Constant-stress Accelerated Degradation Test Research Articles

Residual Life Prediction of Low-Voltage Circuit Breaker Thermal Trip Based on the Wiener Process

A low-voltage circuit breaker thermal trip plays a role in power systems, including opening and closing, control, protection, and more. Their reliability directly affects the security and stability of the power distribution system. The Wiener process model is established according to the accelerated degradation data of thermal trips, and remaining life prediction is carried out. In this paper, firstly, the constant stress accelerated degradation test is carried out on a thermal trip with temperature as the accelerated stress and specific thermal deflection as the degradation eigenquantity to characterise the degradation trajectory according to the degradation data and analyse the degradation law; then, it is verified by the test of normal distribution that the degradation data of the thermal trip conform to the Wiener process. The Wiener process, using the great likelihood estimation method to estimate the parameters of the remaining life, calculates the remaining life probability density function and reliability function under different temperature stresses and obtains the remaining life of the thermal trip under each accelerated stress conditions; finally, the remaining life of the thermal trip at the initial moment is taken as the pseudo-failure life, and the Arrhenius accelerated model is utilised to launch the external thermal trip under normal stress. Finally, the Arrhenius acceleration model is used to extrapolate the lifespan of the thermal trip under normal stress.

Optimal design of constant‐stress accelerated degradation tests based on the Wiener process with manufacturing batches heterogeneity and individual differences

AbstractThe use of Constant‐stress accelerated degradation tests (CSADT) modeling is an effective way to assess the reliability of products. However, when conducting reliability experiments, the data collected may come from various sources such as different manufacturing batches, equipment, and operators. This can result in reduced accuracy of the test evaluations. In this research paper, we propose optimal designs for the Wiener constant‐stress accelerated degradation model that take into account the heterogeneity of manufacturing batches and individual differences. Our goal is to minimize the variability of the mean time to failure (MTTF) while working within a specified budget, test time, and available test units. To achieve this, we utilize particle swarm optimization (PSO) to find the best solution based on a complex objective function. We also compare our model with others using degradation data from LEDs, showing that our model has a better goodness‐of‐fit. Finally, we present examples of optimal CSADT plans under different constraints and conduct sensitivity analysis.

Performance degradation and reliability analysis of a MEMS flow sensor with accelerated degradation testing

In this article, we research the performance degradation of a MEMS flow sensor with accelerated degradation testing (ADT). The degradation of temperature stress (Ts) on sensor is studied. Based on the performance in the aging test, resistance degradation ∆R is selected as a more suitable degradation characteristic parameter. Furthermore, the degradation process of the characteristic parameter results from resistivity decreases, in which Ts leads to stress relief within the bulk of the resistor. By implementing the Constant-stress accelerated degradation test (CSADT), we estimate the lifetime of this MEMS flow sensor based on the Arrhenius model. The calculated lifetime is 6.833 years for the 120°C group, 3.942 years for the150°C group, and 2.492 years for the180°C group. In addition, using statistics analysis, the Weibull distribution (WD) is proved to be the better mode for the MEMS flow sensor acceleration life with the Anderson-Darling (AD) being 235.910. The scale and shape of WD was evaluation. On the other hand, to verify the rationality of the distribution, the Standard residual error method and the Cox-Snell residual error method have been used separately, to perform the Goodness-of-fit tests. The AD value of Standard residual error and Cox-Snell residual error is 3.476. It proves that the selected life distribution model of this MEMS flow sensor is befitting. Finally, in this research the CSADT results are original and novelty. The lifetime distribution results reveal that considering the Goodness-of-fit tests can significantly improve the accuracy of reliability analysis of this MEMS flow sensor. Based on those results, a reliability method for this MEMS flow sensor is established.

Reliability assessment of permanent magnet brake based on accelerated bivariate Wiener degradation process.

Permanent magnet brake (PMB) is a safe and effective braking mechanism used to stop and hold the load in place. Due to its complex structure and high reliability, assessing the reliability of PMB remains a challenge. The main difficulty lies in that there are several performance indicators reflecting the health state of PMB, and they are correlated with each other. In order to assess the reliability of PMB more accurately, a constant stress accelerated degradation test (ADT) is carried out to collect degradation data of two main performance indicators in PMB. An accelerated bivariate Wiener degradation model is proposed to analyse the ADT data. In the proposed model, the relationship between degradation rate and stress levels is described by Arrhenius model, and a common random effect is introduced to describe the unit-to-unit variation and correlation between the two performance indicators. The Markov Chain Monte Carlo (MCMC) algorithm is performed to obtain the point and interval estimates of the model parameters. Finally, the proposed model and method are applied to analyse the accelerated degradation data of PMB, and the results show that the reliability of PMB at the used condition can be quantified quite well.

A life extrapolation model using accelerated equivalent luminance and its application

Aiming at predicting the life of vacuum fluorescent display (VFD) accurately, four groups of constant-stress accelerated degradation tests (ADTs) were conducted, and the life extrapolation model of accelerated equivalent luminance (LEMAEL) based on each test sample was proposed. In this model, firstly, Weibull function was employed to fit luminance degradation data of each sample at each stress. Secondly, Logistic function was determined by Anderson-Darling test to respectively describe the distributions of shape and scale parameters, and the degradation formula of accelerated equivalent luminance was obtained to estimate accelerated life. Finally, Power function was selected by comparing determination coefficients to fit the data points formed by accelerated life and stress, and thereby VFD life was extrapolated. The results indicate that the collected test data of each sample objectively reflect VFD luminance characteristics; the degradation formula intuitively exhibits the luminance variation law at each accelerated stress, and Power function accurately reveals the relationship between life and stress; LEMAEL is characterized by high precision and large amount of data information, which not only actualizes the accurate life estimation for light-emitting devices without conventional life tests, but also provides entirely new modeling ideas and thoughts for reliability evaluation and life prediction of products.

Statistical Inference of Wiener Constant-Stress Accelerated Degradation Model with Random Effects

In the field of reliability analysis, the constant-stress accelerated degradation test is one of the most commonly used methods to evaluate a product’s reliability as degradation data are provided. In this paper, a constant-stress accelerated degradation test model of the Wiener process with random effects is proposed. First, the generalized confidence intervals of the model parameters are developed by constructing generalized pivotal quantities. Second, utilizing the substitution method, the generalized confidence intervals for the reliability function of lifetime, mean time to failure and the generalized prediction intervals for the degradation characteristic at the normal operating condition are also developed. Simulation studies are conducted to investigate the performances of the proposed generalized confidence intervals and prediction intervals. The simulation results reveal that the proposed generalized confidence intervals and prediction intervals work well in terms of the coverage percentage. In particular, a comparative analysis is made with the traditional bootstrap confidence intervals. At last, the proposed procedures are used for a real data analysis.

Estimation of the lifespan distribution of gold nanoparticles stabilized with lipoic acid by accelerated degradation tests and wiener process

Accelerated degradation tests (ADT) are widely used in the manufacturing industry to obtain information on the reliability of components and materials, by degrading the lifespan of the product by applying an acceleration factor that damage to the material. The main objective is to obtain fast information which is modeled to estimate the characteristics of the material life under normal conditions of use and to save time and expenses. The purpose of this work is to estimate the lifespan distribution of gold nanoparticles stabilized with lipoic acid (GNPs@LA) through accelerated degradation tests applying sodium chloride (NaCl) as an acceleration factor. For this, the synthesis of GNPs@LA was carried out, a constant stress ADT (CSADT) was applied, and the non-linear Wiener process was proposed with random effects, error measures, and different covariability for the adjustment of the degradation signals. The information obtained with the test and analysis allows us to obtain the life distribution in GNPs@LA, the results make it possible to determine the guaranteed time for possible commercialization and successful application based on the stability of the material. In addition, for the evaluation and selection of the model, the Akaike and Bootstrapping criteria were used.

Lifetime Prediction of Residual Current Circuit Breaker with Overcurrent Protection Based on GA‐BP and GS‐SVM Combined Model

Residual current circuit breaker with overcurrent (RCBO) is an electrical appliance which involves the safety of users. In order to predict its lifetime, a combined prediction method of Genetic Algorithm‐Back Propagation (GA‐BP) and support vector machine of grid search (GS‐SVM) is proposed. First, the constant stress accelerated degradation test (ADT) is carried out for the RCBO, and the ADT data are statistically analyzed to establish the performance degradation trajectory. Then, the GA‐BP model and GS‐SVM model are established to predict the degradation trend of the residual operating current value. Then, based on the GA‐BP prediction model and GS‐SVM prediction model, the optimal weighted combined prediction based on the least square method is established. The combined prediction model is used to predict the pseudo‐failure life under each accelerated stress, and the Arrhenius accelerated model is used to estimate the pseudo‐failure life by the least square method. The service lifetime of RCBO under normal temperature (25 °C) is predicted. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Optimal time plan in accelerated degradation testing

Many highly reliable products are designed to function for years without failure. For such systems accelerated degradation testing may provide significance information about the reliability properties of the system. In this paper, we propose the c-optimality criterion for obtaining optimal designs of constant-stress accelerated degradation tests where the degradation path follow a linear mixed effects model. The present work is mainly concerned with developing optimal designs in terms of the time variable rather than considering an optimal design of the stress variable which is usually considered in the majority of the literature. Finally, numerical examples are presented and sensitivity analysis procedures are conducted for evaluating the robustness of the optimal as well as standard designs against misspecifications of the nominal values.

Inverse Gaussian process based reliability analysis for constant-stress accelerated degradation data

The constant stress accelerated degradation test has been widely used to evaluate product reliability when degradation measurements of product can be observed. This paper considers interval estimation procedures of the constant stress accelerated degradation model based on the inverse Gaussian process. The exact confidence interval is established for the shape parameter of the inverse Gaussian accelerated degradation model. Using the generalized pivotal quantity procedure, the generalized confidence intervals of other model parameters and some quantities of interest such as the pth percentile and reliability function of lifetime at the normal using stress level are derived. In addition, the generalized prediction interval is developed for the future degradation levels at the normal stress level used. The bootstrap confidence intervals of the proposed inverse Gaussian degradation model are also discussed, and the two interval estimation methods are compared. The performances of the proposed interval estimation procedures are assessed by Monte Carlo simulation in terms of coverage percentage and average interval length. Finally, an example is provided to illustrate the proposed procedures.

Nonlinear Doubly Wiener Constant-Stress Accelerated Degradation Model Based on Uncertainties and Acceleration Factor Constant Principle

Although Wiener process models with the consideration of uncertainties, which are nonlinearity, random effects, and measurement errors, have been developed for lifetime prediction in the accelerated degradation test (ADT), they fail to describe the real degradation process because these models assume that the drift parameter correlates with the applied stress, while the diffusion parameter is constant. This paper put forward a nonlinear doubly Wiener constant-stress accelerated degradation model, where both diffusion and drift parameters were compatible with the applied stress according to the acceleration factor constant principle. When degradation data were available, we obtained the unknown parameters by applying a maximum likelihood estimation (MLE) algorithm in the constant-stress ADT (CSADT) model taking uncertainties into account. In addition, the proposed model’s effectiveness was validated through an illustrative example, and an application to the traveling wave tube (TWT) was carried out to demonstrate the superiority of our model in practical applications.

A novel optimal accelerated degradation test design method considering multiple decision variables

In recent years, there has been considerable interest on the part of scientist and engineers in effectively designing accelerated degradation test, which is very useful to assess product's life information with long-life and high-reliability properties. An effective optimal ADT design method can provide a reasonable arrangement of accelerated stress level setting, sample allocation and test time. However, existing researches can hardly optimize all the multiple decision variables simultaneously in an efficient way. In the current study, an effective stochastic process based constant stress-accelerated degradation test (CSADT) model is constructed, and then an optimization design method is proposed based on the CSADT model, where the multiple decision variables involving stress level, sample allocation and test time arrangement for each stress level can be simultaneously optimized based on genetic algorithm (GA) and Monte Carlo simulation. Meanwhile, a comprehensive sensitivity analysis method incorporating orthogonal experimental design, normalization and range analysis is constructed to illustrate the robustness of the optimal design procedure. Finally, an optimal CSADT design for self-regulating heating cables is presented, and comparative results demonstrate the rationality and effectiveness of the proposed method.

Life Prediction of Residual Current Device Based on Wiener Process with GM (1, 1) Model

Residual current device (RCD), the critical equipment to protect the safety of electrical users, are known to experience performance degrade over time during their use lifetime. Therefore, in order to promptly replace the RCD before failure, it is very important to predict its lifetime. In order to predict the remaining life of the RCD, a constant‐stress accelerated degradation test (CSADT) and a combination prediction model are proposed. First, the CSADT is conducted with temperature as the acceleration stress and the residual operating current as degradation characteristic. Then, based on the prediction result of pseudo failure life, a combination model of Wiener process and GM (1, 1) model is given. Finally, the remaining life of the RCD under normal use environment is extrapolated. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Two-Stage Maximum Likelihood Estimation Procedure for Parallel Constant-Stress Accelerated Degradation Tests

The parallel constant-stress accelerated degradation test (PCSADT) is a popular method used to assess the reliability of highly reliable products in a timely manner. Although the maximum likelihood (ML) method is commonly utilized to estimate the PCSADT parameters, the explicit forms of the ML estimators, and their corresponding Fisher information matrix are usually difficult to obtain. In this article, we propose a two-stage ML (TSML) estimation procedure for a time-transformed model. In the proposed procedure, all the TSML estimators not only have explicit expressions but also possess consistency and asymptotic normality. Hence, this method is tractable for reliability engineers. Furthermore, the TSML estimators can provide constructive information about the unknown accelerated relationship law. The proposed method is also applied to analyze light-emitting diode data and compare the performance of our estimation procedures with the ML method via simulations.

A Life Prediction Model for High-Reliability Products and Its Application to VFD Based on Constant-Stress ADTs

Abstract For many high-reliability and long-life products, the accuracies of some existing life prediction models are not high enough, which may limit their fast development. For this purpose, four groups of constant-stress accelerated degradation tests (ADTs) were carried out by increasing the temperature of a vacuum fluorescent display (VFD) cathodic filament, and the equivalent average luminance degradation model (EALDM) was proposed to predict VFD life. In this model, firstly, a two-parameter Weibull function was used to fit average test data at each accelerated stress, and the corresponding formula of luminance degradation was obtained. Secondly, a power function was determined to fit multi-groups of data points formed by an accelerated stress and time at different given luminance, and then the work time under normal stress was extrapolated. Finally, by reusing the Weibull function to fit the data points, including the work time and given luminance, the life prediction of products was achieved. The results indicate that the test design of constant-stress ADTs is correct and feasible; the Weibull function well reveals the VFD luminance decaying law at both accelerated and normal stresses, and the power function objectively reflects the relationship between work time and stress. It is found by comparing the predicted life with the reference value that EALDM has high precision, which paves the way for following research in life prediction methodology and acts as a guide for professional technicians.

The in-situ testing and modeling on sealing strength deterioration of lithium-ion pouch cell

The pouch cell is of great potential application among a variety of power batteries, because of its higher energy density and lower weight. Due to the existence of internal gas generation in the long lifetime of the pouch cell, the slowly increasing internal gas pressure will cause a time-dependent fracture in its package sealing edge. This process significantly affects the remaining useful life and reliability. In this paper, an in-situ experiment was performed and a modified cohesive zone model (CZM) was proposed to describe the seal strength degradation behavior. Firstly, the in-situ tensile test was conducted to measure the sealing strength curve, and the exponential CZM was used to characterize the constitutive relation of the sealing area based on the load-displacement data. Secondly, constant stress accelerated degradation tests (CSADT) were carried out to simulate the degradation process, where the action of gas pressure on sealing area was converted to accelerated tensile load. Then, the exponential CZM was modified to account for the strength degradation behavior with the effect of constant load duration, based on the traction-separation relationship. The fracture energy was calculated by area integral under the load-displacement curve, whose reduction represented the degradation phenomenon. Finally, the proposed model was validated by the testing data, and a good agreement was observed.

Optimization of the Accelerated Degradation Test Plan for Electrical Connector Contact Pairs Based on a Nonlinear Wiener Process

Accelerated degradation test is an effective method to evaluate the reliability of products with long life and high reliability. The performance of most products fluctuates randomly in the degradation process, so it is suitable to use Wiener process. At present, the diffusion coefficient is regarded as constant in Wiener process, while the drift coefficient is related to stress. However, in practice, the amplitude of product performance fluctuation increases with the increase of stress level, which is not constant. Therefore, for the nonlinear Wiener case where both the drift coefficient and the diffusion coefficient are stress dependent, this paper studies the constant-stress accelerated degradation test theories and methods. Taking the contact pairs of electrical connectors as the research object, the minimum variance of reliable life estimate under normal stress is taken as the target. After determining the censored time at each stress level, the test stress level, the sample distribution ratio at each stress level, and the test interval at the one-third power scale of time are taken as design variables. The test plan under 3, 4, and 5 stress levels is optimized and compared with the general test plan. The influence of the difference between high and low stress levels on the evaluation accuracy is analyzed. Finally, the sensitivity analysis of parameters shows that the optimization plan has good robustness, and the change of stress quantity has little influence on the robustness of the plan.

Effects of silicone lens aging on degradation kinetics of light-emitting diode package in various accelerated testing

Silicone is commonly used in light-emitting diode (LED) package as lens and/or encapsulation owing to its high light transmittance, large refractive index, and good thermal stability. However, the effect of silicone lens aging on the lumen decay and color shift of LED package is a considerable concern for package level reliability. This study empirically investigates the effects of silicone lens aging on lumen decay and color shift of LED package under three accelerated tests, namely, the constant stress-accelerated degradation test, step-up stress-accelerated degradation test, and step-down stress-accelerated degradation test (SDSADT). Results reveal that silicone lens aging substantially contributed to lumen decay and color shift of LEDs and considerably influenced the degradation kinetics of LED package. The color coordinates of LED package covered with aged silicone specimen in three testing methods exhibit a steady yellowing shift law at the same 45-degree direction. Silicone lens aging primarily reduces its transmittance to blue light as accumulated thermal oxidation and hydrolysis reaction, and its effect on the blue peak intensity of LED is independent of the stress-loaded order of step stress-accelerated degradation testing (SSADT). In addition, the effect law of silicone lens aging on LED lumen and color shift could be presented with the exponential and power function models, respectively. Lumen decay and color shift are mostly independent of the historical stress and loaded order in SSADT. The SDSADT testing manner more effectively distinguishes the color shift effect of thermal stress level compared with other accelerated tests. These findings are assumed to benefit the design and reliability assessment of LED products.

Reliability analysis for accelerated degradation data based on the Wiener process with random effects

AbstractOn the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small‐sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit‐to‐unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.

Multi-objective optimization design of accelerated degradation test based on Wiener process

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test.