A Method for Determining the Reliability Index of a Materiel Subsystem

This paper presents a method for determining the reliability index of a subsystem in the materiel demonstration phase-AHP Failure Rate Method. It fully considers the various factors which influence a subsystem reliability index and solves a difficult problem that puzzles the demonstration personnel.

Derivation of Reliability Index Vector Formula for Series System and Its Application

In this study, a reliability index vector formula is proposed for series system with two failure modes in term of the concept of reliability index vector and equivalent failure modes. Firstly, the reliability index vector is introduced to determine the correlation coefficient between two failure modes, and then, the reliability index vector of a series system can be obtained. Several numerical cases and an analysis on offshore platform are performed, and the results show that this scheme provided here has better computational accuracy, and its calculation process is simpler for the series systems reliability calculations compared with the other methods. Also this scheme is more convenient for the engineering applications.

Instantaneous Reliability Index of a Typical Repairable System

A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.

MODIFIED SCHEME BASED ON SEMI-ANALYTIC APPROACH FOR COMPUTING NON-PROBABILISTIC RELIABILITY INDEX

A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.

Reliability Comparison Between Parallel and Cold-standby Two-unit System Under Poisson Shock

This paper investigates the comparison problem of the reliability index between a parallel and a cold-standby system,both of which are consisting of two identical units.On the contrary to the general intuitive result,we proved that,under the condition that the system is shocked by a Poisson stream,the life time of the parallel system is longer than that of the cold-standby one in the sense of probability.

Reliability-Based Load and Resistance Factors Design for Offshore Jacket Platforms in the Bohai Bay:Calibration on Target Reliability Index

The target reliability index has been effectively used as the best solution to deal with the relationship between the structural safety and the optimal economy in any structural design. However, the target reliability index for offshore jacket platforms based on different sea areas in China has never been calibrated. This paper presents an approach for its calibration, and suggests many kinds of associated load cases. The uncertainties of loads and structural resistance are mainly in- vestigated. The target reliability index for structural components, tubular joints and piles of offshore jacket plaffortns are discussed respectively in detail. Finally, through the calibrated results from the offshore jacket platforms of QK18-1, JZ20-2, SZ36-1 and BZ28-1 in the Bohai Bay, it is proposed to adopt 2.8 as the target reliability index of offshore jacket platforms in the Bohai Bay for a 25-year design period. The results provide significant reference for the design of offshore jacket platforms.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

A multi-index coupling system of ice slope stability and its application

Based on the Simplified Bishop Method, the minimum safety factor of ice slope both with and without tension cracks is calculated in combination with triaxial compression tests. It is found that there exists a critical depth for each crack. Then, factors influencing ice slope stability such as slope ratio, slope height, ice cohesion, internal friction angle, unit weight and temperature were analyzed. Meanwhile, a regression equation between the aforementioned factors and safety factor is obtained, with which sensitivity analysis is carried out. The performance function is built in combination with random distribution of physical and mechanical parameters to analyze the reliability index. The Advanced First Order Second Moment Method is employed on the solution to the perfor- mance function. The one-way coupling system of ice slope stability is therefore formed based on safety factor and reliability index. Finally, an illustrated example of ice slope is provided, which shows that failure probability is relatively high, up to 6.18%, alt- hough safety factor is 2.77. Thus, it is objective and reasonable to apply the coupled system method to the slope stability rating.

Semi-Probabilistic Evaluation of System Redundancy for Existing Offshore Structures

In this paper, a new definition of structure system redundancy is proposed in view of the various measures for structure redundancy. By introducing the terms of structure system failure at the mechanism level and equivalent reliability index, the safety for existing offshore platforms can be evaluated by the semi-probabilistic method presented in this paper. Some numerical examples are given and satisfactory results have been obtained.

STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

Comparison of Structural Probabilistic and Non-Probabilistic Reliability Computational Methods under Big Data Condition

In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is classified into different types according to the regularities of the distribution of data.The different stresses which have been subjected by the structure are used in this paper.Secondly,the structural interval reliability and probabilistic pre-diction models are established by using the stress-strength interference theory under big data of random loads after the stresses and structural strength are comprehensively considered.Structural reliability is computed by using various stress types,and the minimum reliability is determined as structural reliability.Finally,the advan-tage and disadvantage of the interval reliability method and probability reliability method are shown by using three examples.It has been shown that the proposed methods are feasible and effective.

A new structural reliability index based on uncertainty theory

The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem, a new quantification method for the reliability of structures is presented based on uncertainty theory, and an uncertainty-theory-based perspective of classical Cornell reliability index is explored. In this paper, by introducing the uncertainty theory, we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables, instead of probabilistic and possibilistic measures. We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters, based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions. Moreover, we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.

Study of Partial Coefficients for Design of Semicircular Breakwaters

In the present study, the reliability design of semicircular breakwater is based on the verification of the rules defined by standard specifications, where partial coefficients are introduced to ensure safety. The reliability of the semicircular breakwaters has been analyzed by using the Hasofer-Lind method to determine the reliability index of structure that has correlated loads, utilizing the long-term observed wave data at a given place. The relation curve between reliability index and safety factor in the traditional design method, as well as the relationships between reliability index and partial coefficients, have been obtained. This paper proposes values of partial coefficients for the design expression of semicircular breakwaters in the cases of anti-sliding and anti-overturning.

Durability of Reinforced Concrete Structures under Coupling Action of Load and Chlorine Erosion

Diffusion behavior of chloride ion in reinforced concrete under bendingmoment was studied by taking the ratio of bending moment to ultimate flexural capacity asload level indicator. The function relationship between load level and chloride iondiffusion coefficient was established, based on that the limit state equation of the chlorideion critical concentration and chloride ion concentration on surface of the steel bar wasestablished. Then by applying Monte-Carlo method the corrosion probability ofreinforcement under different load levels in splash zone was calculated. Calculation resultsdemonstrated that compared with the durability reliability index considering loading effect,the reliability index without considering loading effect could be 100% higher. Inconsideration of requirement for concrete durability, some revision suggestion was putforward. It was recommended that for beam members with different design life in splashzone, the corresponding minimum cover thickness should be adjusted properly as well aswater-cement ratio limit.

Reliability analysis for a cold standby system under stepwise Poisson shocks

In this paper,a two-dissimilar-component cold standby repairable system maintained by a repairmanis investigated.The system fails due to either intrinsic factors or external shocks.Assume that shocks arrive according to a stepwise Poisson process,the intensity of which varies with respect to the number of failures of the working component.Repair after failure is imperfect.Using the supplementary variable method and the vector Markov process theory,we obtain some important reliability index for the system.By the renewal reward theorem,an optimal replacement policy N∗is derived by minimising the average cost rate of the system.Numerical examples are presented to validate the theoretical results.

Calibrating partial factors for Danish railway embankments using probabilistic analyses

High costs are connected with upgrading railway embankments throughout Denmark using the partial factors for geotechnical design calibrated for general application. One way to reduce the costs is reliability-based calibration of the partial factors to a reasonable safety level taking into account the specific design situations and uncertainties relevant to railway embankments. A reliability-based design has been investigated, resulting in an optimal partial factor for the considered subsoil. With a stochastic soil model to simulate the undrained shear strength of soft soil deposits, the partial factor is calibrated using asymptotic sampling for the reliability assessment. The calibration shows that the partial factor can be reduced significantly compared to the value specified in the Danish National Annex to DS/EN 1997-1 （2007）, Eurocode 7.

Reliability measure approach considering mixture uncertainties under insufficient input data

Reliability analysis and reliability-based optimization design require accurate measurement of failure probability under input uncertainties.A unified probabilistic reliability measure approach is proposed to calculate the probability of failure and sensitivity indices considering a mixture of uncertainties under insufficient input data.The input uncertainty variables are classified into statistical variables,sparse variables,and interval variables.The conservativeness level of the failure probability is calculated through uncertainty propagation analysis of distribution parameters of sparse variables and auxiliary parameters of interval variables.The design sensitivity of the conservativeness level of the failure probability at design points is derived using a semi-analysis and sampling-based method.The proposed unified reliability measure method is extended to consider p-box variables,multi-domain variables,and evidence theory variables.Numerical and engineering examples demonstrate the effectiveness of the proposed method,which can obtain an accurate confidence level of reliability index and sensitivity indices with lower function evaluation number.

Stability and Numerical Analysis of a Standby System

A model for repairable standby parallel system consisting of two identical components with common cause failure(CCF)and human error is introduced in this article by a semigroup approach.The stability of the system is verified by the pure analysis technique,the co-final related theory and functional analysis method.It is discussed that four different reliability indices of the studied model are consistent with each other both analytically and numerically.The simulations and comparisons demonstrate the validity of the proposed technique.

Revisiting the Model of Servicing Machines with Repairable Service Facility-A New Analyzing Idea and Some New Results

In this paper the model of servicing machines with repairable facility is further studied.By standard conditioning decomposition argument,two reliability indices-the probability that the service facility fails at time t and the expected number of failure occurring during（0,t] are discussed.Some important relations of them are given.Furthermore,some new reliability problems are presented and discussed as follows：1） The numbers of the service facility failures during the generalized service time and the generalized busy period;2） The asymptotic expansion of the expected failure number of the service facility during（0,t].A series of new reliability results of the service facility are obtained.

Stochastic Boundary Element Analysis of Concrete Gravity Dam

Stochastic boundary integral equations for analyzing large structures are obtained from the partial derivatives of basic random variables. A stochastic boundary element method based on the equations is developed to solve engineering problems of gravity dams using random factors including material parameters of the dam body and the foundation, the water level in the upper reaches, the anti-slide friction coefficient of the dam base, etc. A numerical example shows that the stochastic boundary element method presented in this paper to calculate the reliability index of large construction projects such as a large concrete gravity dam has the advantages of less input data and more precise computational results.