A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress an...A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method展开更多
Let F be a life distribution,F=1-F. F is called a distribution function with decreasing failure rate average (DFRA), if-log(t) is decreasing in t>0. In this paper, using constructive method, sharp upper and lower b...Let F be a life distribution,F=1-F. F is called a distribution function with decreasing failure rate average (DFRA), if-log(t) is decreasing in t>0. In this paper, using constructive method, sharp upper and lower bounds of F(t) are given where F∈DFRA with known mean and variance. In addition, brief tables are provided for practical use.展开更多
The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical...The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.展开更多
The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the...The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the structural system reliability analysis.The first method is SA based reliability bounds theory(RBT),in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly,and then RBT is employed to obtain the upper and the lower bounds of system failure probability.The second method is SA based Nataf approximation,in which SA is used to estimate the probability density function(PDF)and cumulative distribution function(CDF)for the approximately linearized performance function of each failure mode.After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated,Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions,and then the system failure probability can be estimated directly by numerical simulation using the joint PDF.The third method is SA based line sampling(LS).The standardization transformation is needed to eliminate the dimensions of variables firstly in this case.Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions,and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space.By comparing basic concepts,implementations and results of illustrations,the following conclusions can be drawn:(1)The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function;(2)the second method can give the estimation of system failure probability,and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions;(3)the SA based LS method can obtain the estimator of system failure probability,which converges to the actual value along with the increase of sample size.The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability,and it is acceptable for the structural system both with a single failure mode and with multiple failure modes,therefore it has the widest applicability.展开更多
In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some...In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some reliability indices of a system are less (or larger) than the corresponding indices of another system; and then, we obtain the bounds of the main reliability indices of a general system.展开更多
基金supported by the Foundation of Hunan Provincial Natural Science of China(13JJ6095,2015JJ2015)the Key Project of Science and Technology Program of Changsha,China(ZD1601010)
文摘A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method
文摘Let F be a life distribution,F=1-F. F is called a distribution function with decreasing failure rate average (DFRA), if-log(t) is decreasing in t>0. In this paper, using constructive method, sharp upper and lower bounds of F(t) are given where F∈DFRA with known mean and variance. In addition, brief tables are provided for practical use.
基金Natural Science Funds for the Innovative Research Group of China Under Grant No.50621062
文摘The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.
基金supported by the National Natural Science Foundation of China(Grant Nos.10572117,50875213)the Program for New Century Excellent Talents in University(Grant No.NCET-05-0868)+2 种基金Aviation Science Foundation(Grant No.2007ZA53012)the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2007AA04Z401)the Doctorate Foundation of Northwestern Poly-technical University(Grant No.CX200801)
文摘The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the structural system reliability analysis.The first method is SA based reliability bounds theory(RBT),in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly,and then RBT is employed to obtain the upper and the lower bounds of system failure probability.The second method is SA based Nataf approximation,in which SA is used to estimate the probability density function(PDF)and cumulative distribution function(CDF)for the approximately linearized performance function of each failure mode.After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated,Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions,and then the system failure probability can be estimated directly by numerical simulation using the joint PDF.The third method is SA based line sampling(LS).The standardization transformation is needed to eliminate the dimensions of variables firstly in this case.Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions,and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space.By comparing basic concepts,implementations and results of illustrations,the following conclusions can be drawn:(1)The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function;(2)the second method can give the estimation of system failure probability,and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions;(3)the SA based LS method can obtain the estimator of system failure probability,which converges to the actual value along with the increase of sample size.The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability,and it is acceptable for the structural system both with a single failure mode and with multiple failure modes,therefore it has the widest applicability.
文摘In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some reliability indices of a system are less (or larger) than the corresponding indices of another system; and then, we obtain the bounds of the main reliability indices of a general system.
