A Neural Network Approach to Find The Cumulative Failure Distribution: Modeling and Experimental Evidence

The failure prediction of components plays an increasingly important role in manufacturing. In this context, new models are proposed to better face this problem, and, among them, artificial neural networks are emerging as effective. A first approach to these networks can be complex, but in this paper, we will show that even simple networks can approximate the cumulative failure distribution well. The neural network approach results are often better than those based on the most useful probability distribution in reliability, the Weibull. In this paper, the performances of multilayer feedforward basic networks with different network configurations are tested, changing different parameters (e.g., the number of nodes, the learning rate, and the momentum). We used a set of different failure data of components taken from the real world, and we analyzed the accuracy of the approximation of the different neural networks compared with the least squares method based on the Weibull distribution. The results show that the networks can satisfactorily approximate the cumulative failure distribution, very often better than the least squares method, particularly in cases with a small number of available failure times. Copyright © 2015 John Wiley & Sons, Ltd.     

三参数威布尔分布参数估计及在可靠性分析中的应用

威布尔分布是可靠性中应用最广泛的分布之一。三参数威布尔分布尤其适用于在开始使用时有一时间段内不发生故障的情况。由于该分布的位置参数不等于0,在参数估计时不能采用简单的参数估计方法实现,限制了该分布形式在可靠性分析中的应用。根据三参数威布尔分布的特点提出了一种综合图解法和遗传算法的参数估计方法,应用该方法可以获得更精确的参数估计值。随后应用于某系列数控车床计算机数控系统的故障分析中,验证了本文提出的参数估计方法的可行性。     

Reliability analysis of wind turbine subassemblies based on the 3-P Weibull model via an ergodic artificial bee colony algorithm

The Weibull distribution is the most widely used model for the reliability evaluation of wind turbine subassemblies. Considering the important role of the location parameter in the three-parameter (3-P) Weibull model and its rare application in wind turbines, this study conducted a reliability analysis of wind turbine subassemblies based on field data that obeyed the 3-P Weibull distribution model via maximum likelihood estimation (MLE). An improved ergodic artificial bee colony algorithm (ErgoABC) was proposed by introducing the chaos search theory, global best solution, and Lévy flights strategy into the classical artificial bee colony (ABC) algorithm to determine the maximum likelihood estimates of the Weibull distribution parameters. This was validated against simulation calculations and proved to be efficient for high-dimensional function optimization and parameter estimation of the 3-P Weibull distribution. Finally, reliability analyses of the wind turbine subassemblies based on different types of field failure data were conducted using ErgoABC. The results show that the 3-P Weibull model can reasonably evaluate the lifetime distribution of critical wind turbine subassemblies, such as generator slip rings and main shafts, on which the location parameter has a significant effect.     

Reliability analysis using exponentiated Weibull distribution and inverse power law

Today in reliability analysis, the most used distribution to describe the behavior of devices is the Weibull distribution. Nonetheless, the Weibull distribution does not provide an excellent fit to lifetime datasets that exhibit bathtub shaped or upside‐down bathtub shaped (unimodal) failure rates, which are often encountered in the performance of products such as electronic devices (ED). In this paper, a reliability model based on the exponentiated Weibull distribution and the inverse power law model is proposed, this new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. A case study based on the lifetime of a surface‐mounted electrolytic capacitor is presented in this paper. Besides, it was found that the estimation of the proposed model differs from the Weibull classical model and that affects the mean time to failure (MTTF) of the capacitor under analysis.     

More on the mis‐specification of the shape parameter with Weibull‐to‐exponential transformation

When lifetimes follow Weibull distribution with known shape parameter, a simple power transformation could be used to transform the data to the case of exponential distribution, which is much easier to analyze. Usually, the shape parameter cannot be known exactly and it is important to investigate the effect of mis‐specification of this parameter. In a recent article, it was suggested that the Weibull‐to‐exponential transformation approach should not be used as the confidence interval for the scale parameter has very poor statistical property. However, it would be of interest to study the use of Weibull‐to‐exponential transformation when the mean time to failure or reliability is to be estimated, which is a more common question. In this paper, the effect of mis‐specification of Weibull shape parameters on these quantities is investigated. For reliability‐related quantities such as mean time to failure, percentile lifetime and mission reliability, the Weibull‐to‐exponential transformation approach is generally acceptable. For the cases when the data are highly censored or when small tail probability is concerned, further studies are needed, but these are known to be difficult statistical problems for which there are no standard solutions. Copyright © 2000 John Wiley & Sons, Ltd.     

Reliability analysis for electronic devices using beta‐Weibull distribution

Today, in reliability analysis, the most used distribution to describe the behavior of electronic products under voltage profiles is the Weibull distribution. Nevertheless, the Weibull distribution does not provide a good fit to lifetime datasets that exhibit bathtub‐shaped or upside‐down bathtub–shaped (unimodal) failure rates, which are often encountered in the reliability analysis of electronic devices. In this paper, a reliability model based on the beta‐Weibull distribution and the inverse power law is proposed. This new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. To estimate the parameters of the proposed model, a Bayesian analysis is used. A case study based on the lifetime of a surface mounted electrolytic capacitor is presented, the results showed that the estimation of the proposed model differs from the inverse power law–Weibull and that it affects directly the mean time to failure, the failure rate, the behavior, and the performance of the capacitor under analysis.     

On the upper truncated Weibull distribution and its reliability implications

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.     

A Method for Discriminating Between Failure Density Functions Used In Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions.

The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations.

In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when they do not appear to describe the failure density function of a unit.     

用BP神经网络诊断结构破损

提出了一种基于BP神经网络的结构破损诊断方法,该方法以结构残余力向量作为破损诊断的网络输入。对网络训练样本采用广义空间格点法进行了变换,从而较好地解决了由于系统响应样本在数据空间分布不均对网络收敛速度及网络诊断精度的影响问题。应用实例表明,本文方法能准确诊断结构破损位置与严重程度,是一种有效的结构破损诊断方法。     

Reliability assessment for failure-dependent and uncertain systems: A Bayesian network based on copula method and probability-box

Managing failure dependence of complex systems with hybrid uncertainty is one of the hot problems in reliability assessment. Epistemic uncertainty is attributed to complex working environment, system structure, human factors, imperfect knowledge, etc. Probability-box has powerful characteristics for uncertainty analysis and can be effectively adopted to represent epistemic uncertainty. However, arithmetic rules on probability-box structures are mostly used among structures representing independent random variables. In most practical engineering applications, failure dependence is always introduced in system reliability analysis. Therefore, this paper proposes a developed Bayesian network combining copula method with probability-box for system reliability assessment. There are four main steps involved in the reliability computation process: marginal distribution identification and estimation, copula function selection and parameter estimation, reliability analysis of components with correlations and Bayesian forward analysis. The benefits derived from the proposed approach are used to overcome the computational limitations of n-dimensional integral operation, and the advantages of useful properties of copula function in reliability analysis of systems with correlations are adopted. To demonstrate the effectiveness of the developed Bayesian network, the proposed method is applied to a real large piston compressor.     

基于GM-噪声SVR方法的矿山设备可靠性参数估计

为了有效估计小子样条件下矿山设备的三参数威布尔分布可靠性模型参数,提出基于GM-噪声SVR的参数估计方法。该方法以灰色估计法(GM)为基础估计模型的位置参数,采用基于训练样本数量和噪声参数寻优的ε - 带支持向量回归机(ε-SVR)估计尺度参数和形状参数,并通过拟合的三参数威布尔分布函数分析预测和解决设备的可靠性问题。算例结果表明,GM-噪声SVR方法可以很好地用于矿山设备可靠性模型参数估计,估计某带式输送机三参数威布尔分布可靠性模型的位置参数、尺度参数和形状参数依次为3.1525、188.3763、1.0476,平均无故障时间为188 h,标准均方根误差NRMSE为0.0519。这表明该方法的可行性和有效性。     

基于BP神经网络与柔度变化的结构破损诊断

提出了一种基于BP神经网络的结构破损诊断方法,该方法以结构破损前后柔度的变化作为破损诊断的网络输入,为了解由于系统响应样本数据空间分布不均匀对网络收敛速度及网络诊断的影响问题,对网络训练样本采用广义空间格点进行了变换,模拟算例及应用实例均表明,本文方法能准确诊断结构破损位置与严重程度,是一种有效的结构破损诊断方法。     

Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter

The Weibull shape parameter is important in reliability estimation as it characterizes the ageing property of the system. Hence, this parameter has to be estimated accurately. This paper presents a study of the efficiency of using robust regression methods over the ordinary least‐squares regression method based on a Weibull probability plot. The emphasis is on the estimation of the shape parameter of the two‐parameter Weibull distribution. Both the case of small data sets with outliers and the case of data sets with multiple‐censoring are considered. Maximum‐likelihood estimation is also compared with linear regression methods. Simulation results show that robust regression is an effective method in reducing bias and it performs well in most cases. Copyright © 2006 John Wiley & Sons, Ltd.     

Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

Lower percentiles of product lifetime are useful for engineers to understand product failure, and avoiding costly product failure claims. This paper proposes a percentile re‐parameterization model to help reliability engineers obtain a better lower percentile estimation of accelerated life tests under Weibull distribution. A log transformation is made with the Weibull distribution to a smallest extreme value distribution. The location parameter of the smallest extreme value distribution is re‐parameterized by a particular 100pth percentile, and the scale parameter is assumed to be nonconstant. Maximum likelihood estimates of the model parameters are derived. The confidence intervals of the percentiles are constructed based on the parametric and nonparametric bootstrap method. An illustrative example and a simulation study are presented to show the appropriateness of the method. The simulation results show that the re‐parameterization model performs better compared with the traditional model in the estimation of lower percentiles, in terms of Relative Bias and Relative Root Mean Squared Error. Copyright © 2017 John Wiley & Sons, Ltd.     

A study of a storage reliability estimation problem

Storage reliability, which describes the failure or deterioration of items in a dormant state, is considered in this paper. The study presented here is focused on the estimation of the storage reliability after a certain amount of storage time. We start with simple non-parametric estimation of the current reliability and then study the problem of parametric estimation based on a simple Weibull distribution assumption. Both maximum likelihood estimation and graphical techniques are considered in this case. The study is useful for planning a storage environment and making a decision about the maximum length of storage. Furthermore, the information can be used in the design and improvement of products for which the storage is an important part of the product's life cycle. A numerical example is provided to enlighten the idea.     

Estimating S–N curves and their scatter using a differential ant-stigmergy algorithm

We present an alternative approach to the rapid estimation of S–N curves and their scatter. A simultaneous estimation of the S–N curve and its scatter is achieved by applying a two-parametric Weibull distribution to describe the scatter of a number of load cycles to failure at an arbitrary amplitude stress level. The shape of the S–N curve is generally modelled as a linear dependence between the logarithmic value of the number of load cycles to failure and the logarithmic value of the amplitude stress level. This dependence is described by two parameters: a constant term and a scale coefficient of the S–N curve in a log-log scale. Therefore, the same formulation was applied to model the dependence between a scale parameter of the Weibull distribution and the logarithmic value of the amplitude stress level. In this manner the S–N curve and its scatter are described by three parameters: the constant term, the scale coefficient and the shape parameter of the Weibull distribution. The three parameters are estimated with a differential ant-stigmergy algorithm from the experimental data. In the article a mathematical background of the approach is presented and applied to three cases of experimentally obtained durability data. The results are analysed and discussed.     

Parameter estimation for bivariate Weibull distribution using generalized moment method for reliability evaluation

Bivariate Weibull distribution can address the life of a system exhibiting 2‐dimensional characteristics in risk and reliability engineering. The applicability of bivariate Weibull distribution has been hindered by its difficulty with parameter estimation, as the number of parameters in bivariate Weibull distribution is more than those in univariate Weibull distribution. Considering a particular structure of a bivariate Weibull distribution model, this paper proposes a generalized moment method (GMM) for parameter estimation. This GMM method is simple, and it has proved to be efficient. The GMM can guarantee the existence and the uniqueness of the solution. A confidence interval for each estimator is derived from the moments of the bivariate distribution. The paper presents a simulation case and 2 real cases to demonstrate the proposed methods.     

Parametric Estimation

The exponential distribution is often used in reliability work to describe the distribution of time to “chance” failure and is characterized by a constant failure rate. In this paper the small sample powers are compared for four test statistics for the hypothesis of constant failure rate vs. the hypothesis of non-constant failure rate. The tests are compared for samples of size n = 10(5)50 using the Weibull distribution for the alternative distribution. The shape parameter of the Weibull is varied from 0.5 to 2.5. For the two test statistics which involve arbitrary grouping of the data the effect of group size and number was also examined.     

Analysis of field failure data when modeled Weibull slope increases with time

Weibull time‐to‐fail distributions cannot be correctly estimated from field data when manufacturing populations from different vintages have different failure modes. To investigate the pitfalls of ongoing Weibull parameter estimation, two cases, based upon real events, were analyzed. First, a time‐to‐fail distribution was generated assuming the same Weibull shape parameter representing an increasing failure rate for each monthly batch or vintage of production. The shape parameter was estimated from simulated field data at regular periods as the population accumulated service time. Estimates of the shape parameter were not constant, but gradually decreased (as had occurred in a real system) with added service time. In the second case, field reliability performance was modeled to match the actual historical data for one product from a disk drive manufacturer. The actual data was proprietary and was not directly available for analysis. A production schedule was modeled with a mix of two failure characteristics. The population reaching the field in the first 12 months had a low, constant failure rate. For the second and third years of production, higher volumes were introduced that had the higher, increasing failure rates of the first case. Assessment of the mixed population at each month of calendar time resulted in an increasing Weibull shape parameter estimate at each assessment. When the two populations were separated and estimated properly, a better fit with more accurate estimates of Weibull shape parameters resulted. Copyright © 2010 John Wiley & Sons, Ltd.