Existing Reliability Analysis Methods Research Articles

A Fast and Accurate Reliability Approximation Method for Heterogeneous Cold Standby Sparing Systems

Cold standby sparing is a widely-used fault-tolerant technique where spare units are unpowered and non-operational before being activated to replace a malfunctioned on-line unit. The dynamic failure rate behavior of cold standby units poses unique challenges to the reliability analysis of cold standby systems (CSSs). The existing reliability analysis methods developed for CSSs have various limitations, such as being applicable to only the exponential component time-to-failure distribution, CSSs with identical components, and small-scale systems due to high computational complexity. In this paper, we advance the state of the art by proposing a fast and accurate reliability approximation method based on the Lyapunov central limit theorem for heterogeneous 1-out-of-n cold standby systems with non-identical components. The Lyapunov's conditions are proved for CSSs with exponential, Weibull, normal, and mixed component time-to-failure distributions. The accuracy and efficiency of the proposed method are verified and compared with the existing methods through comprehensive case studies on CSSs with different sizes and different types of distributions. The results show that the proposed method can estimate the reliability of large-scale CSSs efficiently and accurately.

Development of surrogate models in reliability-based design optimization: A review.

Reliability-based design optimization (RBDO) is applied to handle the unavoidable uncertainties in engineering applications. To alleviate the huge computational burden in reliability analysis and design optimization, surrogate models are introduced to replace the implicit objective and performance functions. In this paper, the commonly used surrogate modeling methods and surrogate-assisted RBDO methods are reviewed and discussed. First, the existing reliability analysis methods, RBDO methods, commonly used surrogate models in RBDO, sample selection methods and accuracy evaluation methods of surrogate models are summarized and compared. Then the surrogate-assisted RBDO methods are classified into global modeling methods and local modeling methods. A classic two-dimensional RBDO numerical example are used to demonstrate the performance of representative global modeling method (Constraint Boundary Sampling, CBS) and local modeling method (Local Adaptive Sampling, LAS). The advantages and disadvantages of these two kinds of modeling methods are summarized and compared. Finally, summary and prospect of the surrogate-assisted RBDO methods are drown.

A novel risk analysis approach of casing under complex conditions using copulas

Failure accidents of casings, designed obeying traditional design standards that have been amended for many times, are still happening nowadays, and existing reliability analysis methods mostly have not considered the dependence structures of variables, it's badly necessary to seek other methods to compensate these two problems and defects. This study proposes a copula-based risk analysis framework of casing in a casing-formation composite system (CFCS). Firstly, a mechanical analysis model of casing under CFCS is established and verified by the simulation method. Secondly, random data sets of the formation parameters are obtained by using logging data, meanwhile, the acquisition methods of statistical data of casing are also provided. Thirdly, the best uncertainty parameters in the given five copulas are inferred by using Bayesian-based Markov chain Monte Carlo (MCMC) likelihood algorithm, which are compared with those from other algorithms; the optimal copula is determined by the Bayesian-based MCMC-estimated method and the squared Euclidean distance (SED), respectively; the posterior joint probability isolines of the copulas are depicted, and isolines from the optimal copula are compared with that of the empirical copula method; the correlation coefficients of variables in CFCS, relative to performance function value, are sorted in magnitude. Finally, a division method of safety level is adopted, and based on the optimal copula, the risk analysis of casing is conducted with considering the bivariate dependence. The proposed framework can provide unique insights into the risk analysis of casing in CFCS with correlations considered and can also be programmed to use in risk management and decision-making systems of petroleum engineering.

A bounding-limit-state-surface-based active learning Kriging method for hybrid reliability analysis under random and probability-box variables

Abstract This paper presents a new method for efficient hybrid reliability analysis under both random and probability-box variables. Due to the existence of probability-box variables, the failure probability yielded by hybrid reliability analysis is an interval value. In practical engineering, numerical models are becoming more and more time-consuming, which promotes that metamodel-assisted reliability analysis methods gain considerable attention. The failure probability in hybrid reliability analysis under both random and probability-box variables can be calculated by transforming the original uncertainty space into the standard normal space. Then a limit-state band with two bounding limit-state surfaces is generated in the standard normal space. In this paper, it is determined that the lower and upper bounds of failure probability can be accurately estimated based on a Kriging metamodel as it can well describe the two bounding limit-state surfaces. Then, a new active learning strategy based on bounding limit-state surface is proposed to sequentially update Kriging metamodel by adding new update points in the vicinity of the bounding limit-state surfaces into design of experiments. Meanwhile, two error measurement functions are presented to terminate the update process by calculating the metamodel error. Combining the bounding-limit-state-surface-based active learning Kriging with interval Monte Carlo simulation, a new method for hybrid reliability analysis under both random and probability-box variables is developed. In this method, the lower and upper bounds of failure probability are estimated by interval Monte Carlo simulation based on the built Kriging metamodel. The proposed method is tested by six examples. Its comparison with some existing reliability analysis methods is provided. The high accuracy and efficiency of the proposed method are validated by comparative results.

Multi-state system reliability analysis methods based on Bayesian networks merging dynamic and fuzzy fault information

Traditional Bayesian Networks (BNs) have limited abilities to analyse system reliability with fuzzy and dynamic information. To deal with such information in system reliability analysis, a new multi-state system reliability analysis method based on BNs was proposed. The proposed method effectively solved the deficiencies of existing reliability analysis methods based on BNs incorporating fuzziness and fault information. In this work, fuzzy set theory and changing failure probability function of components were introduced into BNs, and the dynamic fuzzy subset was introduced. The curve of the fuzzy dynamic fault probability of the leaf node fault state and fuzzy dynamic importance were developed and calculated. Finally, a case study of a truck system was employed to demonstrate the performance of the proposed methods in comparison with traditional fault tree and T-S fuzzy importance analysis methods. The proposed method proved to be feasible in capturing the fuzzy and dynamic information in real-world systems.

Reliability analysis of imperfect coverage systems with a shared warm standby

Redundancy technique is commonly applied to satisfy the reliability requirements of fault-tolerant systems. Warm standby, a compromise between hot standby and cold standby in term of power consumption and recovery time, has attracted wide attention over the past several decades. However, the existing reliability analysis methods for warm standby system with imperfect coverage are difficult to deal with some cases, such as non-exponential time-to-failure distributions for the system components and the systems with shared standbys. In this paper, a new approach based on step function and impulse function is proposed to overcome the limitations of the existing approaches. The reliability of a system including shared standbys is deduced considering two kinds of imperfect fault coverage models, which contain Element Level Coverage (ELC) and Fault Level Coverage (FLC). The proposed approach can applicable to any type of time-to-failure distributions for the system components subject to imperfect fault coverage. A case study is presented to illustrate the applications and advantages.

A Hybrid Loop Approach Using the Sufficient Descent Condition for Accurate, Robust, and Efficient Reliability-Based Design Optimization

For reliability-based design optimization (RBDO) problems, single loop approaches (SLA) are very efficient but prone to converge to inappropriate point for highly nonlinear constraint functions, and double loop approaches (DLA) are proven to be accurate but require more iterations to achieve stable results. In this paper, an adjusted advanced mean value (AAMV) method is firstly proposed to improve the robustness and efficiency of performance measure approach. The global convergence of the AAMV is guaranteed using sufficient descent condition for the reliability loop in RBDO. Then, a hybrid RBDO method is developed to improve the efficiency of DLA and accuracy of SLA, on the basis of sufficient descent condition and AAMV method, named as hybrid single and double loops (HSD) method. Three nonlinear concave and convex performance functions are used to illustrate the efficiency and robustness of the AAMV method; then the accuracy, robustness, and efficiency of the proposed HSD method are compared to current SLA and DLA through another three benchmark nonlinear RBDO examples. Results show that the AAMV is more robust and efficient than the existing reliability analysis methods. The HSD is more accurate than the SLA for highly nonlinear problems, and also exhibits a better performance than the DLA from the point of view of both robustness and efficiency.

Reliability analysis method based on determination of the performance function’s PDF using the univariate dimension reduction method

In addition to traditional motivations for application of the reliability analysis, significant growth of the structural design optimization utilization can be observed nowadays, where minimization of the structural weight and maximization of the structural safety are the most common objectives. Application of the existing reliability analysis methods in the context of the multi-criteria optimization of complex structures (e.g. ships), which are characterized by a large number of the design and random variables, is very time consuming due to extremely large number of the pertinent calculations. Consequently, an efficient reliability analysis method is proposed within the scope of this article. Proposed method provides very accurate results within significantly lower computational timeframes with respect to the existing reliability analysis methods, which makes it appropriate for application in computationally very demanding reliability based design optimization (RBDO) environment.

Solving reliability analysis problems in the polar space

An optimization model that is widely used in engineering problems is Reliability-Based Design Optimization (RBDO). Input data of the RBDO is non-deterministic and constraints are probabilistic. The RBDO aims at minimizing cost ensuring that reliability is at least an accepted level. Reliability analysis is an important step in two-level RBDO approaches. Although many methods have been introduced to apply in reliability analysis loop of the RBDO, there are still many drawbacks in their efficiencies and stabilities. This paper proposes a novel method that converts the constrained reliability analysis problem to an unconstrained minimization problem in order to improve efficiency of the solution. Number of numerical experiments is conducted and then performance of the proposed method is compared with the existing reliability analysis methods. Keywords: Polar space, Reliability analysis, Reliability-based design optimization.

Reliability analysis of machining systems by considering system cost

In this article, a novel approach is proposed for solving the optimal configuration problem of a machining system by reliability analysis. There are many kinds of alternative schemes with different numbers or types of machines to produce the same part, but there is difference in the system’s reliability and lifecycle cost. Since the mission time could not describe the reliability loss of repairable equipment precisely, a new approach is proposed for the computation of its reliability to estimate the system lifecycle cost. The reason is that in a machining system, the total time spent on each machine includes cutting time and elapsed time. The elapsed time consists of set-up time, waiting time and forced idle time. The reliability loss of a machine mainly occurs within the cutting time. However, in the existing reliability analysis methods, the reliability loss of repairable equipment is always measured using the total time spent on it. Therefore, in this study, based on the mean time between failures (MTBF), a machine’s rate of reliability loss is computed by using its actual machining time rather than the total time. Furthermore, each machine’s failure frequencies in a machining system could be obtained by its MTBF. So that, the lifecycle cost of a machining system can be exactly determined. To demonstrate the validity of the proposed approach, a piston machining system is provided as an example.

An asymmetric dimension-adaptive tensor-product method for reliability analysis

Reliability analysis plays an essential role in the development of structural systems. However, commonly used reliability analysis methods suffer from either the curse of dimensionality or the lack of accuracy in many structural problems. This paper presents an asymmetric dimension-adaptive tensor-product (ADATP) method to resolve the difficulties of existing reliability analysis methods. The proposed method leverages three ideas: (i) an asymmetric dimension-adaptive scheme to efficiently build the tensor-product interpolation considering both directional and dimensional importance, (ii) a hierarchical interpolation scheme using either piecewise multi-linear basis functions or cubic Lagrange splines, (iii) a hierarchical surplus as an error indicator to automatically detect the highly nonlinear regions in a random space and adaptively refine the collocation points in these regions. The proposed method has three distinct features for reliability analysis: (a) automatically detecting and adaptively reproducing tri- and higher-variate interactions, (b) greatly alleviating the curse of dimensionality, and (c) no need of response sensitivities. Several mathematical and engineering problems involving high nonlinearity are used to demonstrate the effectiveness of the ADATP method.

Evolution of reliability engineering discipline over the last six decades: a comprehensive review

The field of reliability engineering has undergone evolutionary progress and breakthroughs during the last six decades. This paper provides a historical perspective of significant developments and systematically enumerates contributions in the field of reliability engineering since the beginning. This paper further delves into the relevance and development of various statistical methods for data and reliability analysis, diagram-based models, analytical methods, physics-of-failure and fuzzy logic-based reliability tools and techniques that have shaped the emergence of the reliability engineering discipline. Finally, this paper highlights limitations with existing reliability analysis methods and identifies a few potential opportunities for further research.

Collaborative Reliability Analysis under the Framework of Multidisciplinary Systems Design

Traditional Multidisciplinary Design Optimization (MDO) generates deterministic optimal designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room to accommodate uncertainties in system input, modeling, and simulation. As a result, the design solution obtained may be highly sensitive to the variations of system input which will lead to performance loss and the solution is often risky (high likelihood of undesired events). Reliability-based design is one of the alternative techniques for design under uncertainty. The natural method to perform reliability analysis in multidisciplinary systems is the all-in-one approach where the existing reliability analysis techniques are applied directly to the system-level multidisciplinary analysis. However, the all-in-one reliability analysis method requires a double loop procedure and therefore is generally very time consuming. To improve the efficiency of reliability analysis under the MDO framework, a collaborative reliability analysis method is proposed in this paper. The procedure of the traditional Most Probable Point (MPP) based reliability analysis method is combined with the collaborative disciplinary analyses to automatically satisfy the interdisciplinary consistency when conducting reliability analysis. As a result, only a single loop procedure is required and all the computations are conducted concurrently at the individual discipline-level. Compared with the existing reliability analysis methods in MDO, the proposed method is efficient and therefore provides a cheaper tool to evaluate design feasibility in MDO under uncertainty. Two examples are used for the purpose of verification.