Step-stress Accelerated Degradation Test Research Articles

Semiparametric evaluation of first‐passage distribution for step‐stress accelerated degradation tests

AbstractIn reliability engineering, different types of accelerated degradation tests have been used to obtain reliability information for evaluating highly reliable or expensive products. The step‐stress accelerated degradation test (SSADT) is one of the useful experimental schemes that can be used to save the resources of an experiment. Motivated by the SSADT data for operational amplifiers collected in Xi'an Microelectronic Technology Institute, in which the underlying degradation mechanism of the operational amplifiers is unknown, we propose a semiparametric approach for SSADT data analysis that does not require strict distributional assumptions. Specifically, the empirical saddlepoint approximation method is proposed to estimate the items' lifetime (first‐passage time) distribution at both stress levels included and not included in the SSADT experiment. Monte Carlo simulation studies are used to evaluate the performance and illustrate the advantages of the proposed approach. Finally, the proposed semiparametric approach is applied to analyze the motivating data set.

A novel machine learning-based imputation strategy for missing data in step-stress accelerated degradation test

The presence of missing data is a significant data quality issue that negatively impacts the accuracy and reliability of data analysis. This issue is especially relevant in the context of accelerated tests, particularly for step-stress accelerated degradation tests. While missing data can occur due to objective factors or human error, high missing rate is an inevitable pattern of missing data that will occur during the conversion process of accelerated test data. This type of missing data manifests as a degradation dataset with unequal measuring intervals. Therefore, developing a more appropriate imputation method for accelerated test data is essential. In this study, we propose a novel hybrid imputation method that combines the LSSVM and RBF models to address missing data problems. A comparison is conducted between the proposed model and various traditional and machine learning imputation methods using simulation data, to justify the advantages of the proposed model over the existing methods. Finally, the proposed model is implemented on real degradation datasets of the super-luminescent diode (SLD) to validate its performance and effectiveness in dealing with missing data in step-stress accelerated degradation test. Additionally, due to the generalizability of the proposed method, it is expected to be applicable in other scenarios with high missing data rates.

A Reliability Analysis of a MEMS Flow Sensor with an Accelerated Degradation Test.

With the wide application of flow sensors, their reliability under extreme conditions has become a concern in recent years. The reliability of a Micro Electro Mechanical Systems (MEMS) flow sensor under temperature (Ts) is researched in this paper. This flow sensor consists of two parts, a sensor chip and a signal-processing system (SPS). Firstly, the step-stress accelerated degradation test (SSADT) is implemented. The sensor chip and the flow sensor system are tested. The results show that the biggest drift is 3.15% for sensor chips under 150 °C testing conditions, while 32.91% is recorded for the flowmeters. So, the attenuation of the SPS is significant to the degeneration of this flowmeter. The minimum drift of the SPS accounts for 82.01% of this flowmeter. Secondly, using the Coffin-Manson model, the relationship between the cycle index and Ts is established. The lifetime with a different Ts is estimated using the Arrhenius model. In addition, Weibull distribution (WD) is applied to evaluate the lifetime distribution. Finally, the reliability function of the WD is demonstrated, and the survival rate within one year is 87.69% under 85 °C conditions. With the application of accelerated degradation testing (ADT), the acquired results are innovative and original. This research illustrates the reliability research, which provides a relational database for the application of this flow sensor.

Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process

In this paper, we are interested in the optimization of step-stress accelerated degradation test plan when the degradation path follows the Tweedie exponential dispersion process which has been shown to be an important family in degradation analysis. We firstly prove that, under the Tweedie exponential dispersion process model with a drift parameter being an exponential function of the (transformed) stress level, a multi-level step-stress accelerated degradation test plan will correspond to a simple step-stress accelerated degradation test plan using only the minimum and maximum stress levels under D-optimality and V-optimality criteria. The optimum step-stress accelerated degradation test plan based on these two optimality criteria is subsequently derived, a numerical example is furthermore presented to compare the efficiency of the proposed optimum simple step-stress accelerated degradation test plans and some step-stress accelerated degradation test plans proposed by a previous study. In addition, a simulation study is conducted for investigating the performances of the proposed step-stress accelerated degradation test plans.

Optimal design of step stress accelerated degradation test with multistress considering stress weight

This paper presents a new optimization criterion considering stress weight based on Ds-optimality to solve the low estimation accuracy problem of some stress model parameters when using the existing optimization design criteria to optimize the multistress accelerated degradation test scheme. First, the accelerated degradation model and constraints are determined by analyzing the test characteristics of step-stress accelerated degradation test (SSADT) with multistress. Then, the weight of each stress is identified by fault tree analysis and potential improvement value methods. Combined with the tabu search–particle swarm optimization (TS-PSO) algorithm, the SSADT with multiple stresses of the optimization design process is given. Finally, taking the SSADT with multistress optimization design of motorized spindle as an example, the practicability of the method is verified, and the optimization results are compared with those under D-optimality and Ds-optimality to validate the effectiveness of the method.

Preload degradation mechanism of double-nut ball screws revealed by an innovative wear distribution model

The preload of ball screws is generally used to confirm the ball screws with a high axial contact stiffness and a high positioning accuracy. Aiming at the preload degradation due to wear on the raceway of double-nut ball screws, a wear distribution model was proposed by calculating the contact stress distribution and the inhomogeneous relative sliding velocity distribution on the contact region to determine the wear profile of the raceway. Firstly, the contact stress distribution and the relative sliding velocity distribution on the contact surface were determined using the kinematics analysis and the force balance analysis. Subsequently, a wear distribution model was established to determine the wear depth distribution of the contact surface based on elastic-plastic contact mechanics of asperity with consideration of the microscopic characteristics of the raceway. Finally, the three-level step-stress accelerated degradation test based on the simulated model was designed and implemented on a self-designed bench to validate the proposed model. Experimentally measured friction torques of the ball screws were used to reflect the preload degradation, and they were compared with the results of the simulated model. The results showed that the degradation curves of the experimental friction torques and the wear profiles of screw raceways were in good agreement with the numerical results, confirming the correctness and effectiveness of the proposed model. The results indicated that the wear profile of the raceway could be accurately calculated based on the proposed model, clearly describing the wear process of the raceway surface and providing a more precise approach to predict preload degradation for ball screws.

Optimal design of step-stress accelerated degradation test oriented by nonlinear and distributed degradation process

The Step-stress accelerated degradation test (SSADT) is an efficient tool to assess the reliability of products. To ensure an accurate evaluation of reliability-related indexes with limited cost, the optimal design for SSADTs is widely applied. Conventional optimal design methods ideally assume the degradation process to be linear and distribution-free, which may cause the designed test plans to be drastically different from the optimal one. To overcome the drawbacks of the unreasonable assumption, this paper develops a new optimal design method for SSADTs, including a generalized Wiener process-based degradation model (GWPDM) considering the distribution feature and a corresponding optimization criterion aiming at accurate prediction of degradation distributions. The GWPDM is first discussed, where the influence of the nonlinearity, unit-to-unit variability, measurement error and stress-related temporal variability on the degradation process is clarified. The statistical inference of the developed GWPDM is conducted to deduce the proposed optimization criterion. Thus, the optimization model is established to determine the optimal SSADT plan. The proposed method is used to design a SSADT plan for the metal-film resistor. Finally, the necessity and the robustness of the proposed method are verified.

Optimization Design of Step Stress Accelerated Degradation Test for Motorized Spindle Based on Ds-Optimality

In the accelerated degradation test (ADT) of motorized spindles, it is necessary to apply a variety of stresses to simulate real working conditions. However, the traditional accelerated test scheme optimization method does not consider the weight of various stresses in the test, resulting in the evaluation accuracy of important stress parameters in the model being too low. In order to solve this problem, an optimal design method of the step stress accelerated degradation test (SSADT) scheme for motorized spindles is proposed based on Ds-optimality. Firstly, the fault tree analysis (FTA) method is used to analyze the collected fault data of motorized spindles and screen the main stress. Then, the accelerated degradation model is established by using drift Brownian motion. Based on the Ds-optimality, the optimization variables and constraints in the test are determined, and the optimization model is established with the objective of minimizing the estimated variance of the main stress parameters in the acceleration model; additionally, the optimization steps are given. Finally, an example is given to verify the effectiveness of the method. Sensitivity analysis of the optimization results shows that the method has good robustness.

Performance Degradation Modeling and Reliability Analysis of Aviation Connectors in Marine Environment

The influence of marine environment on the reliability of a certain type of aviation connectors is studied. Firstly, the step-stress accelerated degradation test which simulates marine environment in South China Sea is designed. And the performance parameter data of four material types of aviation connectors: stainless steel, composite cadmium plating, titanium alloy and aluminum alloy cadmium plating are collected. And then, in order to study the degradation of performance parameters, the mixed effect model is adopted. At last, the reliability lifetime of four material types of aviation connectors are evaluated by means of reliability modeling and analysis. This research provides an effective path for reliability evaluation of aviation connectors, meanwhile it also gives a reference for aviation connectors’ selection.

Synthetic Reliability Assessment Model Involving Temperature–Humidity Step-Stress Based on Wiener Process

There are always some difficulties in storage reliability evaluation of high-reliability, long-life, and high-value products, such as the test sample being small, degradation speed being slow, and failure data being inadequate. Temperature–humidity step-stress accelerated degradation test (THSS-ADT) is an effective method to evaluate the reliability of this type of products, but the test data processing is an extremely complex work. The motivation of this paper is to provide a clear, effective, and convenient method to evaluate the reliability on the basis of THSS-ADT data. Considering the stochastic volatility in degradation process, Wiener process is used to modeling the accelerated degradation process. The methods to estimate the parameters of Peck accelerated model and degradation model are discussed under temperature–humidity step-stress. As ordinary optimization algorithms (such as Newton Iteration Method and impelling function method) find it difficult to get the solutions, particle swarm optimization (PSO) method is used to solve the problem of maximum-likelihood estimation. Finally, the proposed methods are demonstrated for two examples, in which one is a numerical simulation, and another is an engineering practice of a microwave power amplifier.

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.

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.

Reliability prediction of rotary encoder based on multivariate accelerated degradation modeling

The rotary encoder is an important sensor for measuring rotational motion. A step–stress accelerated degradation test (SSADT) is conducted with respect to accuracy to evaluate the reliability rapidly. The existing errors in output signals are identified as degradation indicator to characterize performance degradation. A methodology for the encoder SSADT modeling is presented. Wiener process theory with unit–to–unit variation is utilized in the model to describe the degradation process of each error. Considering the correlation among the degradation processes, a multivariate degradation modeling method is developed based on the Copula function to estimate the reliability of rotary encoder with multiple degradation indicators. The reliability of the encoder under the use–stress level is derived by combining the margin distributions and Copula function.

Investigation of Step-Stress Accelerated Degradation Test Strategy for Ultraviolet Light Emitting Diodes

III-nitride-based ultraviolet light emitting diode (UV LED) has numerous attractive applications in air and water purification, UV photolithography, and in situ activation of drugs through optical stimulus, solid state lighting, polymer curing, and laser surgery. However, the unclear failure mechanisms and uncertainty reliability have limited its application. Therefore, a design of an appropriate reliability test plan for UV LEDs has become extremely urgent. Compared to traditional reliability tests recommended in LED lighting industry, the step-stress accelerated degradation test (SSADT) is more cost-effective and time-effective. This paper compares three SSADT testing plans with temperature and driving currents as stepwise increasing loads to determine an appropriate test strategy for UV LEDs. The study shows that: (1) the failure mechanisms among different SSADT tests seem to be very different, since the driving current determines the failure mechanisms of UV LEDs more sensitively, and (2) the stepped temperature accelerated degradation test with an appropriate current is recommended for UV LEDs.

Planning of step-stress accelerated degradation test based on non-stationary gamma process with random effects

Abstract This paper discusses the design problem of the step-stress accelerated degradation test (SSADT) based on the non-stationary gamma process with random effects. The cumulative exposure (CE) model is used to link the degradation paths of the SSADT under different stress levels. The expectation maximization (EM) algorithm is applied to estimate the model parameters. The purpose is to design an optimal experiment plan by minimizing the asymptotic variance of the estimated reliability of the product at a predesigned mission time of interest. Under the budget and boundary constraints, the design variables such as sample size, the measurement frequency at each stress level, and the number of measurements at each stress level are obtained. In the end, an example about the light emitting diode (LED) chip is used to illustrate the proposed model.

Joint Modeling of Linear Degradation and Multiple Dependent Competing Risks Data under a Step-Stress Accelerated Degradation Test

The step-stress accelerated degradation test (SSADT) is one of the most commonly used time-dependent types of stress loading tests that enables a shorter test duration. This test is more economical and flexible compared to accelerated degradation test or accelerated failure time (ADT/AFT) test plans. This test is suitable when constraints by test facilities, conditions, or samples exist. SSADT is more useful for developing products when there is inadequate knowledge for test conditions. Important aspects here are to evaluate each failure mode in the presence of the other modes by assuming some dependency structure between the failure modes due to the non-applicability of studying test units with isolated competing failure modes. This paper aims to propose a modeling approach to simultaneously analyze linear degradation data and failure time data with dependent competing risks in an SSADT experiment. We use the copula function to consider the dependency structures between two failure modes. The proposed model is applied to acceleration data, to simulation data sets and two real data sets- bus tire data set and plastic substrate active matrix light-emitting diodes (AMOLED) data set, accompanied by sensitivity analysis.

Step-stress accelerated degradation test planning based on Wiener process with correlation

ABSTRACTTo assess the lifetime distribution of highly reliable or expensive product, one of the most commonly used strategies is to construct step-stress accelerated degradation test (SSADT) which can curtail the test duration and reduce the test cost. In reality, it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path. Recently, Ye, Chen, and Shen [(2015). A new class of Wiener process models for degradation analysis. Reliability Engineering and System Safety, 139, 58–67] proposed a Wiener process to capture the positive correlation between the drift rate and the volatility. In this paper, an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation. Firstly, the stochastic diffusion process is introduced to model a typical SSADT problem. Then the design variables, including the sample size, the measurement frequency and the numbers of measurements under each stress level, are optimised by minimising the asymptotic variance of the estimated p-percentile of the product's lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget. Finally, a numerical example is presented to illustrate the proposed method.

Mechanism Equivalence in Designing Optimum Step-Stress Accelerated Degradation Test Plan Under Wiener Process

To obtain enough reliability information of highly reliable products, step-stress accelerated degradation test becomes more and more popular as it helps to shorten test duration and reduce sample size. A reasonable step-stress accelerated degradation test plan provides a possibility to predict product’s lifetime precisely when it is designed by using an appropriate optimization criterion based on the valid degradation information. In this paper, we investigate the mechanism equivalence in designing an optimum step-stress accelerated degradation test plan under Wiener process. In particular, an algorithm for extracting valid test information is formulated based on degradation mechanism equivalence analysis. Then, we propose the $M$ -optimality criterion to improve the mechanism equivalence of a step-stress accelerated degradation test when designing an optimum plan. Subject to the total cost constraint, a comparison is carried out between the optimum plan designed by using $M$ -optimality criterion and other plans designed by using traditional criteria through the case of light intensity degradation of LEDs.

Nonlinear step-stress accelerated degradation modelling considering three sources of variability

In the absence of enough run-to-failure data, step-stress accelerated degradation testing (SSADT) is often an attractive alternative way to evaluate the reliability of a product, with the advantage of requiring small sample size and short test time. However, the development of a statistical SSADT model for reliability assessment should take into account different sources of variability in the degradation process that generate uncertainty: 1) temporal variability determining the inherent variability of degradation process over time; 2) unit-to-unit variability in three aspects: degradation rates, initial degradation values, time-points of elevating stress levels; and 3) measurement errors in both covariates and degradation performance. As a contribution towards this aim, a new nonlinear Wiener-process-based SSADT model considering simultaneously nonlinearity and three sources of variability is proposed. Using the proposed SSADT model, the lifetime law of the tested product under normal conditions is derived based on the concept of first hitting time (FHT) of a predetermined failure threshold. Following an approach based on genetic algorithms (GA), a modified simulation and extrapolation method, called GA-SIMEX, is also developed for the model parameter estimation. Finally, a simulation study of fatigue crack length growth is presented to illustrate the implementation of the proposed SSADT model.

Bayesian step stress accelerated degradation testing design: A multi-objective Pareto-optimal approach

Step-stress accelerated degradation testing (SSADT) aims to access the reliability of products in a short time. Bayesian optimal design provides an effective alternative to capture parameters uncertainty, which has been widely employed in SSADT design by optimizing specified utility objective. However, there exist several utility objectives in Bayesian SSADT design; for the engineers, it causes much difficulty to choose the right utility specification with the budget consideration. In this study the problem is formulated as a multi-objective model motivated by the concept of Pareto optimization, which involves three objectives of maximizing the Kullback-Leibler (KL) divergence, minimizing the quadratic loss function of p-quantile lifetime at usage condition, and minimizing the test cost, simultaneously, in which the product degradation path is described by an inverse Gaussian (IG) process. The formulated programming is solved by NSGA-II to generate the Pareto of optimal solutions, which are further optimally reduced to gain a pruned Pareto set by data envelopment analysis (DEA) for engineering practice. The effectiveness of the proposed methodologies and solution method are experimentally illustrated by electrical connector’s SSADT.