基于率模可靠性的客观确定非对称概型功能函数隶属函数的方法

摒弃目前以主观方法给出功能函数对结构安全模糊集隶属函数的做法,提出并从理论上证明了：当功能函数具有非对称概型时,将功能函数的线性函数假想为集值统计的随机集边界点,通过定积分运算获得隶属函数的方法。算例充分说明文中方法的科学性和客观性。     

Single-use reliability computation of a semi-Markovian system

Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first and second moments of the single-use reliability. The model and the validity of the results are illustrated through a numerical example.     

Optimal replacement policies for a multicomponent reliability system

This paper studies a discrete time, infinite horizon, dynamic programming model for the replacement of components in a binary coherent system. Under quite general conditions, we show that it is optimal to follow a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. We also discuss the problem of computing such policies.     

串并联可修系统的可靠性

本文通过密度演化法讨论了部件的寿命和修理时间都服从一般分布的由n个不同子系统串并联组成的可修系统的可靠性,为串并联系统的可靠性研究提供了理论依据.     

On signature-based expressions of system reliability

The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.     

Experimental and numerical investigation of a degradable collagen foil

A collagen foil, which plays an important role for cultivating and investigating tendon cells, is investigated experimentally and numerically: The foil, which should later serve as a scaffold for tendon cells in a custom made bioreactor, is stimulated periodically in an in situ experiment. Additionally, a material model to describe the anisotropic structure and the relaxation behaviour of the collagen foil is used to simulate the material response. By comparing the measurements and simulations, the stress and strain states in the foil can be determined. Hence, the material parameters for the presented experimental set up are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interval uneffectiveness distribution for a k-out-of-n multistate reliability system with repair

This paper deals with a parallel load-sharing reliability system with cold standby redundancy and ample repair facilities. That is, we have n identical parallel units, of which at most k units are operating simultaneously. If less than k units are available, the system operates at a proportionally reduced level. For this system, an approximate method is given for the calculation of the probability distribution of that proportion of the system capacity that cannot be used in a given time period. The method is based on an approximation of the k-out-of-n multistate system by a two-state single component. Validation of the approximation using Monte-Carlo simulation shows satisfactory performance. Also, sensitivity results are given, showing in particular a decreasing sensitivity of the measures of performance to the distributional form of the unit lifetimes and repair times as the size of the system increases. Furthermore, it is found that the effect of the distributional form of the unit lifetimes dominates that of the unit repair times.     

Approximate confidence limits of the reliability performances for a cold standby series system

This paper is to investigate the approximate confidence limits of the reliability performances (such as failure rate, reliability function and average life) for a cold standby series system. The Bayesian approximate upper confidence limit of failure rate is obtained firstly, and next Bayesian approximate lower confidence limits for reliability function and average life are presented. The expressions for calculating Bayesian lower confidence limits of the reliability function and average life are also obtained, and an illustrative example is examined numerically by means of the Monte-Carlo simulation. Finally, the accuracy of confidence limits is discussed.     

Trend mining for system reliability employing a novel heuristic-based Kriging profiling method

This paper presents a novel integration of heuristic-based regressor for the prediction of system reliability. This is implemented by integrating single layer perceptron (SLP) into Kriging model on the basis of an enhanced Particle Swarm Optimization. The proposed method is labeled here as heuristic SLP-based Kriging, or in short HSK. The backbone of HSK is a Competitive Niching-inspired PSO (CNPSO) that serves as the heuristic for identifying the core parameters of the SLP-based Kriging. CNPSO is composed of an opposition-based competitive initialization and a niching-inspired search scheme. For practicality and validation purposes, realistic datasets in the literature of system reliability are considered in the present study. The experimental results obtained demonstrated that HSK outperformed state-of-the-art methods proposed in the literature for addressing the same issue.     

Estimation of system reliability for redundant stress-strength model

The reliability and an estimate for it are derived for series-parallel and parallel-series stress-strength model under assumption that all components are subjected to a common stress. We also obtain the asymptotic normal distribution of the estimate.     

A system reliability approach to linear programming

Summary A system reliability approach to linear programming is developed here for the case when the restrictions are chance-constrained. Methods of characterizing a system reliability measure for a linear programming system, its implications under alternative probability distribution assumptions and its uses for specifying policies with an improved system reliability routine are analytically discussed.

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Zusammenfassung In der vorliegenden Arbeit wird ein Verfahren zur Untersuchung der Zuverlässigkeit eines Systems für den Fall entwickelt, daß die Beschränkungen eines L. P.-Problems zufallsabhängig sind. Es werden Methoden zur Charakterisierung eines Maßes für die Zuverlässigkeit eines L. P.-Systems, die sich daraus ergebenden Implikationen bei verschiedenen Annahmen über die Wahrscheinlichkeitsverteilung und die Möglichkeit zur Bestimmung von Politik-Arten mittels eines verbesserten Verfahrens zur Untersuchung der System-Zuverlässigkeit diskutiert.

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Work done under the National Science Foundation Project GS 1810/420-41-17 at the Department of Economics, Iowa State University. This work develops the theoretical ideas originally fromulated in a paper by this author: Safety first rules under chance-constrained linear programming.Operations Research: The Journal of Operations Research Society of America, Vol.17, No. 1, 1969, pp. 112–132.

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Vorgel. v.:W. Wittmann     

Learning to improve reliability during system development

Research, conducted in collaboration with a leading aerospace manufacturer, aimed to facilitate learning in order to improve the reliability of engineering systems during their development phase. In particular, the processes and mathematical models used during reliability growth testing were investigated to assess how they might be better used to support this improvement. This required both soft and hard OR approaches to be adopted. For example, information flows were mapped and reengineered in order to provide a basis for more effective data collection and feed-back to decision-makers. A new mathematical model that combines failure data with engineering judgement was developed to estimate reliability growth. The paper presents a case study describing the problem, the modelling conducted, the recommendations made and the actions implemented. The ways in which the researchers and the manufacturer learnt to improve both the modelling and the reliability growth testing process are reflected upon.     

On the reliability function of a double redundant system with general repair time distribution

The reliability function is considered for a hot double redundant repairable heterogeneous system with exponentially distributed lifetimes and generally distributed repair times of its components. The problem of its sensitivity to the repair time distribution is discussed.     

Interval estimation of system reliability using a conditional distribution function of the number of failures

Interval estimators of the no-failure probability of a system are constructed from tests of system elements. The estimators are obtained using the conditional distribution function of the number of failures during the tests.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 58–64, 1986.     

Optimization of system reliability by adaptive randomly directed search

A new adaptive randomly directed search algorithm was developed for optimizing the reliability of a system employing redundancy. This algorithm can handle general nonlinear integer formulations. Its usefulness and advantages in solving reliability problems were demonstrated through three examples given in the literature.     

Bayesian estimation of system reliability in Brownian stress-strength models

A stress-strength system fails as soon as the applied stress,X, is at least as much as the strength,Y, of the system. Stress and strength are time-varying in many real-life systems but typical statistical models for stress-strength systems are static. In this article, the stress and strength processes are dynamically modeled as Brownian motions. The resulting stress-strength system is then governed by a time-homogeneous Markov process with an absorption barrier at O. Conjugate as well as non-informative priors are developed for the model parameters and Markov chain sampling methods are used for posterior inference of the reliability of the stress-strength system. A generalization of this model is described next where the different stress-strength systems are assumed to be exchangeable. The proposed Bayesian analyses are illustrated in two examples where we obtain posterior estimates as well as perform model checking by cross-validation.     

Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm

This paper deals with chance constraints based reliability stochastic optimization problem in the series system. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall system reliability under chance constraints due to resources. The assumption of traditional reliability optimization problem is that the reliability of a component is known as a fixed quantity which lies in the open interval (0, 1). However, in real life situations, the reliability of an individual component may vary due to some realistic factors and it is sensible to treat this as a positive imprecise number and this imprecise number is represented by an interval valued number. In this work, we have formulated the reliability optimization problem as a chance constraints based reliability stochastic optimization problem with interval valued reliabilities of components. Then, the chance constraints of the problem are converted into the equivalent deterministic form. The transformed problem has been formulated as an unconstrained integer programming problem with interval coefficients by Big-M penalty technique. Then to solve this problem, we have developed a real coded genetic algorithm (GA) for integer variables with tournament selection, uniform crossover and one-neighborhood mutation. To illustrate the model two numerical examples have been solved by our developed GA. Finally to study the stability of our developed GA with respect to the different GA parameters, sensitivity analyses have been done graphically.     

The reliability analysis of probabilistic and interval hybrid structural system

The aim of this paper is to evaluate the reliability of probabilistic and interval hybrid structural system. The hybrid structural system includes two kinds of uncertain parameters—probabilistic parameters and interval parameters. Based on the interval reliability model and probabilistic operation, a new probabilistic and interval hybrid reliability model is proposed. Firstly, we use the interval reliability model to analyze the performance function, and then sum up reliability of all regions divided by the failure plane. Based on the presented optimal criterion enumerating the main failure modes of hybrid structural system and the relationship of failure modes, the reliability of structure system can be obtained. By means of the numerical examples, the hybrid reliability model and the traditional probabilistic reliability model are critically contrasted. The results indicate the presented reliability model is more suitable for analysis and design of these structural systems and it can ensure the security of system well, and it only needs less uncertain information.     

Fuzzy Bayesian system reliability assessment based on exponential distribution

The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO).