With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in th...With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.展开更多
The main electrical properties of advanced Silicon On Insulator MOSFETs are addressed. The subthreshold and high field operations are analysed as a function of device architecture. The special SOI parasitic phenomena,...The main electrical properties of advanced Silicon On Insulator MOSFETs are addressed. The subthreshold and high field operations are analysed as a function of device architecture. The special SOI parasitic phenomena, such as the floating body potential and temperature, are critically reviewed. The main limitations of submicron MOSFET are comparatively evaluated for various SOI structures. Short channel and hot carrier effects as well as the reliability of the SOI technology are investigated for gate length down to sub\|0 1 micron.展开更多
In order to evaluate the failure probability of a complicated structure,the structural responses usually need to be estimated by some numerical analysis methods such as finite element method( FEM). The response surfac...In order to evaluate the failure probability of a complicated structure,the structural responses usually need to be estimated by some numerical analysis methods such as finite element method( FEM). The response surface method( RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However,the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network( LONN)-based RSM to estimate the structural reliability. In this method,the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method,i.e. first-order reliability methods( FORM) to calculate the failure probability of the structure.Numerical examples show that the proposed approach is applicable to structural reliability analysis,as well as the structure with implicit performance functions.展开更多
Software reliability models describe the failure behavior of the software. The models are used to evaluate the software quantitatively. They assess the reliability of the software by predicting faults or failures for ...Software reliability models describe the failure behavior of the software. The models are used to evaluate the software quantitatively. They assess the reliability of the software by predicting faults or failures for a software. Reliability is one of important quality attributes of the software in which software end user is more interested rather than the software developer. Hence, the performance of a software can be improved by incorporating important quality attributes like reliability, maintainability and availability of the software along with performance attributes like response time and throughput. The paper discusses about the role played by important software reliability models in analyzing the failure prediction of the software. It also explores the strong relationship that exists between quality attributes and performance attributes. With some illustrations highlighting the necessity of in-depth understanding of the link that exists between reliability and performance of the software. The derived knowledge helps in improving the performance of the software sustainably over a period of time and manage the software more effectively.展开更多
In this paper, the operating conditions, technical requirements, performance characteristics, design ideas, application experiences and development trends of aerospace engine bearings, including material technology, i...In this paper, the operating conditions, technical requirements, performance characteristics, design ideas, application experiences and development trends of aerospace engine bearings, including material technology, integration design and reliability, are reviewed. The development history of aerospace engine bearing is recalled briefly at first. Then today's material technologies and the high bearing performances of the bearings obtained through the new materials are introduced, which play important roils in the aeroengine bearing developments. The integration design ideas and practices are explained to indicate its significant advantages and importance to the aerospace engine bearings. And the reliability of the shaft-bearing system is pointed out and treated as the key requirement with goals for both engine and bearing. Finally, as it is believed that the correct design comes from practice, the pre-qualification rig testing conducted by FAG Aerospace GmbH & Co. KG is briefly illustrated as an example. All these lead to the development trends of aerospace engine bearings from different aspects.展开更多
Research infrastructure is crucial for development of research,and thus the evaluation of its performance is important.However,existing researches mostly focus on its past observations,lacking of a prediction for futu...Research infrastructure is crucial for development of research,and thus the evaluation of its performance is important.However,existing researches mostly focus on its past observations,lacking of a prediction for future. In this paper, procedures are proposed to predict the distribution for the number of papers published in a certain future year. The publication reliability,which is defined as the probability that the number of published papers in the future year is bigger than a pre-specified number,is evaluated. Illustrative examples are proposed to show the applications of the model.展开更多
Aiming to investigate the mix design of eco-friendly UHPC with supplementary cementitious materials and coarser aggregates, we comprehensively studied the workability, microstructure, porosity, compressive strength, f...Aiming to investigate the mix design of eco-friendly UHPC with supplementary cementitious materials and coarser aggregates, we comprehensively studied the workability, microstructure, porosity, compressive strength, flexural strength, and Young’s modulus of UHPC. Relationship between compressive strength and Young’s modulus was obtained eventually. It is found that the compressive strength, flexural strength, and Young’s modulus of UHPC increase by 19.01%, 10.81%, and 5.99%, respectively, when 40 wt% cement is replaced with supplementary cementitious materials. The relationship between compressive strength and Young’s modulus of UHPC is an exponential form.展开更多
Heterogeneity is inevitable in enterprises due to their various input requirements. The usage of proprietary integration products results in the increased cost of enterprises. During the integration, the focus area ha...Heterogeneity is inevitable in enterprises due to their various input requirements. The usage of proprietary integration products results in the increased cost of enterprises. During the integration, the focus area has been found to often address only the functional requirements, while the non-functional requirements are side-stepped during the initial stages of a project. Moreover, the use of proprietary integration products and non-standards-based integration platform has given rise to an inflexible integration infrastructure resulting in adaptability concerns. Web services-based integration, based on open standards, is deemed to be the only feasible solution in such cases. This paper explains the performance analysis of enterprise integration in heterogeneous environments for the distributed and the transactional applications. The analysis presented in this paper is seen as a step towards making intelligent decisions well in advance when choosing the integration mechanism/products to address the functional as well as the non-functional requirements considering the future integration needs.展开更多
A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a su...A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a sub-system can be transmitted to other deficient sub-systems. The transmission capacity of the common bus performance sharing mechanism is a random variable. Effects of load on element performance and failure rate were considered in this paper. A reliability evaluation algorithm based on the universal generating function technique was suggested. Numerical experiments were conducted to illustrate the algorithm.展开更多
Importance measures are being widely used to characterize the importance of component in systems.Focus on the integrated importance measure(IIM)of the whole lifetime measure based on the transition rates of component ...Importance measures are being widely used to characterize the importance of component in systems.Focus on the integrated importance measure(IIM)of the whole lifetime measure based on the transition rates of component states.To describe the impact of each component in whole lifetime,the IIM is generalized in nonrepairable and repairable systems at first.Then,their formulas are computed in series and parallel systems.Finally,the characteristics of generalized IIM in typical series systems and parallel systems are analyzed.The results show that the generalized IIM of component can evaluate the expected effect of component state on the system performance in whole lifetime.展开更多
A Bayesian method for estimating human error probability(HEP) is presented.The main idea of the method is incorporating human performance data into the HEP estimation process.By integrating human performance data an...A Bayesian method for estimating human error probability(HEP) is presented.The main idea of the method is incorporating human performance data into the HEP estimation process.By integrating human performance data and prior information about human performance together,a more accurate and specific HEP estimation can be achieved.For the time-unrelated task without rigorous time restriction,the HEP estimated by the common-used human reliability analysis(HRA) methods or expert judgments is collected as the source of prior information.And for the time-related task with rigorous time restriction,the human error is expressed as non-response making.Therefore,HEP is the time curve of non-response probability(NRP).The prior information is collected from system safety and reliability specifications or by expert judgments.The(joint) posterior distribution of HEP or NRP-related parameter(s) is constructed after prior information has been collected.Based on the posterior distribution,the point or interval estimation of HEP/NRP is obtained.Two illustrative examples are introduced to demonstrate the practicality of the aforementioned approach.展开更多
The growing need for high-performance networking is achieved with parallel processing;several networking functions are processed concurrently in order to accomplish a performance Networking Architecture. Open systems ...The growing need for high-performance networking is achieved with parallel processing;several networking functions are processed concurrently in order to accomplish a performance Networking Architecture. Open systems interconnection (OSI) model is an example of multi-layering structure, and each layer performs definite function unique to that layer. OSI model works on pass it on principle, and it is divided in two stacks lower stack and upper stack. Layers 4 - 7 represent upper stack and responsible for data applications. The remaining 1 - 3 layers represent the lower stack and mostly involve in data movement. There are many techniques are available for server optimization enhancing the availability by distributing the load among peer servers. According to our knowledge, nobody has implemented such splitting architecture across the entire OSI model. In this paper, we present multilayer Split-protocol (MLSP) a high performance, reliable and secure technique for spiting an application or network protocol across OSI model, and we present the design, implementation, and empirical performance evaluation of MLSP. It is the ideal choice for Cloud services where each functional component is considered an independent of each other.展开更多
The semiclassical transport equations are used to study the high frequency performance of AlGaAs / GaAs HBTs. Electron velocity overshoot effect and its influence on the cut off frequency characteristics of AlGaAs / G...The semiclassical transport equations are used to study the high frequency performance of AlGaAs / GaAs HBTs. Electron velocity overshoot effect and its influence on the cut off frequency characteristics of AlGaAs / GaAs HBTs with different collector design parameters are analyzed and discussed.展开更多
To verify the effectiveness of the integrated importance measure (IIM) for multi-state coherent systems of k level, the definition and physical meaning of IIM are demonstrated. Then, the improvement potential and Δ...To verify the effectiveness of the integrated importance measure (IIM) for multi-state coherent systems of k level, the definition and physical meaning of IIM are demonstrated. Then, the improvement potential and Δ-importance measures are generalized to multi-state coherent systems based on the system performance level, and the relationships between IIM and traditional importance measures are discussed. The characteristics of IIM are demonstrated in both series and parallel systems. Also, an application to an oil transportation system is given. The comparison results show that: (i) IIM has some useful properties that are not possessed by traditional importance measures; (ii) IIM is effective in evaluating the component role in multi-state systems when the component reliability and the failure rate are simultaneously considered.展开更多
Evaluating the expected sliding distance of a vertical slit caisson breakwater is proposed. Time history for the wave load to a vertical slit caisson is made. It consists of two impulsive wave pressures followed by a ...Evaluating the expected sliding distance of a vertical slit caisson breakwater is proposed. Time history for the wave load to a vertical slit caisson is made. It consists of two impulsive wave pressures followed by a smooth sinusoidal pressure. In the numerical analysis, the sliding distance for an attack of single wave was shown and the expected sliding distance during 50 years was also presented. Those results were compared with a vertical front caisson breakwater without slit. It was concluded that the sliding distance of a vertical slit caisson may be over-estimated if the wave pressure on the caisson is evaluated without considering vertical slit.展开更多
In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of...In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.展开更多
基金Shanghai Rising-Star Program(Grant No.21QA1403400)Shanghai Sailing Program(Grant No.20YF1414800)Shanghai Key Laboratory of Power Station Automation Technology(Grant No.13DZ2273800).
文摘With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.
文摘The main electrical properties of advanced Silicon On Insulator MOSFETs are addressed. The subthreshold and high field operations are analysed as a function of device architecture. The special SOI parasitic phenomena, such as the floating body potential and temperature, are critically reviewed. The main limitations of submicron MOSFET are comparatively evaluated for various SOI structures. Short channel and hot carrier effects as well as the reliability of the SOI technology are investigated for gate length down to sub\|0 1 micron.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51406067)Science and Technology Program of Jilin,China(Grant No.20140203008SF)
文摘In order to evaluate the failure probability of a complicated structure,the structural responses usually need to be estimated by some numerical analysis methods such as finite element method( FEM). The response surface method( RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However,the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network( LONN)-based RSM to estimate the structural reliability. In this method,the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method,i.e. first-order reliability methods( FORM) to calculate the failure probability of the structure.Numerical examples show that the proposed approach is applicable to structural reliability analysis,as well as the structure with implicit performance functions.
文摘Software reliability models describe the failure behavior of the software. The models are used to evaluate the software quantitatively. They assess the reliability of the software by predicting faults or failures for a software. Reliability is one of important quality attributes of the software in which software end user is more interested rather than the software developer. Hence, the performance of a software can be improved by incorporating important quality attributes like reliability, maintainability and availability of the software along with performance attributes like response time and throughput. The paper discusses about the role played by important software reliability models in analyzing the failure prediction of the software. It also explores the strong relationship that exists between quality attributes and performance attributes. With some illustrations highlighting the necessity of in-depth understanding of the link that exists between reliability and performance of the software. The derived knowledge helps in improving the performance of the software sustainably over a period of time and manage the software more effectively.
文摘In this paper, the operating conditions, technical requirements, performance characteristics, design ideas, application experiences and development trends of aerospace engine bearings, including material technology, integration design and reliability, are reviewed. The development history of aerospace engine bearing is recalled briefly at first. Then today's material technologies and the high bearing performances of the bearings obtained through the new materials are introduced, which play important roils in the aeroengine bearing developments. The integration design ideas and practices are explained to indicate its significant advantages and importance to the aerospace engine bearings. And the reliability of the shaft-bearing system is pointed out and treated as the key requirement with goals for both engine and bearing. Finally, as it is believed that the correct design comes from practice, the pre-qualification rig testing conducted by FAG Aerospace GmbH & Co. KG is briefly illustrated as an example. All these lead to the development trends of aerospace engine bearings from different aspects.
基金Ministry of Education Project,China(No.2014GL15)
文摘Research infrastructure is crucial for development of research,and thus the evaluation of its performance is important.However,existing researches mostly focus on its past observations,lacking of a prediction for future. In this paper, procedures are proposed to predict the distribution for the number of papers published in a certain future year. The publication reliability,which is defined as the probability that the number of published papers in the future year is bigger than a pre-specified number,is evaluated. Illustrative examples are proposed to show the applications of the model.
基金Funded by the National Natural Science Foundation of China,China(No.51438003)the National Key R&D Program of China,China(2018YFC0705400)
文摘Aiming to investigate the mix design of eco-friendly UHPC with supplementary cementitious materials and coarser aggregates, we comprehensively studied the workability, microstructure, porosity, compressive strength, flexural strength, and Young’s modulus of UHPC. Relationship between compressive strength and Young’s modulus was obtained eventually. It is found that the compressive strength, flexural strength, and Young’s modulus of UHPC increase by 19.01%, 10.81%, and 5.99%, respectively, when 40 wt% cement is replaced with supplementary cementitious materials. The relationship between compressive strength and Young’s modulus of UHPC is an exponential form.
文摘Heterogeneity is inevitable in enterprises due to their various input requirements. The usage of proprietary integration products results in the increased cost of enterprises. During the integration, the focus area has been found to often address only the functional requirements, while the non-functional requirements are side-stepped during the initial stages of a project. Moreover, the use of proprietary integration products and non-standards-based integration platform has given rise to an inflexible integration infrastructure resulting in adaptability concerns. Web services-based integration, based on open standards, is deemed to be the only feasible solution in such cases. This paper explains the performance analysis of enterprise integration in heterogeneous environments for the distributed and the transactional applications. The analysis presented in this paper is seen as a step towards making intelligent decisions well in advance when choosing the integration mechanism/products to address the functional as well as the non-functional requirements considering the future integration needs.
基金National Natural Science Foundations of China(Nos.71231001,11001005,71301009)China Postdoctoral Science Foundation(No.2013M530531)+1 种基金the Fundamental Research Funds for the Central Universities of China(Nos.FRF-M P-13-009A,FRF-TP-13-026A)the MOE PhD Supervisor Fund of China(No.20120006110025)
文摘A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a sub-system can be transmitted to other deficient sub-systems. The transmission capacity of the common bus performance sharing mechanism is a random variable. Effects of load on element performance and failure rate were considered in this paper. A reliability evaluation algorithm based on the universal generating function technique was suggested. Numerical experiments were conducted to illustrate the algorithm.
基金National Natural Science Youth Foundations of China(Nos.71501173,61401403)Basic Research Project of Henan Province,China(Nos.52120185,52110636)+2 种基金Scientific and Technological Project of Henan Province,China(No.52110633)The Specialized Research Fund for Young Teachers Program of Zhengzhou University,China(No.51099068)Basic Research Fund of General Design and Research Institute of Zhengzhou University,China(No.53210424)
文摘Importance measures are being widely used to characterize the importance of component in systems.Focus on the integrated importance measure(IIM)of the whole lifetime measure based on the transition rates of component states.To describe the impact of each component in whole lifetime,the IIM is generalized in nonrepairable and repairable systems at first.Then,their formulas are computed in series and parallel systems.Finally,the characteristics of generalized IIM in typical series systems and parallel systems are analyzed.The results show that the generalized IIM of component can evaluate the expected effect of component state on the system performance in whole lifetime.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20114307120032)the National Natural Science Foundation of China(71201167)
文摘A Bayesian method for estimating human error probability(HEP) is presented.The main idea of the method is incorporating human performance data into the HEP estimation process.By integrating human performance data and prior information about human performance together,a more accurate and specific HEP estimation can be achieved.For the time-unrelated task without rigorous time restriction,the HEP estimated by the common-used human reliability analysis(HRA) methods or expert judgments is collected as the source of prior information.And for the time-related task with rigorous time restriction,the human error is expressed as non-response making.Therefore,HEP is the time curve of non-response probability(NRP).The prior information is collected from system safety and reliability specifications or by expert judgments.The(joint) posterior distribution of HEP or NRP-related parameter(s) is constructed after prior information has been collected.Based on the posterior distribution,the point or interval estimation of HEP/NRP is obtained.Two illustrative examples are introduced to demonstrate the practicality of the aforementioned approach.
文摘The growing need for high-performance networking is achieved with parallel processing;several networking functions are processed concurrently in order to accomplish a performance Networking Architecture. Open systems interconnection (OSI) model is an example of multi-layering structure, and each layer performs definite function unique to that layer. OSI model works on pass it on principle, and it is divided in two stacks lower stack and upper stack. Layers 4 - 7 represent upper stack and responsible for data applications. The remaining 1 - 3 layers represent the lower stack and mostly involve in data movement. There are many techniques are available for server optimization enhancing the availability by distributing the load among peer servers. According to our knowledge, nobody has implemented such splitting architecture across the entire OSI model. In this paper, we present multilayer Split-protocol (MLSP) a high performance, reliable and secure technique for spiting an application or network protocol across OSI model, and we present the design, implementation, and empirical performance evaluation of MLSP. It is the ideal choice for Cloud services where each functional component is considered an independent of each other.
文摘The semiclassical transport equations are used to study the high frequency performance of AlGaAs / GaAs HBTs. Electron velocity overshoot effect and its influence on the cut off frequency characteristics of AlGaAs / GaAs HBTs with different collector design parameters are analyzed and discussed.
基金supported by the National Natural Science Foundation of China (7110111671271170)+2 种基金the National Basic Research Program of China (973 Progrom) (2010CB328000)the National High Technology Research and Development Program of China (863 Progrom) (2012AA040914)the Basic Research Foundation of Northwestern Polytechnical University (JC20120228)
文摘To verify the effectiveness of the integrated importance measure (IIM) for multi-state coherent systems of k level, the definition and physical meaning of IIM are demonstrated. Then, the improvement potential and Δ-importance measures are generalized to multi-state coherent systems based on the system performance level, and the relationships between IIM and traditional importance measures are discussed. The characteristics of IIM are demonstrated in both series and parallel systems. Also, an application to an oil transportation system is given. The comparison results show that: (i) IIM has some useful properties that are not possessed by traditional importance measures; (ii) IIM is effective in evaluating the component role in multi-state systems when the component reliability and the failure rate are simultaneously considered.
基金supported by the Human Resources Development Program(Grant No.20144030200590)of the Korea Institute of Energy Technology Evaluation and Planning(KETEP)grant funded by the Korea Government Ministry of Knowledge Economythe Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.NRF-2016R1A6A1A03013567)
文摘Evaluating the expected sliding distance of a vertical slit caisson breakwater is proposed. Time history for the wave load to a vertical slit caisson is made. It consists of two impulsive wave pressures followed by a smooth sinusoidal pressure. In the numerical analysis, the sliding distance for an attack of single wave was shown and the expected sliding distance during 50 years was also presented. Those results were compared with a vertical front caisson breakwater without slit. It was concluded that the sliding distance of a vertical slit caisson may be over-estimated if the wave pressure on the caisson is evaluated without considering vertical slit.
基金support from the Key R&D Program of Shandong Province(Grant No.2019JZZY010431)the National Natural Science Foundation of China(Grant No.52175130)+1 种基金the Sichuan Science and Technology Program(Grant No.2022YFQ0087)the Sichuan Science and Technology Innovation Seedling Project Funding Projeet(Grant No.2021112)are gratefully acknowledged.
文摘In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.