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Generalized equations for calculating the probability of failure on demand (PFD) in accordance with the IEC 61508 standard and a model based on Markov processes, taking into account common cause failures, are proposed in this paper. The solutions presented in the standard and in many references concentrate on simple k‐out‐of‐n architectures. The equations proposed in the standard concern cases for n ≤ 3. In safety‐related systems applied in industry, architectures of a number of elements n larger than three often occur. For this reason, a generalized equation for calculating PFD was proposed. For cases presented in the standard, the proposed equation provides identical results. The presented simplified Markov model allows the determination of the system availability (A(t)) and unavailability (1–A(t)) as well as their values in the steady state (A and 1–A). This model can be an alternative method of PDF calculations for various k‐out‐of‐n architectures with self‐diagnostic elements. Calculations performed according to the proposed models provide very similar results. The developed models are suitable for practical implementations in calculations of the safety integrity level. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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This paper presents the design optimization by a multi-objective genetic algorithm of a safety-instrumented system based on RAMS+C measures. This includes optimization of safety and reliability measures plus lifecycle cost. Diverse redundancy is implemented as an option for redundancy allocation, and special attention is paid to its effect on common cause failure and the overall system objectives. The requirements for safety integrity established by the standard IEC 61508 are addressed, as well as the modelling detail required for this purpose. The problem is about reliability and redundancy allocation with diversity for a series-parallel system. The objectives to optimize are the average probability of failure on demand, which represents the system safety integrity, Spurious Trip Rate and Lifecycle Cost. The overall method is illustrated with a practical example from the chemical industry: a safety function against high pressure and temperature for a chemical reactor. In order to implement diversity, each subsystem is given the option of three different technologies, each technology with different reliability and diagnostic coverage characteristics. Finally, the optimization with diversity is compared against optimization without diversity.  相似文献   

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This paper introduces a new development for modelling the time-dependent probability of failure on demand of parallel architectures, and illustrates its application to multi-objective optimization of proof testing policies for safety instrumented systems. The model is based on the mean test cycle, which includes the different evaluation intervals that a module goes periodically through its time in service: test, repair and time between tests. The model is aimed at evaluating explicitly the effects of different test frequencies and strategies (i.e. simultaneous, sequential and staggered). It includes quantification of both detected and undetected failures, and puts special emphasis on the quantification of the contribution of the common cause failure to the system probability of failure on demand as an additional component. Subsequently, the paper presents the multi-objective optimization of proof testing policies with genetic algorithms, using this model for quantification of average probability of failure on demand as one of the objectives. The other two objectives are the system spurious trip rate and lifecycle cost. This permits balancing of the most important aspects of safety system implementation. The approach addresses the requirements of the standard IEC 61508. The overall methodology is illustrated through a practical application case of a protective system against high temperature and pressure of a chemical reactor.  相似文献   

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This paper addresses the modeling of probability of dangerous failure on demand and spurious trip rate of safety instrumented systems that include MooN voting redundancies in their architecture. MooN systems are a special case of k-out-of-n systems. The first part of the article is devoted to the development of a time-dependent probability of dangerous failure on demand model with capability of handling MooN systems. The model is able to model explicitly common cause failure and diagnostic coverage, as well as different test frequencies and strategies. It includes quantification of both detected and undetected failures, and puts emphasis on the quantification of common cause failure to the system probability of dangerous failure on demand as an additional component. In order to be able to accommodate changes in testing strategies, special treatment is devoted to the analysis of system reconfiguration (including common cause failure) during test of one of its components, what is then included in the model. Another model for spurious trip rate is also analyzed and extended under the same methodology in order to empower it with similar capabilities. These two models are powerful enough, but at the same time simple, to be suitable for handling of dependability measures in multi-objective optimization of both system design and test strategies for safety instrumented systems. The level of modeling detail considered permits compliance with the requirements of the standard IEC 61508. The two models are applied to brief case studies to demonstrate their effectiveness. The results obtained demonstrated that the first model is adequate to quantify time-dependent PFD of MooN systems during different system states (i.e. full operation, test and repair) and different MooN configurations, which values are averaged to obtain the PFDavg. Also, it was demonstrated that the second model is adequate to quantify STR including spurious trips induced by internal component failure and by test itself. Both models were tested for different architectures with 1≤N≤5 and 2≤M≤5 subject to uniform staggered test. The results obtained also showed the effects that modifying M and N has on both PFDavg and STR, and also demonstrated the conflicting nature of these two measures with respect to one another.  相似文献   

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Safety instrumented systems (SISs) are usually divided into two modes of operation, low-demand and high-demand. Unfortunately, this classification is not easy to justify and the available formulas that are used to quantify the reliability performance in these two modes of operation are unable to capture combined effects of functional testing, spurious activations, and successful responses to demands. This article discusses some important modeling issues for SIS reliability performance quantification, and demonstrates their implementation in a Markov model. The accuracy of the Markov model for a simple case study of a pressure transmitter is verified through comparison with a scenario-based formula, and it is shown that the Markov approach gives a sufficiently accurate result for all demand rates, covering both low- and high-demand modes of operation.  相似文献   

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This paper presents the general content and results of a safety program and comments on its application. The safety file, which was used to support the safety assessment of an automatic mining truck system, was developed in accordance with the general requirements of a standard of the International Electrotechnical Commission for the functional safety of safety-related systems, and using some parts of the European standard for control systems. Conclusions on the assessed system and on the use of the methodology in similar applications are presented.  相似文献   

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In the last ten years, layer of protection analysis (LOPA) emerged as a simplified form of quantitative risk assessment (QRA). The European Commission funded project Accidental Risk Assessment Methodology for Industries in the context of the Seveso 2 Directive (ARAMIS) has recently been completed. ARAMIS has several modules which give a consistent simplified approach to risk assessment which does not approach the complexity or expense of full QRA. LOPA is potentially a means of carrying out the assessment of barriers required in ARAMIS. This paper attempts to explain the principles of LOPA and the means by which it can be used within ARAMIS.  相似文献   

9.
Methods for estimating the instrument error for quantum-optical systems using active and passive optical measures of length are suggested. One is based on simulation of measured pulses reflected from the object and entering the receiving device; another is based on using a section of the fiber optical path. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 19–22, May, 2006.  相似文献   

10.
针对平面阵列,推导出基于一般阵列误差模型的信号时空DOA矩阵,采用总体最小二乘法(TLS)估计出多个信号的方位角。俯仰角和多普勒频率,解决了大多数估计算法的性能因阵列误差而严重下降和“频率兼并”问题。此算法对噪声不敏感,不需进行谱峰搜索,仿真结果表明了此算法的有效性。  相似文献   

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地源热泵系统在工程中的应用形式多种多样,各有优缺点,本文介绍了合肥某创业试验区科技创新公共服务和应用技术研发中心地源热泵系统机房冷、热源的设计,并分析了整个系统的运行。  相似文献   

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针对电动振动台和数字式电动振动试验系统使用中的交越频率的定义及其推理过程加以阐述,探讨了影响电动振动台和数字式振动试验系统正确使用的因素及相关技术问题,同时针对检定规程中所规定的一些检定方法提出了值得商榷的看法,并给出相应的计算公式,供参考使用。  相似文献   

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