A Bayesian Predictive Analysis of Step‐Stress Accelerated Tests in Gamma Degradation‐Based Processes

Degradation modeling might be an alternative to the conventional life test in reliability assessment for high quality products. This paper develops a Bayesian approach to the step‐stress accelerated degradation test. Reliability inference of the population is made based on the posterior distribution of the underlying parameters with the aid of Markov chain Monte Carlo method. Further sequential reliability inference on individual product under normal condition is also proposed. Simulation study and an illustrative example are presented to show the appropriateness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust Estimation for Weibull Distribution in Partially Accelerated Life Tests with Early Failures

Maximum likelihood estimation (MLE) is a frequently used method for estimating distribution parameters in constant stress partially accelerated life tests (CS‐PALTs). However, using the MLE to estimate the parameters for a Weibull distribution may be problematic in CS‐PALTs. First, the equation for the shape parameter estimator derived from the log‐likelihood function is difficult to solve for the occurrence of nonlinear equations. Second, the sample size is typically not large in life tests. The MLE, a typical large‐sample inference method, may be unsuitable. Test items unsuitable for stress conditions may become early failures, which have extremely short lifetimes. The early failures may cause parameter estimate bias. For addressing early failures in the Weibull distribution in CS‐PALTs, we propose an M‐estimation method based on a Weibull Probability Plot (WPP) framework, which leads a closed‐form expression for the shape parameter estimator. We conducted a simulation study to compare the M‐estimation method with the MLE method. The results show that, with early‐failure samples, the M‐estimation method performs better than the MLE does. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress, such as pressure, temperature, vibration, voltage, or load to induce early failures. In this paper, a step stress partially accelerated life test (SS-PALT) is regarded under the progressive type-II censored data with random removals. The removals from the test are considered to have the binomial distribution. The life times of the testing items are assumed to follow length-biased weighted Lomax distribution. The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax. The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix. The Bayesian estimators cannot be obtained in the explicit form, so the Markov chain Monte Carlo method is employed to address this problem, which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters. The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations. In addition, to compare the performance of the considered confidence intervals for different parameter values and sample sizes. The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter, for different sample sizes, observed failures, and censoring schemes, in most cases. Also, the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes, observed failures, and censoring schemes, in most cases. Further performance comparison is conducted by the experiments with real data.     

Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis

Accelerated life testing (ALT) design is usually performed based on assumptions of life distributions, stress–life relationship, and empirical reliability models. Time‐dependent reliability analysis on the other hand seeks to predict product and system life distribution based on physics‐informed simulation models. This paper proposes an ALT design framework that takes advantages of both types of analyses. For a given testing plan, the corresponding life distributions under different stress levels are estimated based on time‐dependent reliability analysis. Because both aleatory and epistemic uncertainty sources are involved in the reliability analysis, ALT data is used in this paper to update the epistemic uncertainty using Bayesian statistics. The variance of reliability estimation at the nominal stress level is then estimated based on the updated time‐dependent reliability analysis model. A design optimization model is formulated to minimize the overall expected testing cost with constraint on confidence of variance of the reliability estimate. Computational effort for solving the optimization model is minimized in three directions: (i) efficient time‐dependent reliability analysis method; (ii) a surrogate model is constructed for time‐dependent reliability under different stress levels; and (iii) the ALT design optimization model is decoupled into a deterministic design optimization model and a probabilistic analysis model. A cantilever beam and a helicopter rotor hub are used to demonstrate the proposed method. The results show the effectiveness of the proposed ALT design optimization model. Copyright © 2015 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.     

Utilizing Accelerated Degradation and Field Data for Life Prediction of Highly Reliable Products

For newly developed, highly reliable, and long‐lifespan products, it is quite difficult to implement effective remaining useful life (RUL) prediction in the early usage under limited time cost. However, accelerated degradation testing (ADT) is generally used for lifetime evaluation for such products with harsher test conditions and shorter test time in the late research and development phase. Thus, in this paper, we propose a life prediction framework to integrate the information from ADT to conduct field RUL prediction for highly reliable products. Because ADT belongs to reliability testing used for inferring the population information from the selected test samples, we at first present the modified Wiener process (MWP) model. Different from traditional methods that embody both the random variability and unit‐to‐unit variability into the diffusion coefficient, the proposed method describes them separately in ADT analysis. Then, the MWP model from ADT is used as a prior for field RUL prediction of the target product during which the strong tracking filtering algorithm is introduced for updating the hidden state and computing the RUL prediction results when the new monitoring data are available. Because of the complexity of the MWP model, the Markov chain Monte Carlo method is provided to estimate the unknown parameters. Finally, the simulation study and the light‐emitting diode application verify the effectiveness of the proposed framework that can achieve reasonable life prediction results for highly reliable products for both linear and nonlinear scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability Estimation for Accelerated Life Tests Based on a Cox Proportional Hazard Model with Error Effect

In this paper, a Cox proportional hazard model with error effect applied on the study of an accelerated life test is investigated. Statistical inference under Bayesian methods by using the Markov chain Monte Carlo techniques is performed in order to estimate the parameters involved in the model and predict reliability in an accelerated life testing. The proposed model is applied to the analysis of the knock sensor failure time data in which some observations in the data are censored. The failure times at a constant stress level are assumed to be from a Weibull distribution. The analysis of the failure time data from an accelerated life test is used for the posterior estimation of parameters and prediction of the reliability function as well as the comparisons with the classical results from the maximum likelihood estimation. Copyright © 2017 John Wiley & Sons, Ltd.     

用加速寿命试验法研究瓦楞纸箱寿命初探

选用空气相对湿度H和垂直载荷G为加速应力，用加速寿命试验法对瓦楞纸箱寿命进行研究，建立了瓦楞纸箱双应力加速方程，并计算出正常工作应力下瓦楞纸箱的平均寿命及可靠度。     

Integrated Approach for Field Reliability Prediction Based on Accelerated Life Testing

ABSTRACT

To predict field reliability using analytical modeling, several important reliability activities should be conducted, including failure mode and effect analysis, stress and usage condition analysis, physics of failure analysis, accelerated life testing and modeling, and cumulative damage modeling if needed. With all of the mentioned activities and results, the field reliability confidence limit can be predicted at a certain confidence level, if a modeling framework can be established. This article builds such an integrated process and comprehensive modeling framework, especially with cumulative damage rules when the certain field stresses are random processes. An engineering product is provided as an application to illustrate the effectiveness of proposed method.     

竞争失效产品加速寿命试验的非参数统计方法

研究了竞争失效产品恒定应力加速寿命试验（简称恒加试验）的非参数统计方法，给出了恒加试验的矩估计的最小二乘估计，并研究了它们的优良性。     

Statistical Inference on Constant Stress Accelerated Life Tests under Generalized Gamma Lifetime Distributions

We will discuss the reliability analysis of the constant stress accelerated life tests when a parameter in the generalized gamma lifetime distribution is linear in the stress level. Statistical inference on the estimation of the underlying model parameters as well as the mean time to failure and the reliability function will be addressed on the basis of the maximum likelihood approach. Large sample theory will be derived for the goodness of fit of the data. Some simulation study and an illustrative real example will be presented to show the appropriateness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Bayesian Analysis of Step‐Stress Accelerated Life Test with Exponential Distribution

In this article, we propose a general Bayesian inference approach to the step‐stress accelerated life test with type II censoring. We assume that the failure times at each stress level are exponentially distributed and the test units are tested in an increasing order of stress levels. We formulate the prior distribution of the parameters of life‐stress function and integrate the engineering knowledge of product failure rate and acceleration factor into the prior. The posterior distribution and the point estimates for the parameters of interest are provided. Through the Markov chain Monte Carlo technique, we demonstrate a nonconjugate prior case using an industrial example. It is shown that with the Bayesian approach, the statistical precision of parameter estimation is improved and, consequently, the required number of failures could be reduced. Copyright © 2011 John Wiley & Sons, Ltd.     

An approach that can quickly assess product reliability

One of the ways to determine the inherent reliability of a design is to test it under controlled environments based on the product usage that is understood by the development requirements. This can be accomplished by performing a reliability growth test on the product. A testing approach can be developed that enhances the product reliability and reduces the production testing cycle. Research performed to date points to the fact that this proposed methodology may not exist, and is the focus of continued research to refine the development of an approach to fill this gap. The combining of multiple testing approaches in order to ensure that the reliability requirement is met or exceeded while at the same time having the capability to reduce the testing cycle time when required due to schedule and cost constraints has not been addressed in the open literature till date. The methodology is to utilize a combination of multiple testing approaches to accomplish this task by exploring complementary testing ideas from various technologies that have been utilized previously with documented success. This approach demonstrated that component‐level testing reduced the product‐level failures by greater than 80% while at the same time reducing the schedule to complete all testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Bridging the Gap between Nonliving Matter and Cellular Life

A cell, the fundamental unit of life, contains the requisite blueprint information necessary to survive and to build tissues, organs, and systems, eventually forming a fully functional living creature. A slight structural alteration can result in data misprinting, throwing the entire life process off balance. Advances in synthetic biology and cell engineering enable the predictable redesign of biological systems to perform novel functions. Individual functions and fundamental processes at the core of the biology of cells can be investigated by employing a synthetically constrained micro or nanoreactor. However, constructing a life-like structure from nonliving building blocks remains a considerable challenge. Chemical compartments, cascade signaling, energy generation, growth, replication, and adaptation within micro or nanoreactors must be comparable with their biological counterparts. Although these reactors currently lack the power and behavioral sophistication of their biological equivalents, their interface with biological systems enables the development of hybrid solutions for real-world applications, such as therapeutic agents, biosensors, innovative materials, and biochemical microreactors. This review discusses the latest advances in cell membrane-engineered micro or nanoreactors, as well as the limitations associated with high-throughput preparation methods and biological applications for the real-time modulation of complex pathological states.     

An inference method for temperature step‐stress accelerated life testing

This paper deals with step‐stress accelerated life testing. It presents a practical method to analyse temperature step‐stress accelerated life test data. The Arrhenius model is considered. Activation energy and failure rate under operational conditions are estimated both graphically and using maximum likelihood. Applications on simulated data and on real data are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Different Estimation Methods for Constant Stress Accelerated Life Test under the Family of the Exponentiated Distributions

The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain information on the reliability of product components and materials under operating conditions in a much shorter time. One of the main purposes of applying ALT is to estimate the failure time functions and reliability performance under normal conditions. This paper concentrates on the estimation procedures under ALT and how to select the best estimation method that gives accurate estimates for the reliability function. For this purpose, different estimation methods are used, such as maximum likelihood, least squares (LS), weighted LS, and probability weighted moment. Moreover, the reliability function under usual conditions is predicted. The estimation procedures are applied under the family of the exponentiated distributions in general, and for the exponentiated inverted Weibull (EIW) as a special case. Numerical analysis including simulated data and a real life data set is conducted to compare the performances between these four methods. It is found that the ML method gives the best results among other estimation methods. Finally, a comparison between the EIW and the Inverted Weibull (IW) distributions based on a real life data set is made using a likelihood ratio test. It is observed that the EIW distribution can provide better fitting than the IW in case of ALT. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of Field Stress Variance on Test to Field Correlation in Accelerated Reliability Demonstration Testing

This paper discusses the effect of field stress variance on the value of demonstrated reliability. In many cases, the acceleration factor for a reliability demonstration test is calculated based on a high percentile field stress level, typically corresponding to severe user or environmental conditions. In those cases, the actual field reliability for the population will be higher than that demonstrated by the test. This paper presents a mathematical approach to estimating ‘true’ field reliability based on the acceleration model and stress variable distribution over the product field population. This method is illustrated by an example of automotive electronics reliability demonstration testing and has a wide range of practical applications. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayes approach to reliability prediction utilizing data from accelerated life tests and field failure observations

A Bayes approach is proposed to improve product reliability prediction by integrating failure information from both the field performance data and the accelerated life testing data. It is found that a product's field failure characteristic may not be directly extrapolated from the accelerated life testing results because of the variation of field use condition that cannot be replicated in the lab‐test environment. A calibration factor is introduced to model the effect of uncertainty of field stress on product lifetime. It is useful when the field performance of a new product needs to be inferred from its accelerated life test results and this product will be used in the same environment where the field failure data of older products are available. The proposed Bayes approach provides a proper mechanism of fusing information from various sources. The statistical inference procedure is carried out through the Markov chain Monte Carlo method. An example of an electronic device is provided to illustrate the use of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimum step‐stress for temperature accelerated life testing

Step‐stress accelerated life testing is a design strategy where the stress is modified several times during the test. In this work we address the problem of designing such a test. We focus on temperature accelerated life testing and we address the problems of setting the step duration and the stress levels. Assuming an Arrhenius model, maximum likelihood estimates of the parameters are computed. Relying on the properties of these estimators we compare different criteria for assessing the optimality of the plans produced. Some tables are presented to illustrate the method. For a fixed number of steps and a set of temperatures, a table of optimal length steps can be computed. For fixed step lengths, sets of temperatures leading to optimal plans are also available. Thus, this work provides useful tools to help engineers make decisions in testing strategy. Copyright © 2007 John Wiley & Sons, Ltd.