Fault tree analysis in the R programming environment
Abstract: Аннотация. Цель. Анализ дерева отказов (АДО) -это один из основных методов анализа надежности сложных технических систем. Для его проведения часто применяются коммерческие программные средства, такие как Saphire, Risk Spectrum, Арбитр и т.д. Каждый из них обладает как определенными преимуществами, так и отдельными недостатками. Необходимо отметить, что основная цель вышеуказанных программных средств состоит в проведении качественного анализа дерева отказов. При этом в качестве дополнительных возможностей прогр… Show more
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Cited by 4 publications
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Aim. This paper is the continuation of [1] that proposes using the R programming language for fault tree analysis (FTA). In [1], three examples are examined: fault tree (FT) calculation per known probabilities, dynamic FT calculation per known distributions of times to failure for a system’selements. In the latter example, FTA is performed for systems with elements that are described by different functional and service models. Fault tree analysis (FTA) is one of the primary methods of dependability analysis of complex technical systems. This process often utilizes commercial software tools like Saphire, Risk Spectrum, PTC Windchill Quality, Arbitr, etc. Practically each software tool allows calculating the dependability of complex systems subject to possible common cause failures (CCF). CCF are the associated failures of a group of several elements that occur simultaneously or within a short time interval (i.e. almost simultaneously) due to one common cause (e.g. a sudden change in the climatic service conditions, flooding of the premises, etc.). An associated failure is a multiple failure of several system elements, of which the probability cannot be expressed simply as the product of the probabilities of unconditional failures of individual elements. There are several generally accepted models used in CCF probability calculation: the Greek letters model, the alpha, beta factor models, as well as their variations. The beta factor model is the most simple in terms of associated failures simulation and further dependability calculation. The other models involve combinatorial search associated events in a group of n events, that becomes labor-consuming if the number n is large. Therefore, in the above software tools there are some restrictions on the n, beyond which the probability of CCF is calculated approximately. In the current R FaultTree package version there are no above CCF models, therefore all associated failures have to be simulated manually, which is not complicated if the number of associated events is small, as well as useful in terms of understanding the various CCF models. In this paper, for the selected diagram a detailed analysis of the procedure of associated failures simulation is performed for alpha and beta factor models. The Purposeof this paper consists in the detailed analysis of the alpha and beta factor methods for a certain diagram, in the demonstration of fault tree creation procedure taking account of ССF using R’s FaultTree package. Methods. R’s FaultTree scripts were used for the calculations and FTA capabilities demonstration.Conclusions. Two examples are examined in detail. In the first example, for the selected block diagram that contains two groups of elements subject to associated failures, the alpha factor model is applied. In the second example, the beta factor model is applied. The deficiencies of the current version of FaultTree package are identified. Among the main drawbacks we should indicate the absence of some basic logical gates.
Aim. This paper is the continuation of [1] that proposes using the R programming language for fault tree analysis (FTA). In [1], three examples are examined: fault tree (FT) calculation per known probabilities, dynamic FT calculation per known distributions of times to failure for a system’selements. In the latter example, FTA is performed for systems with elements that are described by different functional and service models. Fault tree analysis (FTA) is one of the primary methods of dependability analysis of complex technical systems. This process often utilizes commercial software tools like Saphire, Risk Spectrum, PTC Windchill Quality, Arbitr, etc. Practically each software tool allows calculating the dependability of complex systems subject to possible common cause failures (CCF). CCF are the associated failures of a group of several elements that occur simultaneously or within a short time interval (i.e. almost simultaneously) due to one common cause (e.g. a sudden change in the climatic service conditions, flooding of the premises, etc.). An associated failure is a multiple failure of several system elements, of which the probability cannot be expressed simply as the product of the probabilities of unconditional failures of individual elements. There are several generally accepted models used in CCF probability calculation: the Greek letters model, the alpha, beta factor models, as well as their variations. The beta factor model is the most simple in terms of associated failures simulation and further dependability calculation. The other models involve combinatorial search associated events in a group of n events, that becomes labor-consuming if the number n is large. Therefore, in the above software tools there are some restrictions on the n, beyond which the probability of CCF is calculated approximately. In the current R FaultTree package version there are no above CCF models, therefore all associated failures have to be simulated manually, which is not complicated if the number of associated events is small, as well as useful in terms of understanding the various CCF models. In this paper, for the selected diagram a detailed analysis of the procedure of associated failures simulation is performed for alpha and beta factor models. The Purposeof this paper consists in the detailed analysis of the alpha and beta factor methods for a certain diagram, in the demonstration of fault tree creation procedure taking account of ССF using R’s FaultTree package. Methods. R’s FaultTree scripts were used for the calculations and FTA capabilities demonstration.Conclusions. Two examples are examined in detail. In the first example, for the selected block diagram that contains two groups of elements subject to associated failures, the alpha factor model is applied. In the second example, the beta factor model is applied. The deficiencies of the current version of FaultTree package are identified. Among the main drawbacks we should indicate the absence of some basic logical gates.
Refinement of the engineering practice of evaiuation of the wear rate of excavator impiement components
The existence of humankind on Earth largely depends on the energy at its disposal. It is mostly generated by processing minerals extracted from the Earth’s crust by open-cut mining. The quality and low cost of extraction are largely defined by the dependability of employed machines and mechanisms, plants and process engineering solutions. Various types of excavators are the backbone of a mining machine fleet. Their parts that principally interact with the environment (rock) are components of implements, i.e. primarily the buckets and components of bucket(s). It must be noted that in the process of interaction with the environment (rock) the excavator implements and their components are exposed to so-called abrasive wear. Since abrasive wear of implement components (most frequently excavator bucket teeth) causes their recurrent replacement, this inevitably affects the performance of the excavator as a whole and those process flows it is part of. Occasional interruptions of operation and repairs reduce the availability factor, the most important complex indicator of equipment dependability. Given the above, the aim of this paper is to refine the previously known formula proposed more than thirty years ago in VNIISDM (Reysh A.K.) for evaluation of the rate of abrasive wear of excavator bucket teeth. For the first time, with a sufficient accuracy we examined the multitude of operating modes of mining equipment, i.e. operation of excavators in various conditions, e.g. on different soils. Additionally, we extended Reysh’s approach from single-bucket machines to continuous operation multi-bucket ones. For that purpose, the authors used a method of data integration from known sources, method of full-scale experiment under the operating conditions of a specific excavator and method of mathematical simulation (a form of the Monte Carlo method). All of that allowed revising the values of the parameters in the Reysh formula. The refined formula that we obtained can now be used for the dependability evaluation of machines operating under varying conditions, as well as for the purpose of appointing the time of preventive inspections.
Aim. Common cause failures (CCFs) are dependent failures of groups of certain elements that occur simultaneously or within a short period of time (i.e. almost simultaneously) due to a single common cause (e.g. a sudden change of climatic operating conditions, flooding of premises, etc.). A dependent failure is a multiple failure of several elements of a system, whose probability cannot be expressed as a simple product of the probabilities of unconditional failures of individual elements. ССА probabilities calculation uses a number of common models, i.e. the Greek letter model, alpha, beta factor and their variants. The beta-factor model is the most simple in terms of simulation of dependent failures and further dependability calculations. Other models, when used in simulation, involve combinatorial enumeration of dependent events in a group of n events that becomes labour-intensive if the number n is high. For the selected structure diagrams of dependability, the paper analyzes the calculation method of system failure probability with CCF taken into account for the beta-factor model. The Aim of the paper is to thoroughly analyze the beta-factor method for three structure diagrams of dependability, research the effects of the model parameters on the final result, find the limitations of beta-factor model applicability. Methods. The calculations were performed using numerical methods of solution of equations, analytical methods of function studies. Conclusions. The paper features an in-depth study of the method of undependability calculation for three structure diagrams that accounts for CCF and uses the beta-factor model. In the first example, for the selected structure diagram out of n parallel elements with identical dependability, it is analytically shown that accounting for CCF does not necessarily cause increased undependability. In the second example of primary junction of n elements with identical dependability, it is shown that accounting for CCF subject to parameter values causes both increased and decreased undependability. A number of beta factor model parameter values was identified that cause unacceptable values of system failure probability. These sets of values correspond to relatively high model parameter values and are hardly practically attainable as part of engineering of real systems with highly dependable components. In the third example, the conventional bridge diagram with two groups of CCFs is considered. The complex ambivalent effect of beta factor model parameters on the probability of failure is shown. As in the second example, limitations of the applicability of the beta-factor model are identified.
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