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.     

Robustness of asymptotic accelerated life test plans to small‐sample settings

Much of the statistical literature on optimal test planning for accelerated life testing utilize asymptotic methods to derive optimal test plans. While sufficient effort is made to assess the robustness of these test plans to the choice of design parameters and distribution assumptions, there is very little literature on the performance of asymptotic test plans relative to small samples (on the order of 10‐15 samples). An alternative concern is that the asymptotic test plans may not necessarily be the true “optimal” test plan for a given sample size. The purpose of this research is to present exact or “near‐exact” methods for developing test plans and compare the performance of these test plans with corresponding asymptotic test plans in small‐sample settings. The optimal location of design points and sample allocation is determined using each method for lognormal and Weibull lifetime distributions with both complete and Type 1 right‐censored data under two selected acceleration factor models. The investigations reveal that asymptotic test plans tend to corroborate quite well with exact test plans and thus are suitably robust to small‐sample settings in terms of optimal variance.     

Optimal accelerated life tests under a cost constraint with non-uniform stress durations

ABSTRACT

To collect the information about the lifetime distribution of a product, a standard life testing method at normal working conditions is impractical when the product has a substantially long lifespan. Accelerated life testing solves this problem by subjecting the test units at higher stress levels for quicker and more failure data. Due to constrained resources in practice, several decision variables such as the allocation proportions and stress durations must be determined carefully at the design stage in order to run an accelerated life test efficiently. These decision variables directly affect the experimental cost as well as the estimate precision of the parameters of interest. This article investigates these optimal decision variables based on several well-known optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget. A general scale family of distributions is considered for the underlying lifetimes to accommodate different lifetime models at different stress levels for flexible modeling. The constant-stress and step-stress accelerated life tests are then studied in detail with linearly decreasing stress durations as the stress level progresses. Under the identical budget constraint, the efficiencies of these two stress loading schemes are compared using two case studies.     

A Comparison of Accelerated Test Plans to Estimate the Survival Probability at a Design Stress

In a previous paper [3], the authors presented large sample optimum accelerated test plans to estimate the survival probability at a design stress assuming a linear logistic model, i.e. a linear relationship between stress and the log survival odds at that stress. The optimum plans required testing at two accelerated stresses with a larger allocation of units assigned to the lower of the two stresses. In practice, however, it is often desirable to conduct the accelerated tests at more than two stresses and/or use equal or otherwise prespecified allocation. In this paper we compare the large sample variance of each of ten such non-optimum test plans (and also that of testing exclusively at the design stress) with that of the optimum plan under a variety of conditions.     

Planning constant-stress accelerated life tests with multiple stresses based on D-optimal design

With the rapid technological advances, products are becoming more reliable. Then, multistress accelerated life testing (MALT) has been adopted in engineering to obtain failure information in a limited time. In order to make the testing procedure more efficient, it is necessary to better design the test plan. However, to date, relevant research on planning of MALT is limited. Multiple stresses will lead to plenty of stress-level combinations that require too much cost and time to implement. Besides, there may be interactions among multiple stresses, which need more experiments for parameter estimation. To solve these problems, we propose a novel planning method for constant-stress MALT under lognormal distribution using D-optimal design, which can reduce required test points efficiently and deal with second-order effects in models. In ALT, the log-linear model is often used to describe the life-stress relationship. Hence, D-optimal design is adopted in this paper to select test points from the whole test region. Then, optimal unit allocation plans are formulated under V/D-optimality criterion, respectively, where type I and type II censoring are both discussed. A real case of light-emitting device (LED) is presented to compare the proposed approach with other two existing methods. The results show that the proposed method performs better than other two existing methods both in prediction accuracy and estimation precision. Moreover, a sensitivity analysis reveals the robustness of the optimal plans determined by the proposed method.     

基于仿真的竞争失效产品综合应力加速寿命试验优化设计

针对竞争失效产品综合应力加速寿命试验存在试验时间长、费用高、效率低的问题,提出一种基于仿真的竞争失效产品综合应力加速寿命试验优化设计方法。采用Monte-Carlo进行仿真模拟,以正常使用应力下的p阶分位寿命渐进方差估计最小为目标,在各应力组合下试验截尾数大小给定的条件下,以试验应力水平大小作为设计变量,利用MLE理论进行统计分析,建立基于仿真的竞争失效产品综合应力加速寿命试验优化设计模型。通过实例分析表明该方法有效、可行,为电子装备寿命预测的加速试验方案优化设计提供技术支撑。     

Optimal design of a simple step‐stress accelerated life test under progressive type I censoring with nonuniform durations for exponential lifetimes

Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step‐stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D‐optimality, C‐optimality, A‐optimality, and E‐optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion is assessed on the design efficiency.     

Accelerated Reliability Demonstration Testing Design Based on Reliability Allocation of Environmental Stresses

The traditional reliability demonstration testing based on statistical method requires a large number of samples and long testing time, failing to satisfy the demand for short cycle and low cost. This paper proposes a new accelerated approach for determining reliability target of each environment stress, accelerated test profile, and comprehensive acceleration factor for multi‐failure mode product to conduct assembly level accelerated demonstration testing under multiple stresses and levels. By decomposing the product from four levels, namely function, structure, mechanism, and stress, the products' weaknesses can be identified. The main failure modes and sensitive environmental stresses are determined based on environmental profile and FMMEA. In this design, the reliability is apportioned to each actual environmental stress by AHP. And the SSI model is used to establish accelerated stress profile. The overall acceleration factor can be derived from the model of assembly level accelerated testing. Combined with a statistical plan, the accelerated reliability demonstration testing plan and test profile is built. A case example is presented to illustrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Weibull analysis for normal/accelerated and fatigue random vibration test

In this paper, the formula to estimate the sample size n to perform a random vibration test is derived only from the desired reliability (R(t)). Then, the addressed n value is used to design the ISO16750‐3 random vibration test IV for both normal and accelerated conditions. For the normal case, the applied random vibration stress (S) is modeled by using the Weibull stress distribution [W(s)]. Similarly, for the testing time (t), the Weibull time distribution [W(t)] is used to model its random behavior. For the accelerated case, by using the over‐stress factor fitted from the W(t) and W(s) distributions, four accelerated scenarios are formulated with their corresponding testing's profiles. Additionally, from the W(s) analysis, the stress formulation to perform the fatigue and Mohr stress analysis is given. Since the given Weibull/fatigue formulation is general, then the formulas to determine the W(s) parameters, which correspond to any principal stresses values and/or vice versa, are given. Although the application is performed to demonstrate R(t) = 0.97 by testing only n₂ = 6 parts, the guidelines to use the values given in columns n, S, and t of the Weibull analysis table to generate several accelerated testing plans are given.     

Measurement Plan Optimization for Degradation Test Design based on the Bivariate Wiener Process

This article concerns the optimization of measurement plans in the design of bivariate degradation tests for bivariate Wiener processes. After describing an unbalanced measurement scheme for bivariate degradation tests, we derive the likelihood function and provide a method for estimating the model parameters that is based on maximum likelihood and least squares. From the corresponding Fisher information matrix, we deduce an important insight, namely that longer degradation tests and longer intervals between measurements in the test design result in more precise parameter estimates. We introduce a model for optimizing the degradation test measurement plan that incorporates practical constraints and objectives in the test design framework. We also present a search‐based algorithm to identify the optimal test measurement plan that is based on the aforementioned measurement rule. Via a simulation study and a case study involving the Rubidium Atomic Frequency Standard, we demonstrate the characteristics of optimal measurement plans for bivariate degradation test design and show the superiority of longer duration tests involving fewer samples compared to alternative designs that specify testing more samples over shorter periods of time. Copyright © 2013 John Wiley & Sons, Ltd.     

COMPARISONS OF OPTIMAL ACCELERATED TEST PLANS FOR ESTIMATING QUANTILES OF LIFETIME DISTRIBUTION AT THE USE CONDITION

Accelerated life tests (ALTs) and accelerated degradation tests (ADTs) are widely used for the reliability assessment of components or materials. In an ALT, failure times of test units are observed while in an ADT the failure-causing performance characteristic is measured. This article develops optimal ALT and ADT plans for estimating the qth Quantile of the lifetime distribution at the use condition, the latter being an extension of Park and Yum. Then, the two test plans are compared in terms of the asymptotic efficiency in estimating the qth quantile and of the robustness to the mis-specifications of failure probabilities. Computational results show that the ADT provides a more precise estimator than the corresponding ALT, especially when the failure probabilities are small. Concerning the robustness of a test plan to the departures of the guessed failure probabilities from their true values, neither plan completely dominates the other.     

An innovative testing technique for assessing the VHCF response of adhesively bonded joints

In the last few years, the use of adhesive joints for structural applications has rapidly increased and adhesives are more often subject to fatigue loads during their in‐service life. In presence of a rapidly varying load, such as a high‐frequency vibration, adhesively bonded joints may undergo fatigue lives in the Very High Cycle Fatigue (VHCF) region that are significantly larger than those investigated in usual high‐cycle fatigue tests. The present paper proposes an innovative testing technique for performing accelerated fully reversed tension‐compression VHCF tests on adhesive butt‐joints. The procedure for the design of the adherends is described and then experimentally validated. Ultrasonic VHCF tests are finally carried out on a cyanoacrylate butt‐joint up to 10⁹ cycles: experimental results show that the proposed testing equipment permits an effective assessment of the VHCF response of the adhesive in a limited testing time.     

Designing an accelerated degradation experiment by optimizing the estimation of the percentile

Degradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean‐squared error of the estimated 100 th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

基于ADT的电阻型湿度传感器可靠性评估

传统的寿命试验对电子元件可靠性进行评估需较长时间。如何快速、准确获取电子元件的性能指标是工程实践和试验研究迫切需要解决的问题。本文以电阻型湿度传感器为研究对象,基于加速退化试验(ADT)的可靠性评估方法,建立加速模型和退化轨迹,结合最大似然估计和最小二乘法求解加速应力下伪失效寿命分布参数,从而得出正常应力水平下可靠度函数。结果表明,采用ADT能够准确获取湿度传感器的可靠性信息,缩短试验周期,此评估方法同样适用于其它电子元件的可靠性研究,存在广泛的应用价值。     

Optimal Design of Step‐stress Accelerated Degradation Test with Multiple Stresses and Multiple Degradation Measures

Products with high reliability and long lifetimes undergo different types of stresses in use conditions. Often there are multiple performance indicators for products that gradually degrade over time. An accelerated degradation test (ADT) with multiple stresses and multiple degradation measures (MSMDM) may provide a more accurate prediction of the lifetime of these products. However, the ADT requires a moderate sample size, which is not practical for newly developed or costly products with only a few available test specimens on hand. Therefore, in this study, a step‐stress ADT (SSADT) with MSMDM is developed. However, it is a difficult endeavor to design SSADT with MSMDM to predict accurate reliability estimation under several constraints. Previous methods are used only for cases with a single stress or degradation measure, and are not suitable for SSADT with MSMDM. In this paper, an approach of optimal design is proposed for SSADT with MSMDM and its steps for a rubber sealed O‐ring are demonstrated to illustrate its validity. Results of the sensitivity analysis for the optimal test plan indicate robustness when the deviation of model parameters is within 10% of the estimated values. Copyright © 2017 John Wiley & Sons, Ltd.     

A sequential constant‐stress accelerated life testing scheme and its Bayesian inference

In the analysis of accelerated life testing (ALT) data, some stress‐life model is typically used to relate results obtained at stressed conditions to those at use condition. For example, the Arrhenius model has been widely used for accelerated testing involving high temperature. Motivated by the fact that some prior knowledge of particular model parameters is usually available, this paper proposes a sequential constant‐stress ALT scheme and its Bayesian inference. Under this scheme, test at the highest stress is firstly conducted to quickly generate failures. Then, using the proposed Bayesian inference method, information obtained at the highest stress is used to construct prior distributions for data analysis at lower stress levels. In this paper, two frameworks of the Bayesian inference method are presented, namely, the all‐at‐one prior distribution construction and the full sequential prior distribution construction. Assuming Weibull failure times, we (1) derive the closed‐form expression for estimating the smallest extreme value location parameter at each stress level, (2) compare the performance of the proposed Bayesian inference with that of MLE by simulations, and (3) assess the risk of including empirical engineering knowledge into ALT data analysis under the proposed framework. Step‐by‐step illustrations of both frameworks are presented using a real‐life ALT data set. Copyright © 2008 John Wiley & Sons, Ltd.     

A method of assessing the strength of metal surface using film samples on titanium alloy Ti‐1023

The fatigue life of aerospace components depends greatly on the mechanical properties of the finished surface layer. However, no independent strength test of this layer has been reported because of the lack of suitable samples. Therefore, a direct method of assessing the surface tensile strength using film samples with thicknesses of approximately 40 μm is proposed in this paper. The immediate objective of this research is to demonstrate the fundamentals of surface strength testing and prove the feasibility of preparing films by tracking the evolution of the surface integrity. The test results show that layer‐by‐layer grinding and polishing is a feasible method for preparing film samples with sufficient area, controllable thickness, and well‐maintained surface integrity. During the preparation of the film samples, the roughness and micro‐hardness of the test side (the side kept unprepared for testing) are protected, and those of the processed side (the side that is ground and polished) are controlled. The residual stress on both sides is released to zero. The film specimens exhibit regular fracture behaviour in the tensile tests, and their stress–strain curves can be explained as weighted averages of the stress–strain functions of multiple layers.     

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.     

A Bayesian zero‐failure reliability demonstration test of high quality electro‐explosive devices

Usually, for high reliability products the production cost is high and the lifetime is much longer, which may not be observable within a limited time. In this paper, an accelerated experiment is employed in which the lifetime follows an exponential distribution with the failure rate being related to the accelerated factor exponentially. The underlying parameters are also assumed to have the exponential prior distributions. A Bayesian zero‐failure reliability demonstration test is conducted to design forehand the minimum sample size and testing length subject to a certain specified reliability criterion. Probability of passing the test design as well as predictive probability for additional experiments is also derived. Sensitivity analysis of the design is investigated by a simulation study. Copyright © 2009 John Wiley & Sons, Ltd.     

Corrosion fatigue and electrochemical behaviour of steel wires used in bridge cables

In‐service bridge wires often fail prior to the design life subjected to alternating stresses and environmental erosion. In this paper, a novel corrosion fatigue test device, integrating fatigue testing machine and electrochemical accelerated corrosion assemblies, was developed to characterize the corrosion fatigue and electrochemical behaviour of the wires. Using the developed device, corrosion fatigue tests of corroded bridge wires under different corrosion and loading conditions were conducted. Electrochemical characteristics, corrosion fatigue behaviour, failure mechanism, and so forth were investigated according to electrochemical measurements, fracture morphologies and the lifetime of wires. Results evidence the synchronization of corrosion and fatigue and show the accelerated corrosion due to static and fatigue stresses. Additionally, cracking and fracture induced by multiple crack initiation was dominant in corrosion fatigue of corroded wires, and the coexistence of multiple corrosion pits decreased the lifetime significantly.