Review of Reliability Theory, Analytical Techniques, and Basic Statistics (original) (raw)
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2001
& CONCLUSIONS In reliability analysis of computer systems, models such as fault trees, Markov chains, and stochastic Petri nets(SPN) are built to evaluate or predict the reliability of the system. In general, the parameters in these models are usually obtained from field data, or by the data from systems with similar functionality, or even by guessing. In this paper, we address the parameter uncertainty problem. First, we review and classify three ways to describe the parameter uncertainty in the model: reliability bounds, confidence intervals, and probability distributions. Second, by utilizing the second-order approximation and the normal approximation, we propose an analytic method to derive the confidence interval of the system reliability from the confidence intervals of parameters in the transient solution of Markov models. Then, we study the Monte Carlo simulation method to derive the uncertainty in the system reliability, and use it to validate our proposed analytic method. Our effort makes the reliability prediction more realistic compared with the result without the uncertainty analysis.
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International Journal of Industrial and Systems Engineering, 2011
Existing reliability evaluation methods are based on the availability of knowledge about component states. However, component states are often uncertain or unknown, especially during the early stages of the development of new systems. In such cases it is important to understand how uncertainties will affect system reliability assessment. Another shortcoming of existing methods is that they only consider systems whose components have discrete states. For those whose components have continuous states, these methods may not be applicable. Using Monte-Carlo simulation, this paper proposed a method to assess the reliability of systems with continuous distribution of component states. This method will also be useful when we do not have enough knowledge on component states and related probabilities. Comparison of two examples proves that component uncertainty has significant influence on the assessment of system reliability.
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The purpose of this project was to investigate the use of Bayesian methods for the estimation of the reliability of complex systems. The goals were to find methods for dealing with continuous data, rather than simple pass/fail data; to avoid assumptions of specific probability distributions, especially Gaussian, or normal, distributions; to compute not only an estimate of the reliability of the system, but also a measure of the confidence in that estimate; to develop procedures to address time-dependent or aging aspects in such systems, and to use these models and results to derive optimal testing strategies. The system is assumed to be a system of systems, i.e., a system with discrete components that are themselves systems. Furthermore, the system is "engineered" in the sense that each node is designed to do something and that we have a mathematical description of that process. In the time-dependent case, the assumption is that we have a general, nonlinear, time-dependent function describing the process.
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The objective of this paper is to present a survey of recent research work of high quality that deal with reliability in different fields of engineering and physical sciences. This paper covers several important areas of reliability, significant research efforts being made all over the world. The survey provides insight into past, current and future trends of reliability in different fields of Engineering, Technology and medical sciences with applications with specific problems.
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Firstly, this paper reports about the probabilistic solutions of the problems in engineering design (i.e. applications in mining industry hard rock disintegration process, and applications in biomechanics & traumatology designing of the external fixators applied in traumatology and orthopaedics).Secondly,this paper reports about the new probabilistic application in economics (evaluation of an investment project). Theory and applications of the Simulation-Based Reliability Assessment (SBRA) Method (i.e.direct probabilistic Monte Carlo approach) are presented in the solutions and evaluations. Applications of the SBRA method in these areas of are new and innovative trends in mechanics and economics. Keywords—Probability, Simulation-Based Reliability Assessment (SBRA) Method, design, mining, rock mechanics, biomechanics, traumatology, economics, investment, net present value.
Efficient reliability analysis of complex systems in consideration of imprecision
Reliability Engineering & System Safety, 2021
In this work, the reliability of complex systems under consideration of imprecision is addressed. By joining two methods coming from different fields, namely, structural reliability and system reliability, a novel methodology is derived. The concepts of survival signature, fuzzy probability theory and the two versions of non-intrusive stochastic simulation (NISS) methods are adapted and merged, providing an efficient approach to quantify the reliability of complex systems taking into account the whole uncertainty spectrum. The new approach combines both of the advantageous characteristics of its two original components: 1. a significant reduction of the computational effort due to the separation property of the survival signature, i.e., once the system structure has been computed, any possible characterization of the probabilistic part can be tested with no need to recompute the structure and 2. a dramatically reduced sample size due to the adapted NISS methods, for which only a single stochastic simulation is required, avoiding the double loop simulations traditionally employed. Beyond the merging of the theoretical aspects, the approach is employed to analyze a functional model of an axial compressor and an arbitrary complex system, providing accurate results and demonstrating efficiency and broad applicability.
Quantifying reliability uncertainty : a proof of concept
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This paper develops Classical and Bayesian methods for quantifying the uncertainty in reliability for a system of mixed series and parallel components for which both go/no-go and variables data are available. Classical methods focus on uncertainty due to sampling error. Bayesian methods can explore both sampling error and other knowledge-based uncertainties. To date, the reliability community has focused on qualitative statements about uncertainty because there was no consensus on how to quantify them. This paper provides a proof of concept that workable, meaningful quantification methods can be constructed. In addition, the application of the methods demonstrated that the results from the two fundamentally different approaches can be quite comparable. In both approaches, results are sensitive to the details of how one handles components for which no failures have been seen in relatively few tests.
Introduction to Reliability Analysis: Probability Models and Statistical Methods
Technometrics, 1993
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A Novel Concept for Reliability Evaluation Using Multiple Deterministic Analyses
INAE Letters, 2016
A novel reliability analysis concept for large Structural/Mechanical systems represented by finite elements using multiple deterministic analyses is presented in this paper. The intent is to extract reliability information by conducing only tens instead of millions of deterministic analyses as an alternative to the classical Monte Carlo Simulation. It is particularly applicable when a deterministic analysis requires a considerable amount of computational time to satisfy the underlying physics. It is developed by integrating the second-order reliability method and an improved response surface method by removing its deficiencies. The efficiency of the integrated scheme is further improved by using advanced statistical and factorial schemes producing compounding beneficial effect. The concept is elaborated using two different illustrative examples. To validate the procedure, the underlying reliabilities are estimated by using the basic Monte Carlo simulation technique to develop the reference or benchmark value. Then, the accuracy and efficiency of the method are compared and verified.