Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint

By running life tests at higher stress levels than normal operating conditions, accelerated life testing (ALT) quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant‐stress testing, a unit is tested at a fixed stress level until failure or the termination time point of test, whereas step‐stress testing allows the experimenter to gradually increase the stress levels at some prefixed time points during the test. In this work, the optimal k‐level constant‐stress and step‐stress ALTs are compared for the exponential failure data under complete sampling and Type‐I censoring. The objective is to quantify the advantage of using the step‐stress testing relative to the constant‐stress one. Assuming a log‐linear life–stress relationship with the cumulative exposure model for the effect of changing stress in step‐stress testing, the optimal design points are determined under C/D/A‐optimality criteria. The efficiency of step‐stress testing to constant‐stress one is then discussed in terms of the ratio of optimal objective functions based on the information matrix. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013     

Equivalent accelerated life testing plans for log‐location‐scale distributions

Accelerated life testing (ALT) is widely used to determine the failure time distribution of a product and the associated life‐stress relationship in order to predict the product's reliability under normal operating conditions. Many types of stress loadings such as constant‐stress, step‐stress and cyclic‐stress can be utilized when conducting ALT. Extensive research has been conducted on the analysis of ALT data obtained under a specified stress loading. However, the equivalency of ALT experiments involving different stress loadings has not been investigated. In this article, a log‐location‐scale distribution under Type I censoring is considered in planning ALT. An idea is provided for the equivalency of various ALT plans involving different stress loadings. Based on this idea, general equivalent ALT plans and some special types of equivalent ALT plans are explored. For demonstration, a constant‐stress ALT and a ramp‐stress ALT for miniature lamps are presented and their equivalency is investigated. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

Optimal design of accelerated life testing plans for periodical replacement with penalty

Accelerated life testing (ALT), enhanced by optimal test plans, has been widely accepted in practice as a quick approach for estimating the reliability of a product. From the estimation result, preventive maintenance schedules can be determined to ensure the performance of the product under its normal operating conditions. By default, maintenance decision‐making is regarded as the last and least rewarding step. However, sometimes the maintenance schedules, such as preventive maintenance intervals, are predetermined due to customer concerns and/or by various mandatory regulations and rules. Under such circumstances, how to accurately estimate the expenditure (e.g., on maintenance or spare parts management) associated with these maintenance requirements becomes an important issue. A viable solution is to incorporate the maintenance requirements into ALT plans. This paper provides an approach for the optimal design of ALT plans oriented by a mandatory periodical replacement schedule subject to a discounted penalty. The objective is to improve the estimation accuracy of the economic impact of this maintenance requirement. A numerical experiment is provided to demonstrate the approach in practical use. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution

Accelerated life testing (ALT) is commonly used to obtain reliability information about a product in a timely manner. Several stress loading designs have been proposed and recent research interests have emerged concerning the development of equivalent ALT plans. Step‐stress ALT (SSALT) is one of the most commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This article considers two fundamental questions when designing a SSALT and provides formal proofs in answer to each. Namely: (1) can a simple SSALT be designed so that it is equivalent to other stress loading designs? (2) when optimizing a multilevel SSALT, does it degenerate to a simple SSALT plan? The answers to both queries, under certain reasonable model assumptions, are shown to be a qualified YES. In addition, we provide an argument to support the rationale of a common practice in designing a SSALT, that is, setting the higher stress level as high as possible in a SSALT plan. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Reliability inference for field conditions from accelerated degradation testing

Accelerated degradation testing (ADT) is usually conducted under deterministic stresses such as constant‐stress, step‐stress, and cyclic‐stress. Based on ADT data, an ADT model is developed to predict reliability under normal (field) operating conditions. In engineering applications, the “standard” approach for reliability prediction assumes that the normal operating conditions are deterministic or simply uses the mean values of the stresses while ignoring their variability. Such an approach may lead to significant prediction errors. In this paper, we extend an ADT model obtained from constant‐stress ADT experiments to predict field reliability by considering the stress variations. A case study is provided to demonstrate the proposed statistical inference procedure. The accuracy of the procedure is verified by simulation using various distributions of field stresses. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

A general model for accelerated life testing with time‐dependent covariates

This paper introduces a general or “distribution‐free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution‐free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time‐dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time‐dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time‐dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 303–321, 1999     

竞争失效产品恒应力加速寿命试验优化新方法

对加速寿命试验设计优化的相关知识进行研究分析,确定以竞争失效产品恒应力加速寿命试验为应用背景。在对加速寿命试验统计分析深入研究的基础上,通过分析方案要素、约束条件等建立优化目标函数,提出基于模拟退火算法的优化方法和具体实现思路。最后通过实例验证方法的可行性和实用性。     

Optimum step‐stress accelerated life test plans for log‐location‐scale distributions

This article presents new tools and methods for finding optimum step‐stress accelerated life test plans. First, we present an approach to calculate the large‐sample approximate variance of the maximum likelihood estimator of a quantile of the failure time distribution at use conditions from a step‐stress accelerated life test. The approach allows for multistep stress changes and censoring for general log‐location‐scale distributions based on a cumulative exposure model. As an application of this approach, the optimum variance is studied as a function of shape parameter for both Weibull and lognormal distributions. Graphical comparisons among test plans using step‐up, step‐down, and constant‐stress patterns are also presented. The results show that depending on the values of the model parameters and quantile of interest, each of the three test plans can be preferable in terms of optimum variance. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

数据拟合加速寿命试验智能优化设计

加速寿命试验方案的优劣,直接影响着试验的成本、效益和试验结果的准确性,因此有必要对试验方案进行优化设计,寻找最佳应力水平和试样分配比例,使加速寿命试验的结果最准确、代价最小.利用目标函数的连续性,提出一种基于离散数据的拟合方法,将加速寿命试验的优化设计转化为显函数的约束极值求解问题,然后将智能优化算法应用到加速寿命试验...     

A nonparametric approach to accelerated life testing under multiple stresses

Accelerated life testing (ALT) is concerned with subjecting items to a series of stresses at several levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of items under normal levels. A parametric approach to this problem requires two assumptions. First, the lifetime of an item is assumed to have the same distribution under all stress levels, that is, a change of stress level does not change the shape of the life distribution but changes only its scale. Second, a functional relationship is assumed between the parameters of the life distribution and the accelerating stresses. A nonparametric approach, on the other hand, assumes a functional relationship between the life distribution functions at the accelerated and nonaccelerated stress levels without making any assumptions on the forms of the distribution functions. In this paper, we treat the problem nonparametrically. In particular, we extend the methods of Shaked, Zimmer, and Ball [7] and Strelec and Viertl [8] and develop a nonparametric estimation procedure for a version of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We obtain consistent estimates as well as confidence intervals of the parameters of the life distribution under normal stress level and compare our nonparametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using both real life and simulated data. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 629–644, 1998     

Two‐stage component test plans for testing the reliability of a series system

A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i‐th component follows exponential distribution with parameter λ_i. Assuming test costs for the components are different, we develop an efficient algorithm to design a two‐stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λ_i's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two‐stage component test plans are cost effective compared to single‐stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 95–116, 2002; DOI 10.1002/nav.1051     

基于似然比检验的橡胶密封件加速试验机理一致性判别方法

加速退化试验广泛应用于橡胶密封件等长寿命产品的可靠性评估，试验过程中需要将高应力水平下的试验结果外推到正常应力水平。要获得准确的产品可靠性评估结果，需要保证加速应力下的退化失效机理与正常应力下的退化失效机理一致。基于似然比检验原理，提出加速退化试验机理一致性判别方法及流程。针对失效机理一致与失效机理变化两种场合，提出对数线性及非对数线性两类加速模型，并结合混合效应模型描述产品退化过程。利用似然比检验判断加速模型参数是否变化，完成失效机理一致性判别。仿真算例和应用实例表明，该方法能够有效判别橡胶密封件失效机理是否变化，并找到失效机理不变的应力水平边界。     

Development programs for one‐shot systems using multiple‐state design reliability models

Design reliability at the beginning of a product development program is typically low, and development costs can account for a large proportion of total product cost. We consider how to conduct development programs (series of tests and redesigns) for one‐shot systems (which are destroyed at first use or during testing). In rough terms, our aim is to both achieve high final design reliability and spend as little of a fixed budget as possible on development. We employ multiple‐state reliability models. Dynamic programming is used to identify a best test‐and‐redesign strategy and is shown to be presently computationally feasible for at least 5‐state models. Our analysis is flexible enough to allow for the accelerated stress testing needed in the case of ultra‐high reliability requirements, where testing otherwise provides little information on design reliability change. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

指数型产品可靠性验收试验的一种贝叶斯方法

采用贝叶斯方法 ,利用大量的历史数据和工程技术人员的丰富经验确定先验分布 ,制定出验收试验的一种新方案 .按照这一方案 ,在确保产品质量的前提下 ,可大大节省试验时间 ,从而得到十分可观的经济效益 .     

Global planning of accelerated degradation tests based on exponential dispersion degradation models

The accelerated degradation test (ADT) is an efficient tool for assessing the lifetime information of highly reliable products. However, conducting an ADT is very expensive. Therefore, how to conduct a cost-constrained ADT plan is a great challenging issue for reliability analysts. By taking the experimental cost into consideration, this paper proposes a semi-analytical procedure to determine the total sample size, testing stress levels, the measurement frequencies, and the number of measurements (within a degradation path) globally under a class of exponential dispersion degradation models. The proposed method is also extended to determine the global planning of a three-level compromise plan. The advantage of the proposed method not only provides better design insights for conducting an ADT plan, but also provides an efficient algorithm to obtain a cost-constrained ADT plan, compared with conventional optimal plans by grid search algorithms.     

光栅过滤法测试陶瓷磨削表面残余应力

采用表面形貌技术对陶瓷磨削表面残余应力进行测试研究,对表面粗糙度曲线经过数据截取、滤波以及规范化处理后可得到表面挠度曲线,认为,此方法与X射线衍射法相比测试结果较接近,是测试残余应力的有效方法;其数据处理过程是保证测试精度的关键;挠度变化是个渐变的过程。     

引信湿热强化试验技术研究

针对传统引信湿热试验的缺点,以某型引信的电子头组件为研究对象,开展了引信的湿热强化试验技术研究。首先分析了湿热强化应力对缺陷的激发效果,即温度和湿度越高,对缺陷的激发效果越好。在此基础上,设计了湿热强化试验方案,并通过试验,暴露了电子头组件的薄弱环节,为提高其环境适应性奠定了基础,同时体现了湿热强化试验在激发引信潜在缺陷、缩短试验周期和降低试验费用方面的优势。还根据试验的反馈信息,对试验方案进行了优化。     

Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Equity in genetic newborn screening

State‐level newborn screening allows for early treatment of genetic disorders, which can substantially improve health outcomes for newborns. As the cost of genetic testing decreases, it is becoming an essential part of newborn screening. A genetic disorder can be caused by many mutation variants; therefore, an important decision is to determine which variants to search for (ie, the panel design), under a testing budget. The frequency of variants that cause a disorder and the incidence of the disorder vary by racial/ethnic group. Consequently, it is important to consider equity issues in panel design, so as to reduce disparities among different groups. We study the panel design problem using cystic fibrosis (CF) as a model disorder, considering the trade‐offs between equity and accuracy, under a limited budget. Most states use a genetic test in their CF screening protocol, but panel designs vary, and, due to cost, no state's panel includes all CF‐causing variants. We develop models that design equitable genetic testing panels, and compare them with panels that maximize sensitivity in the general population. Our case study, based on realistic CF data, highlights the value of equitable panels and provides important insight for newborn screening practices.