Estimating Probability of Failure of a Complex System Based on Inexact Information about Subsystems and Components, with Potential Applications to Aircraft Maintenance

In many real-life applications (e.g., in aircraft maintenance), we need to estimate the probability of failure of a complex system (such as an aircraft as a whole or one of its subsystems). Complex systems are usually built with redundancy allowing them to withstand the failure of a small number of components. In this paper, we assume that we know the structure of the system, and, as a result, for each possible set of failed components, we can tell whether this set will lead to a system failure. For each component A, we know the probability P(A) of its failure with some uncertainty: e.g., we know the lower and upper bounds P(A) and P(A) for this probability. Usually, it is assumed that failures of different components are independent events. Our objective is to use all this information to estimate the probability of failure of the entire the complex system. In this paper, we describe several methods for solving this problem, including a new efficient method for such estimation based on Cauchy deviates

An Improved Estimation of Multiple-Point Fault Probabilities if the Faults Have Different Periodic Latencies

Fault tree analysis (FTA), reliability block diagrams (RBD) and event tree analysis (ETA) are established methods for assessing potential risks of hazardous events, in particular when resulting from coincidental events. Combining the Boolean algebra, probability theory and reliability data, they allow quantitative estimation of intrinsic risks from technical equipment like machinery control, aerospace systems or vehicle functions, among many others. The quantitative reliability theory was mainly developed between the 1960s and the 1980s. At that time, simplifications and approximations for the mathematical formulae were needed to achieve calculation results within acceptable time, regarding restricted computer resources. Our investigation revealed that some of these simplifications and approximations, often assumed as precise calculations in secondary literature, can lead to wrong results in quantitative risk assessment. When faults are combined, and individual latency periods exist, the currently established approximations may lead to results which are too optimistic in comparison with a precise probabilistic approach. This publication proposes a new approximation for the computation of the related probabilities. The approach provides an upper-bound estimation. Using the developed formulae, the under-estimation of multipleevent probabilities can be avoided. In addition, certain vagueness and over-simplification in the probabilistic treatment of events with latency periods can be eliminated. Examples of related shortcomings in the literature can be found, down to the early roots of reliability theory

Identification of uncertainty sources in distributed hydrological modelling: Case study of the Grote Nete catchment in Belgium

The quest for good practice in modelling merits thorough and sustained attention since good practice increases the credibility and impact of the information, and insight that modelling seeks to generate. This paper presents the findings of an evaluation whose goal was to understand the uncertainty in applying a distributed hydrological model to the Grote Nete catchment in Flanders, Belgium. Uncertainties were selected for investigation depending on how significantly they affected the model’s decision variables. A Fault Tree was used to determine various combinations of inputs, mathematical code, and human error failures that could result in a specified risk. A combination of forward and backward approaches was used in developing the Fault Tree. Eleven events were identified as contributing to the top event. A total of 7 gates were used to describe the Fault Tree. A critical path analysis was carried out for the events and established their rank or order of significance. Three measures of importance were applied, namely the F-Vesely, the Birnbaum, and the B-Proschan importance measures. Model development of distributed models involves considerable uncertainty. Many of these dependencies arise naturally and their correct evaluation is crucial to the accurate analysis of the modelling system reliability.Keywords: distributed hydrological models, Grote Nete, MIKE SHE, uncertaint

Failure analysis of a complex system based on partial information about subsystems, with potential applications to aircraft maintenance

In many real-life applications (e.g., in aircraft maintenance), we need to estimate the probability of failure of a complex system (such as an aircraft as a whole or one of its subsystems). Complex systems are usually built with redundancy allowing them to withstand the failure of a small number of components. In this paper, we assume that we know the structure of the system, and, as a result, for each possible set of failed components, we can tell whether this set will lead to a system failure. For each component A, we know the probability P(A) of its failure with some uncertainty: e.g., we know the lower and upper bounds P(A) and P(A) for this probability. Usually, it is assumed that failures of different components are independent events. Our objective is to use all this information to estimate the probability of failure of the entire the complex system. In this paper, we describe several methods for solving this problem, including a new efficient method for such estimation based on Cauchy deviates

Fault Tree Analysis: a survey of the state-of-the-art in modeling, analysis and tools

Fault tree analysis (FTA) is a very prominent method to analyze the risks related to safety and economically critical assets, like power plants, airplanes, data centers and web shops. FTA methods comprise of a wide variety of modelling and analysis techniques, supported by a wide range of software tools. This paper surveys over 150 papers on fault tree analysis, providing an in-depth overview of the state-of-the-art in FTA. Concretely, we review standard fault trees, as well as extensions such as dynamic FT, repairable FT, and extended FT. For these models, we review both qualitative analysis methods, like cut sets and common cause failures, and quantitative techniques, including a wide variety of stochastic methods to compute failure probabilities. Numerous examples illustrate the various approaches, and tables present a quick overview of results

AVAILABILITY MODEL FOR A COG EN ERA TION SYSTEM SUBJECTED TO REDUNDANCY

The main emphasis of cogeneration system is to provide electrical energy, steam, hot and chilled water to their customers. The failure of this system could lead to the disruption of the supply of these items. If failure occurs, it will result in reduction of availability as well as economic loss. In order to mitigate such effects, it is required to study availability of the cogeneration system together with associated economic loss. However, there are factors which affect the availability assessment of the cogeneration system. These factors are system redundancy and limitation of maintenance data. Use of redundancy in cogeneration helps to achieve higher availability but the operation cost of redundancy is expensive due to maximum demand charge cost. Thus, it is important to consider the economic effect of redundancy