Amin Abdellatif, Florian Holzapfel

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Model-Based Safety Analysis (MBSA) is an approach in which the system and safety engineers share a common system model created using a model-based development process. The model can also be extended by the failure modes of the system components. There are two famous approaches for the addition of fault behaviors to system models. The first one is to enclose the failure into the system design directly. The second approach is to develop a fault model separately from the system model, thus combining both independent models for safety analysis. This paper introduces a hybrid approach of MBSA. The approach tries to use informal abstracted models to investigate failure behaviors. The approach will combine various concepts such as directed graph traversal, event lists and Constraint Satisfaction Problems (CSP). The approach is implemented using an Object Oriented programming language. The components are abstracted to its failure logic and relationships of connected components. The implemented approach is tested on various flight control systems, including electrical and multi-domain examples. The various tests are analyzed, and a comparison to different approaches is represented.

Keywords: flight control systems, model based safety analysis, safety assessment analysis, system modelling

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

Abstract:

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 centre

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Authors: Siqi Qiu, Yijian Zheng, Xin Guo Ming

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In many reliability and risk analysis, failures of components are supposed to be independent. However, in reality, the ignorance of failure dependencies among components may render the results of reliability and risk analysis incorrect. There are two principal ways to incorporate failure dependencies in system reliability and risk analysis: implicit and explicit methods. In the implicit method, failure dependencies can be modeled by joint probabilities, correlation values or conditional probabilities. In the explicit method, certain types of dependencies can be modeled in a fault tree as mutually independent basic events for specific component failures. In this paper, explicit and implicit methods based on BDD will be proposed to evaluate the reliability of systems considering failure dependencies. The obtained results prove the equivalence of the proposed implicit and explicit methods. It is found that the consideration of failure dependencies decreases the reliability of systems. This observation is intuitive, because more components fail due to failure dependencies. The consideration of failure dependencies helps designers to reduce the dependencies between components during the design phase to make the system more reliable.

Keywords: reliability assessment, risk assessment, failure dependencies, binary decision diagram

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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: Payel Datta, Abhishek Das, Abhishek Roychoudhury, Dhiman Chattopadhyay, Tanushyam Chattopadhyay

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Machine learning (ML) and deep learning (DL) is most predominantly used in image/video processing, natural language processing (NLP), audio and speech recognition but not that much used in system performance evaluation. In this paper, authors are going to describe the architecture of an abstraction layer constructed using ML/DL to detect the system failure. This proposed system is used to detect the system failure by evaluating the performance metrics of an IoT service deployment under constrained infrastructure environment. This system has been tested on the manually annotated data set containing different metrics of the system, like number of threads, throughput, average response time, CPU usage, memory usage, network input/output captured in different hardware environments like edge (atom based gateway) and cloud (AWS EC2). The main challenge of developing such system is that the accuracy of classification should be 100% as the error in the system has an impact on the degradation of the service performance and thus consequently affect the reliability and high availability which is mandatory for an IoT system. Proposed ML/DL classifiers work with 100% accuracy for the data set of nearly 4,000 samples captured within the organization.

Keywords: machine learning, system performance, performance metrics, IoT, edge

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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: Bhupinder Kaur, O. P. Pandey

Abstract:

An automobile industry is using variety of materials for better comfort and utility. The present work describes the details of failure analysis done for windshield glass of a four-wheeler class. The failure occurred in two different models of the heavy duty class of four wheelers, which analysed separately. The company reported that the failure has occurred only in their rear windshield when vehicles parked under shade for several days. These glasses were characterised by dilatometer, differential thermal analyzer, and X-ray diffraction. The glasses were further investigated under scanning electron microscope with energy dispersive X-ray spectroscopy and X-ray dot mapping. The microstructural analysis of the glasses done at the surface as well as at the fractured area indicates that carbon as an impurity got segregated as banded structure throughout the glass. Since carbon absorbs higher heat, it causes thermal mismatch to the entire glass system, and glass shattered down. In this work, the details of sequential analysis done to predict the cause of failure are present.

Keywords: failure, windshield, thermal mismatch, carbon

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Authors: Inuwa Abdu Ibrahim

Abstract:

The research assessed representative democracy as an administrative system in Nigeria, by highlighting the failure of the state. It also looked at some components of direct democracy in Switzerland. Therefore, the paper focused on direct democracy, using secondary sources of data. In conclusion, the research offers direct democracy as a solution to the failure of the Nigerian administrative system especially as it affects participation, developmental programmes and institutionalized corruption.

Keywords: corruption, direct democracy, national development, Nigeria, participation

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Authors: Said Fares, Mary Fares

Abstract:

It is well documented that introductory computer programming courses are difficult and that failure rates are high. The aim of this project was to reduce the high failure and withdrawal rates in learning to program. This paper presents a number of changes in module organization and instructional delivery system in teaching CS1. Daily out of class help sessions and tutoring services were applied, interactive lectures and laboratories, online resources, and timely feedback were introduced. Five years of data of 563 students in 21 sections was collected and analyzed. The primary results show that the failure and withdrawal rates were cut by more than half. Student surveys indicate a positive evaluation of the modified instructional approach, overall satisfaction with the course and consequently, higher success and retention rates.

Keywords: failure rate, interactive learning, student engagement, CS1

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

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In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: Srinivasan Chandrasekaran, Manda Hari Venkata Ramachandra Rao

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Increase in the oil and gas exploration in ultra deep-water demands an adaptive structural form of the platform. Triceratops has superior motion characteristics compared to that of the Tension Leg Platform and Single Point Anchor Reservoir platforms, which is well established in the literature. Buoyant legs that support the deck are position-restrained to the sea bed using tethers with high axial pretension. Environmental forces that act on the platform induce dynamic tension variations in the tethers, causing the failure of tethers. The present study investigates the dynamic response behavior of the restraining system of the platform under the failure of a single tether of each buoyant leg in high sea states. Using the rain-flow counting algorithm and the Goodman diagram, fatigue damage caused to the tethers is estimated, and the fatigue life is predicted. Results shows that under failure conditions, the fatigue life of the remaining tethers is quite alarmingly low.

Keywords: fatigue life, pm spectrum, rain flow counting, triceratops, failure analysis

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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: Ramanpreet Kaur, Upasana Sharma

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The purpose of this paper is to address the challenges facing the water supply for the Machine Learning Database (MLDB) system at the piston foundry plant. In the MLDB system, one main unit, i.e., robotic, is connected by two sub-units. The functioning of the system depends on the robotic and water supply. Lack of water supply causes system failure. The system operates at full capacity with the help of two sub-units. If one sub-unit fails, the system runs at a low capacity. Reliability modeling is performed using semi-Markov processes and regenerative point techniques. Several system effects such as mean time to system failure, availability at full capacity, availability at reduced capacity, busy period for repair and expected number of visits have been achieved. Benefits have been analyzed. The graphical study is designed for a specific case using programming in C++ and MS Excel.

Keywords: MLDB system, robotic, semi-Markov process, regenerative point technique

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Authors: Chin-Chih Chang

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Many manufacturing systems suffer failures due to complex degradation processes and various environment conditions such as random shocks. Consider an operating system is subject to random shocks and works at random times for successive jobs. When successive jobs often result in production losses and performance deterioration, it would be better to do maintenance or replacement at a planned time. A preventive replacement (PR) policy is presented to replace the system before a failure occurs at a continuous time T. In such a policy, the failure characteristics of the system are designed as follows. Each job would cause a random amount of additive damage to the system, and the system fails when the cumulative damage has exceeded a failure threshold. Suppose that the deteriorating system suffers one of the two types of shocks with age-dependent probabilities: type-I (minor) shock is rectified by a minimal repair, or type-II (catastrophic) shock causes the system to fail. A corrective replacement (CR) is performed immediately when the system fails. In summary, a generalized maintenance model to scheduling replacement plan for an operating system is presented below. PR is carried out at time T, whereas CR is carried out when any type-II shock occurs and the total damage exceeded a failure level. The main objective is to determine the optimal continuous schedule time of preventive replacement through minimizing the mean cost rate function. The existence and uniqueness of optimal replacement policy are derived analytically. It can be seen that the present model is a generalization of the previous models, and the policy with preventive replacement outperforms the one without preventive replacement.

Keywords: preventive replacement, working time, cumulative damage model, minimal repair, imperfect maintenance, optimization

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Authors: Roham Rafiee, Hadi Hesamsadat

Abstract:

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: A. S. Grewal, R. S. Sangwan, Dharambir, Vikas Dhanda

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The purpose of this paper is to develop and analyze two reliability models for a system of non-identical firearms – one is standard firearm (called as original unit) and the other is a country-made firearm (called as duplicate /substandard unit). There is a single server who comes immediately to do inspection and repair whenever needed. On the failure of standard firearm, the server inspects the operative country-made firearm to see whether the unit is capable of performing the desired function well or not. If country-made firearm is not capable to do so, the operation of the system is stopped and server starts repair of the standard firearms immediately. However, no inspection is done at the failure of the country-made firearm as the country-made firearm alone is capable of performing the given task well. In model I, priority to repair the standard firearm is given in case system fails completely and country-made firearm is already under repair, whereas in model II there is no such priority. The failure and repair times of each unit are assumed to be independent and uncorrelated random variables. The distributions of failure time of the units are taken as negative exponential while that of repair and inspection times are general. By using semi-Markov process and regenerative point technique some econo-reliability measures are obtained. Graphs are plotted to compare the MTSF (mean time to system failure), availability and profit of the models for a particular case.

Keywords: non-identical firearms, inspection, priority to repair, semi-Markov process, regenerative point

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Authors: Daehyun Baek, Seungmin Lee, Minju Kim Jangik Park, Hyeong-Soon Moon

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SPM (Single Point Mooring) is one of the mooring buoy facilities installed on a coast near oil and gas terminal which is not able to berth FPSO or large oil tankers under the condition of high draft due to geometrical limitation. Loading and unloading of crude oil and gas through a subsea pipeline can be carried out between the mooring buoy, ships and onshore facilities. SPM is an offshore-standalone system which has to withstand the harsh marine environment with harsh conditions such as high wind, current and so on. Therefore, SPM is required to have high stability, reliability and durability. Also, SPM is comprised to be integrated systems which consist of power management, high pressure valve control, sophisticated hardware/software and a long distance communication system. In order to secure required functions of SPM system, a simulation model for the integrated system of SPM using MATLAB Simulink and State flow tool has been developed. The developed model consists of configuration of hydraulic system for opening and closing of PLEM (Pipeline End Manifold) valves and control system logic. To verify functions of the model, an integrated simulation model for overall systems of SPM was also developed by considering handshaking variables between individual systems. In addition to the dynamic model, a self-diagnostic function to determine failure of the system was configured, which enables the SPM system itself to alert users about the failure once a failure signal comes to arise. Controlling and monitoring the SPM system is able to be done by a HMI system which is capable of managing the SPM system remotely, which was carried out by building a communication environment between the SPM system and the HMI system.

Keywords: HMI system, mooring buoy, simulink simulation model, single point mooring, stateflow

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Authors: Yen-Luan Chen

Abstract:

Maintenance has a great impact on the capacity of production and on the quality of the products, and therefore, it deserves continuous improvement. Maintenance procedure done before a failure is called preventive maintenance (PM). Sequential PM, which specifies that a system should be maintained at a sequence of intervals with unequal lengths, is one of the commonly used PM policies. This article proposes a generalized sequential PM policy for a system subject to shocks with imperfect maintenance and random working time. The shocks arrive according to a non-homogeneous Poisson process (NHPP) with varied intensity function in each maintenance interval. As a shock occurs, the system suffers two types of failures with number-dependent probabilities: type-I (minor) failure, which is rectified by a minimal repair, and type-II (catastrophic) failure, which is removed by a corrective maintenance (CM). The imperfect maintenance is carried out to improve the system failure characteristic due to the altered shock process. The sequential preventive maintenance-last (PML) policy is defined as that the system is maintained before any CM occurs at a planned time Ti or at the completion of a working time in the i-th maintenance interval, whichever occurs last. At the N-th maintenance, the system is replaced rather than maintained. This article first takes up the sequential PML policy with random working time and imperfect maintenance in reliability engineering. The optimal preventive maintenance schedule that minimizes the mean cost rate of a replacement cycle is derived analytically and determined in terms of its existence and uniqueness. The proposed models provide a general framework for analyzing the maintenance policies in reliability theory.

Keywords: optimization, preventive maintenance, random working time, minimal repair, replacement, reliability

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