Step-stress Accelerated Degradation Test Research Articles

Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

Optimal step-stress accelerated degradation test plans for inverse Gaussian process based on proportional degradation rate model

ABSTRACTThe purpose of this paper is to address the optimal design of the step-stress accelerated degradation test (SSADT) issue when the degradation process of a product follows the inverse Gaussian (IG) process. For this design problem, an important task is to construct a link model to connect the degradation magnitudes at different stress levels. In this paper, a proportional degradation rate model is proposed to link the degradation paths of the SSADT with stress levels, in which the average degradation rate is proportional to an exponential function of the stress level. Two optimization problems about the asymptotic variances of the lifetime characteristics' estimators are investigated. The optimal settings including sample size, measurement frequency and the number of measurements for each stress level are determined by minimizing the two objective functions within a given budget constraint. As an example, the sliding metal wear data are used to illustrate the proposed model.

Photometric and Colorimetric Assessment of LED Chip Scale Packages by Using a Step-Stress Accelerated Degradation Test (SSADT) Method.

By solving the problem of very long test time on reliability qualification for Light-emitting Diode (LED) products, the accelerated degradation test with a thermal overstress at a proper range is regarded as a promising and effective approach. For a comprehensive survey of the application of step-stress accelerated degradation test (SSADT) in LEDs, the thermal, photometric, and colorimetric properties of two types of LED chip scale packages (CSPs), i.e., 4000 °K and 5000 °K samples each of which was driven by two different levels of currents (i.e., 120 mA and 350 mA, respectively), were investigated under an increasing temperature from 55 °C to 150 °C and a systemic study of driving current effect on the SSADT results were also reported in this paper. During SSADT, junction temperatures of the test samples have a positive relationship with their driving currents. However, the temperature-voltage curve, which represents the thermal resistance property of the test samples, does not show significant variance as long as the driving current is no more than the sample’s rated current. But when the test sample is tested under an overdrive current, its temperature-voltage curve is observed as obviously shifted to the left when compared to that before SSADT. Similar overdrive current affected the degradation scenario is also found in the attenuation of Spectral Power Distributions (SPDs) of the test samples. As used in the reliability qualification, SSADT provides explicit scenes on color shift and correlated color temperature (CCT) depreciation of the test samples, but not on lumen maintenance depreciation. It is also proved that the varying rates of the color shift and CCT depreciation failures can be effectively accelerated with an increase of the driving current, for instance, from 120 mA to 350 mA. For these reasons, SSADT is considered as a suitable accelerated test method for qualifying these two failure modes of LED CSPs.

Consistency analysis of degradation mechanism in step-stress accelerated degradation testing

Consistency analysis of degradation mechanism in step-stress accelerated degradation testing

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 General Accelerated Degradation Model Based on the Wiener Process.

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

Optimal design of step-stress accelerated degradation tests based on the Wiener degradation process

Statistically optimal and compromise step-stress accelerated degradation test (ADT) plans are developed under the assumption that the degradation characteristic follows a Wiener process. Compromise plans are provided for the case where the experimenter wants to check the validity of the assumed stress-parameter relationship. Two and three step-stress levels are respectively considered in the statistically optimal and compromise ADT plans. For both types of plans, step-stress level(s) and stress level change time(s) are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized. A distinctive feature of the proposed ADT plans is that the stress level can be changed not only at a measurement time but also between two successive measurement times. This feature allows a more general formulation of the two-step-stress ADT planning problem and more flexible three-step-stress compromise ADT plans. Computational results show that in a statistically optimal ADT plan (with two-step-stress levels) the stress change time always coincides with a measurement time. On the other hand, for a compromise plan the stress level sometimes needs to be changed between two successive measurement times to satisfy certain planning requirements. Using an example, the above planning methods are illustrated, the sensitivity of a plan with respect to the uncertainty in the pre-estimate of a model parameter is assessed, and the proposed step-stress ADTs are compared with the constant-stress ADTs and conventional step-stress ADTs in terms of the sample size and/or total testing time.

Lumen degradation modeling of white-light LEDs in step stress accelerated degradation test

In this paper, lumen degradation is described by using a modified Brownian motion process for mid-power white-light LED packages, which were aged under step stress accelerated degradation test (SSADT). First, a SSADT model has been established based on the theory of equivalent accumulative damage. Then, a method was proposed to improve the accuracy of the parameter estimation by carefully modifying the estimator, which was proposed in the previous research. Experimental data show that parameters estimated by using SSADT model are very close to those estimated by using constant stress accelerated degradation test (CSADT) model, indicating the feasibility of the SSADT model. The experiment also indicates that SSADT can be used as an alternative to CSADT, as it enables comparable estimation accuracy, while using less testing time, a smaller sample size and less test capacity.

Planning of step-stress accelerated degradation test based on the inverse Gaussian process

The step-stress accelerated degradation test (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable or expensive product. Some efficient SSADT plans have been proposed when the underlying degradation follows the Wiener process or Gamma process. However, how to design an efficient SSADT plan for the inverse Gaussian (IG) process is still a problem to be solved. The aim of this paper is to provide an optimal SSADT plan for the IG degradation process. A cumulative exposure model for the SSADT is adopted, in which the product degradation path depends only on the current stress level and the degradation accumulated, and has nothing to do with the way of accumulation. Under the constraint of the total experimental budget, some design variables are optimized by minimizing the asymptotic variance of the estimated p-quantile of the lifetime distribution of the product. Finally, we use the proposed method to deal with the optimal SSADT design for a type of electrical connector based on a set of stress relaxation data. The sensitivity and stability of the SSADT plan are studied, and we find that the optimal test plan is quite robust for a moderate departure from the values of the parameters.

Determining the thermal stress limit of LED lamps using highly accelerated decay testing

Highly accelerated decay testing (HADT) based on the subsystem isolation method for light-emitting diode (LED) lamps is proposed. The proposed test identifies the desired thermal stress limit (TSL) in a given humidity stress for LED light engine subsystems. In HADT, a monitoring procedure for the in situ pseudo-junction temperature (Tpj) of LED lamps and a step-fitting analysis procedure for the monitored parameters are suggested to detect abnormal thermal stress levels. The obtained TSL is applied to step-stress accelerated degradation testing (SSADT) to verify the uniform decay mechanisms at various stress levels. Results show that the goodness-of-step fit analysis of the monitored parameters effectively identifies the abnormal thermal stress levels. Consequently, the TSL of LED light engines can be clearly observed through the in situ Tpj and optical parameters monitored in HADT. The application study shows that SSADT rapidly and effectively accelerates the decay process of LED lamps, and the tested samples undergo uniform decay mechanisms at three reasonable stresses, which are selected based on the obtained TSL. The proposed HADT has significant potential use in the qualification specification of LED lamps.

Reliability Estimation from Linear Degradation and Failure Time Data With Competing Risks Under a Step-Stress Accelerated Degradation Test

The accelerated degradation test (ADT) has become critical for product reliability assessment. In performing the ADT for newly developed products, a constant-stress ADT may be impractical or sometimes impossible where the available size of testing units and the testing duration are heavily bounded to meet the short development period of the products. As an alternative, a step-stress accelerated degradation test (SSADT) can be a useful tool for satisfying the test limitation, and for making up for uncertainty in selecting appropriate levels of stress. Occasionally, the elevated stress under SSADT not only accelerates the performance degradation of products, but it may also expedite traumatic failures. This paper proposes a modeling approach to simultaneously analyze linear degradation data and traumatic failures with competing risks in an SSADT experiment. Under the modeling approach, a cumulative exposure model is considered. The failure rate corresponding to each failure mode is described as a function of the degradation level at the moment of failure. No parametric assumptions are made regarding the failure-time distribution to extend the proposed method to more general cases. We derive maximum likelihood estimates of the model parameters, then estimate failure rates and product reliability based on the degradation level to failure. Asymptotic properties of the maximum likelihood estimates are also discussed. The proposed model is applied to accelerated degradation data from plastic substrate active matrix light-emitting diodes (AMOLEDs), along with sensitivity analysis.

Step-stress accelerated testing of high-power LED lamps based on subsystem isolation method

The lifetimes of high-power light-emitting diode (LED) lamps are investigated by step-stress accelerated test. The entire lamp is divided into three subsystems, namely, the LED light source, the driver, and the mechanical fixture. Step-stress accelerated tests are conducted on the LED light source only, which is placed in a thermal chamber and connected to other subsystems outside the aging furnace. Thus, the highest possible stress level can be reached for the LED light source. The reliability characteristics of the LED light source are analyzed based on the step-stress accelerated degradation test model. The fault tree and Monte Carlo algorithm are used to deduce the reliability of the entire LED lamp. The case study shows that the tested samples underwent similar degradation mechanisms under three reasonable stress levels and that the proposed procedure is fast and effective in accelerating the decay process of LED lamps. The predicted LED lamp lifetime is close to the value specified by the LED lamp manufacturer. The proposed subsystem isolation method can overcome the obstacle resulting from the significant difference between the breakdown stress limits of each subsystem.

Bayesian optimal design of step stress accelerated degradation testing

This study presents a Bayesian methodology for designing step stress accelerated degradation testing (SSADT) and its application to batteries. First, the simulation-based Bayesian design framework for SSADT is presented. Then, by considering historical data, specific optimal objectives oriented Kullback-Leibler (KL) divergence is established. A numerical example is discussed to illustrate the design approach. It is assumed that the degradation model (or process) follows a drift Brownian motion; the acceleration model follows Arrhenius equation; and the corresponding parameters follow normal and Gamma prior distributions. Using the Markov Chain Monte Carlo (MCMC) method and WinBUGS software, the comparison shows that KL divergence is better than quadratic loss for optimal criteria. Further, the effect of simulation outliers on the optimization plan is analyzed and the preferred surface fitting algorithm is chosen. At the end of the paper, a NASA lithium-ion battery dataset is used as historical information and the KL divergence oriented Bayesian design is compared with maximum likelihood theory oriented locally optimal design. The results show that the proposed method can provide a much better testing plan for this engineering application.

Optimum step-stressaccelerateddegradationtestfor Wiener degradationprocessunderconstraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.

Step-stress accelerated degradation test modeling and statistical analysis methods

In order to get a rapid assessment on the storage reliability of high-reliable and long-life products within the storage period, accelerated degradation test data with a large amount of reliability information of product is adopted. Conducting a constant-stress accelerated degradation test(CSADT) is generally very costly as it requires a large sample size and long time for test. To overcome this problem, it is necessary to carry out research on modeling and statistical analysis methods of step-stress accelerated degradation test (SSADT). Taking electrical connectors as the object, a research is conducted on statistical model and assessment method for SSADT. On the basis of mixed-effect degradation path model, the statistical model of SSADT for electrical connectors is presented, the maximum likelihood method for SSADT data based on mixed-effect degradation model is proposed. SSADT accelerated by temperature stress is conducted to Y11X-1419 type of electrical connectors, and the storage reliability is assessed with the SSADT data. Compared with the result obtained from accelerated life test, the reliability estimation of 32-year storage period for electrical connectors obtained from SSADT data only have a difference of 0.869%, which validates the accuracy of the degradation model and the feasibility of the test data statistic analysis method put forward.

Reliability Estimation based on Step-Stress Accelerated Degradation Testing by Unequal Interval Time Series Analysis

This paper proposes a reliability estimation method based on Step-Stress Accelerated Degradation Testing (SSADT) data analysis using unequal interval time series analysis. A Multi-Regression Time Varying Auto-Regressive (MRTVAR) degradation time series model is proposed. Product SSADT data are treated as unequal interval composite time series and described using MRTVAR time series model and utilized to predict long-term trend of degradation. By using the suggested method, product reliability is obtained. An example is presented as a verification of the modeling technique and estimation method. A reasonable estimation of lifetime and reliability of the product is obtained by employing the present method. DOI: http://dx.doi.org/10.11591/telkomnika.v11i10.3402

Optimal Design for Step-Stress Accelerated Degradation Test with Multiple Performance Characteristics Based on Gamma Processes

Step-stress accelerated degradation test (SSADT) plays an important role in assessing the lifetime distribution of highly reliable products under normal operating conditions when there are not enough test units available for testing purposes. Recently, the optimal SSADT plans are presented based on an underlying assumption that there is only one performance characteristic. However, many highly reliable products usually have complex structure, with their reliability being evaluated by two or more performance characteristics. At the same time, the degradation of these performance characteristics would be always positive and strictly increasing. In such a case, the gamma process is usually considered as a degradation process due to its independent and nonnegative increments properties. Therefore, it is of great interest to design an efficient SSADT plan for the products with multiple performance characteristics based on gamma processes. In this work, we first introduce reliability model of the degradation products with two performance characteristics based on gamma processes, and then present the corresponding SSADT model. Next, under the constraint of total experimental cost, the optimal settings such as sample size, measurement times, and measurement frequency are obtained by minimizing the asymptotic variance of the estimated 100 qth percentile of the product’s lifetime distribution. Finally, a numerical example is given to illustrate the proposed procedure.

A Reliability Model of Concentrator Solar Receivers

The degradation mechanism of GaInP/GaInAs/Ge triple-junction solar cells without coating with any protective film was analyzed. After the step stress accelerated degradation test (SSADT) was performed on the solar cells under the sequential conditions of 90 °C for 25 h, 110 °C for 30 h, 130 °C for 30 h, and 150 °C for 50 h, the degradation of dark and light current vs voltage (I–V) characteristics was observed. It is supposed that the recombination current in the depletion region at the chip perimeter of solar cells is the most important degradation mechanism for GaInP/GaInAs/Ge triple-junction solar cells as well as the decreases in open-circuit voltage (VOC), fill factor (FF), and energy efficiency (η).

Reliability demonstration based on accelerated degradation testing for unknown model parameters

Conventional reliability demonstration tests are becoming increasingly difficult to apply for high-reliability and long-lifetime products owing to the excessive test duration, which conflicts with the marketplace demands for decreased development time. Accelerated degradation testing has been strongly recommended to reduce test time, but few studies employ this method for reliability demonstrations. In this article, a test methodology based on accelerated degradation testing is developed to demonstrate the reliability target for the case in which the model parameters for the test plan design are unknown. In the proposed procedure, step-stress accelerated degradation testing is employed as a preliminary test to estimate the model parameters. The data from step-stress accelerated degradation testing are converted based on equivalent degradation criterion and then used to make decisions by the method of two steps accelerated reliability demonstration test. If there are not enough converted data to make a decision, an accelerated degradation testing as a complementary test is conducted to complete the demonstration according to the estimates of the model parameters from the preliminary test; the two steps accelerated reliability demonstration test method is applied. The proposed methodology incorporates step-stress accelerated degradation testing with two steps accelerated reliability demonstration test to permit the test duration to be reduced as much as possible. It is useful to demonstrate a high-reliability target at long mission times within a feasible test duration when the design parameters are unknown.

Multiple-Steps Step-Stress Accelerated Degradation Modeling Based on Wiener and Gamma Processes

During the step-stress accelerated degradation test (SSADT) experiment, the operator usually elevates the stress level at a predetermined time-point for all tested products that had not failed. This time-point is determined by the experience of the operator and the test is carried on until the performance degradation value of the product crosses the threshold value. In fact, this mode only works when a lot of products have been used in the experiment. But in the SSADT experiment, the number of products is relatively few, and so the test control to the products should be done more carefully. Considering the differences in products, we think the time-point of elevating stress level varies randomly from product-to-product. We consider a situation in which when the degradation value crosses a pre-specified value, the stress level is elevated. Under the circumstances, the time at which the degradation path crosses the pre-specified value is uncertain, and so we may regard it as a random variable. We discuss multiple-steps step-stress accelerated degradation models based on Wiener and gamma processes, respectively, and we apply the Bayesian Markov chain Monte Carlo (MCMC) method for such analytically intractable models to obtain the maximum likelihood estimates (MLEs) efficiently and present some computational results obtained from our implementation.