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.     

Reliability analysis incorporating exponentiated inverse Weibull distribution and inverse power law

In reliability research, electronic devices are an important part of our lives and modelling their lives is the most difficult and fascinating area. To investigate the failure functioning of electronic equipments, reliability monitoring of systems is widely used. However, it is stated in the literature that one in five electronic system collapses are a consequence of degradation and saving energy and forecasting future losses, it is necessary to summarize the data through certain versatile models of probability . In current article, a model of reliability formed on inverse power law and generalized inverse Weibull model is suggested. This current distribution presents a clearer framework to modelling the efficiency and functionality lifespan of electronic equipments. In this article, an empirical analysis is discussed related to life cycle of a surface-mounted electrolytic capacitor (SMEC). In addition, it has noticed that evaluation of suggested distribution varies from classical model of inverse Weibull and that influences average time to failure (ATTF) of the studied capacitor.     

Shewhart Control Charts for Monitoring Reliability with Weibull Lifetimes

In this paper, we present Shewhart‐type and S² control charts for monitoring individual or joint shifts in the scale and shape parameters of a Weibull distributed process. The advantage of this method is its ease of use and flexibility for the case where the process distribution is Weibull, although the method can be applied to any distribution. We illustrate the performance of our method through simulation and the application through the use of an actual data set. Our results indicate that and S² control charts perform well in detecting shifts in the scale and shape parameters. We also provide a guide that would enable a user to interpret out‐of‐control signals. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability approximation using finite Weibull mixture distributions

The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions. The scope of the paper is to prove that the reliability of an arbitrary system can be approximated well by a finite Weibull mixture with positive component weights only, without knowing the structure of the system, on condition that the unknown parameters of the mixture can be estimated. To support the main idea, five examples are presented. In order to estimate the unknown component parameters and the component weights of the Weibull mixture, some of the already existing methods are applied and the EM algorithm for the m-fold Weibull mixture is derived. The fitted distributions obtained by different methods are compared to the empirical ones by calculating the AIC and δ_C values. It can be concluded that the suggested Weibull mixture with an arbitrary but finite number of components is suitable for lifetime data approximation. For parameter estimation the combination of the alternative and EM algorithm is suggested.     

Reliability analysis of electronic devices with multiple competing failure modes involving performance aging degradation

This paper presents an extension of reliability analysis of electronic devices with multiple competing failure modes involving performance aging degradation. The probability that a product fails on a specific mode is derived. Using this probability, the dominant failure mode on the product can be predicted. A practical example is presented to analyze an electronic device with two kinds of major failure modes–solder/Cu pad interface fracture (a catastrophic failure) and light intensity degradation (a degradation failure). Reliability modeling of an individual failure mode and device reliability analysis is presented and results are discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

An Approach for Reliability Demonstration Test Based on Power‐Law Growth Model

Reliability demonstration test (RDT) is a critical and necessary step before the acceptance of an industrial system. Generally, a RDT focuses on designing a test plan through which one can judge whether the system reliability indices meet specific requirements. There are many established RDT plans, but few have incorporated the reliability growth aspects of the corresponding products. In this paper, we examine a comprehensive test plan that involves information concerning the reliability growth stage. An approach for RDT under the assumption of the power‐law model is proposed. It combines data related to the growth stage with those pertaining to the test stage of the product to reduce the cost of the test. Through simulation studies and numerical examples, we illustrate the characteristics of the test plan and significant reduction in test costs through our approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Bayesian estimation of mixed Weibull distributions

Estimation of mixed Weibull distribution by maximum likelihood estimation and other methods is frequently difficult due to unstable estimates arising from limited data. Bayesian techniques can stabilize these estimates through the priors, but there is no closed-form conjugate family for the Weibull distribution. This paper reduces the number of numeric integrations required for using Bayesian estimation on mixed Weibull situations from five to two, thus making it a more feasible approach to the typical user. It also examines the robustness of the Bayesian estimates under a variety of different prior distributions. It is found that Bayesian estimation can improve accuracy over the MLE for situations with low mixture ratios so long as the prior on the weak subpopulation's characteristic life has an expected value less than or equal to the true characteristic life.     

Reliability inference for VGA adapter from dual suppliers based on contaminated type‐I interval‐censored data

Type‐I interval‐censoring scheme only documents the number of failed units within two prespecified consecutive exam times at the larger time point after putting all units on test at the initial time schedule. It is challenging to use the collected information from type‐I interval‐censoring scheme to evaluate the reliability of unit when not all admitted units are operated or tested at the same initial time and a majority of units are randomly selected to replace the failed test units at unrecorded time points. Moreover, the lifetime distribution of all pooled units from dual resources usually follows a mixture distribution. To overcome these two problems, a two‐stage inference process that consists of a data‐cleaning step and a parameter estimation step via either Markov chain Monte Carlo (MCMC) algorithm or profile likelihood method is proposed based on the contaminated type‐I interval‐censored sample from a mixture distribution with unknown proportion. An extensive simulation study is conducted under the mixture smallest extreme value distributions to evaluate the performance of the proposed method for a case study. Finally, the proposed methods are applied to the mixture lifetime distribution modeling of video graphics array adapters for the support of reliability decision.     

Estimation of mixed Weibull distribution parameters using the SCEM-UA algorithm: Application and comparison with MLE in automotive reliability analysis

The shuffled complex-evolution metropolis algorithm (SCEM-UA) is used to estimate mixed Weibull distribution parameters in automotive reliability analysis. The results are compared with maximum likelihood estimation (MLE) results. The comparison shows that, in the examples given, SCEM-UA can deliver more accurate results than MLE overall.     

基于MCMC稳态模拟的Weibull共享异质性模型及其可靠性应用

针对传统假设中个体寿命独立同分布的不足，构建了贝叶斯Weibull共享异质性模型，提出了对寿命服从Weibull分布的产品，运用基于Gibbs抽样的马尔可夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)方法动态模拟出参数后验分布的马尔可夫链，在异质性因子的先验分布为Gamma分布时，给出随机截尾条件下，参数在Weibull共享异质性模型中的贝叶斯估计，提高了计算的精度。借助数据仿真说明了利用WinBUGS (Bayesian inference using Gibbs samp     

Reliability analysis of Weibull multicomponent system with stress-dependent parameters from accelerated life data

In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life-stress assumption that there are multiple nonconstant and stress-dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.     

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.     

一类基于改进Weibull分布模型的 电力电缆寿命评估方法

对电缆的剩余寿命进行评估是电缆寿命管理的关键环节,以往电缆寿命评估的方法中有Arrhenius方法和Weibull分布模型。对这两种方法分别进行分析,特别是确定Arrhenius模型中激活能的计算,以及应用Weibull分布模型对电缆寿命进行评估。最后以实际电缆的状态监测数据,对简化的Arrhenius模型进行仿真,说明所提出的方法是有效的。     

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 new variable control chart under failure‐censored reliability tests for Weibull distribution

In this paper, we propose a new variable control chart under type II or failure‐censored reliability tests by assuming that the lifetime of a part follows the Weibull distribution with fixed and stable shape parameter. The purpose is to monitor the mean and the variance of a Weibull process. In fact, the mean and the variance are related to the scale parameter. The necessary measures are given to calculate the average run length (ARL) for in‐control and shifted processes. The tables of ARLs are presented for various shift constants and specified parameters. A simulation study is given to show the performance of the proposed control chart. The efficiency of the proposed control chart is compared with a control chart based on the conditional expected value under type II censoring. An example is also given for the illustration purpose.     

Non‐normal Capability Indices for the Weibull and Lognormal Distributions

Because the normal process capability indices (PCIs) C_p, C_pu, C_pl, and C_pk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs P_p, P_pu, P_pl, and P_pk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard C_p, C_pu, C_pl, and C_pk if a short‐term variance is analyzed. An application to a set of simulated data is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

飞机可靠性分析中的混合威布尔分布参数估计方法

为更真实地描述飞机系统的失效规律,提高可靠性分析的准确性,利用混合威布尔分布建立了飞机可靠性分析模型.针对所建立的模型中参数估计困难的问题,基于K-S检验思想,以拟合优度最好为优化目标,将参数估计转化为无约束优化模型,建立了混合威布尔分布参数估计方法.将改进粒子群算法用于优化模型的求解,利用粒子群的适应度方差自动调整加速度因子,提高了优化求解效率并降低了陷入局部最优的概率.计算实例表明,该方法的参数估计精度高于其他方法,而且算法简单、易于实现,收敛速度较快,不易陷入局部最优解.     

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.     

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

This paper presents a reliability analysis for electronic devices (ED) with bathtub curve-shaped failure times. An extension of the exponentiated perks distribution (EPD) is proposed for the analysis. The extension of this new distribution is based on the Alpha Power Transformation, so the Alpha Exponentiated Perks Distribution (AEXP) is introduced. The AEXP has three shape parameters and one scale parameter, allowing greater flexibility to represent failure rates in an increasing, decreasing, or bathtub curve form. Some useful properties in the reliability engineering context are presented. AEXP parameters were estimated via the Maximum Likelihood Method. Finally, two case studies focused on ED are used to compare the proposed distribution and other distributions with similar failure rate representation properties. The obtained results show that the AEXP better describes the behavior of ED than the distributions considered in the analysis.     

Weighted least‐squares estimation of the shape parameter of the Weibull distribution

The purpose of this paper is to propose the weighted least‐squares procedure for estimating the shape parameter of the Weibull distribution. Results from simulation studies illustrate the mean‐squared error of the weighted least‐squares estimator is smaller than competing procedures in all cases considered. Copyright © 2001 John Wiley & Sons, Ltd.