A General Accelerated Degradation Model Based on the Wiener Process

Collecting accelerated degradation test (ADT) data can provide useful lifetime information for highly reliable products if there exists a product quality characteristic whose degradation over time can be related to reliability. However, conducting a constant-stress ADT is very costly. This is obviously not applicable for assessing the lifetime of a newly developed product because typically only a few test samples (prototypes) are available. To overcome this difficulty, we propose a step-stress accelerated degradation test (SSADT) in this paper. A case study of light emitting diodes data is used to illustrate the proposed procedure. It is seen that SSADT has several advantages over a constant-stress ADT. SSADT not only reduces the experimental cost significantly, but also provides the reliability analysts an efficient tool to assess the lifetime distribution of highly reliable products.

Accelerated Degradation Testing (ADT) is proposed as a means to obtain degradation data of products in a short time period and extrapolate the lifetime and reliability of products under use condition. There are two optimality criterion could be defined in designing an accelerated test plan. Criterion D : some testing planners are interest in the prediction of products' lifetime, so their objective is minimizing the variance (or asymptotic variance) of the MLE of parameter Θ which can include the quantiles and the mean of the lifetime distribution at a pre-specified stress level. Criterion II : if engineers are interest in the estimation of model parameters, their objective may be maximizing the determinant of the Fisher information matrix, which has a reciprocal relationship with variance-covariance matrix. This criterion is D-optimality, wherein the `information' is maximized and the `variance' is minimized at the same time. Criterion I for Step Stress Accelerated De gradation Testing (SSADT) planning is already proposed, however Criterion II (D-optimality) is seldom discussed. In this study, a method to optimal design for SSADT based on D-optimality is present. First, drift Brownian motion is applied to describe a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal plan gives sample size, total testing time, stress levels and testing time at each stress level. Finally, an example is used to illustrate this test planning method.

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

Estimating the long term performance of highly reliable products has been a difficult problem as accelerated life testing (ALT), which involves testing at highly elevated stresses, often results in too few failures for drawing useful inferences. To overcome this problem, accelerated degradation testing (ADT) has been proposed as a means to predict performance for highly reliable products. It requires one to identify a performance measure that would exhibit degradation and to monitor it over time. Product reliability can then be inferred from the degradation paths without the need of observing actual failures. Although physical failures are not needed in ADT, one usually defines failure as the first time when the degradation process exceeds a pre-specified threshold, so that the degradation path can be correlated to product reliability. As a result, reliability information of a product is embedded in degradation paths of units tested under ADT. In this paper, we look into planning of an ADT in which the test stress is increased in steps from lower stress to higher stress during the test, so that specimens are gradually conditioned to the stressed environment thus avoiding over-stressing. Our objective is to minimize the cost of testing, which is a function of sample size, test duration and number of inspections, as well as obtaining a reliability estimate of a requisite level of precision. Data from degradation paths are used to characterize the appropriate stochastic model underlying the product degradation process. We then derive the maximum likelihood estimators and the mean life at the use stress and its asymptotic variance. This variance is then used as a constraint, in a test plan which minimizes the testing cost. The optimal test plan gives the optimal sample size, number of inspections at each intermediate stress level and number of total inspections.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

For the highly reliable products, an accelerated degradation test (ADT) is a useful tool which has been employed in industry to obtain reliability-related information within an affordable amount of time and cost. In an ADT, as all other reliability tests, it is important to carefully design the ADT beforehand to obtain estimates of the quantities of interest as precisely as possible. In this paper, optimal ADTs are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Under the constraint that the total cost does not exceed a pre-specified budget, the stress levels, the number of test units allocated to each stress level and the number of measurement (termination time) 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.

According to the present works, it is more efficient by carrying out accelerated degradation test (ADT) with step-down stress than constant and step-up stress. However, maximum likelihood estimation (MLE) is currently the main analysis method for step-down stress accelerated degradation test (SDSADT), which is difficult to be applied into small sample size occasion. To solve this problem, the paper proposes a Bayesian analysis method for SDSADT based on Wiener process. Firstly, degradation path of product performance is described by Wiener process, and then data analysis of SDSADT is carried out by a segmented Bayesian method which can update the evaluation values of model parameters under different accelerated stresses. Lastly, recursive algorithm for parameters estimation is established for reliability assessment of SDSADT. Simulation studies show that the method is more accuracy by comparing with MLE in case of small sample size.

Degradation data always contains useful information on life and reliability, even if no failure has occurred. By applying additional stress, accelerated degradation testing(ADT) can shorten testing time. Many factors can affect the measured degradation data. Besides the degradation process itself and measurement errors, the measurement methods will also have impact on the degradation level. This paper considers the impact of data under two different data collection methods on the results of lifetime inference. Different statistical models are applied to the data from two measurement methods, both of which are based on a linear regression model. Likelihood inference for these models are developed. Simulation is used to demonstrate the effect of data collection methods on the inference results.

In order to evaluate lifetime of electron multiplier(EM), which is a key component of a cesium atomic frequency standard system, step stress accelerated degradation test in a two-way design is presented. The investigation of test design, establishment of lifetime evaluation model and model analyses is made. Then lifetime evaluation of EM is carried out.

For the accelerated degradation test (ADT) of lithium-ion battery, the degradation path models are usually applied with the fixed parameters. To optimize the degradation path models, so many battery cells are required for the ADT models based on the degradation path. However, for some lithium-ion batteries with long cycle life and high reliability, the samples are limited due to experimental cost constraints. Meanwhile, owing to the differences in raw materials and manufacturing processes, it is easy to observe variations among the degradation path of lithium-ion battery cells. Fortunately, Wiener process model considering the individual difference can express the variations and be modeled with limited samples for lithium-ion battery. Motivated by this issue, an improved method with random effects Wiener process (REWP) is proposed in this article. First, to verify the degradation process following the Wiener process, the Shapiro-Wilk test is carried out on the basis of a significance level of 0.05. Second, we analyze the varieties of every lithium-ion battery cell. To select a suitable Wiener process model, we apply the coefficient of variation as a measure of random parameters selection for Wiener process. Meanwhile, the maximum likelihood estimation (MLE) is used to optimize parameters of the proposed model. Next, the three different REWP models and general Wiener process model are compared. Finally, to demonstrate the proposed method, the lithium-ion battery cells used for a spacecraft in low Earth orbit (LEO) are conducted for ADTs. The results suggest that the REWP model has a better performance for assessing reliability of lithium-ion battery with long cycle life.

Accelerated degradation test (ADT) has become an efficient approach to evaluate the reliability for highly reliable products. However, when modeling accelerated degradation data with degradation models, it is difficult to exactly figure out the changing rules of parameters with stress variables varying. At present, the changing rules are mainly assumed according to engineering experience or subjective judgements, which probably results in inaccurately extrapolating the reliability. To figure out the changing rules of parameters with stress variables varying, the acceleration factor constant principle and its application under ADT are studied in the paper. It is well known that the acceleration factor between any two different stress levels should be a constant under an effective ADT. For each degradation model, its parameters should obey special changing rules to satisfy that the acceleration factor maintains a constant throughout an ADT. Taking three extensively used stochastic process models as examples, including Wiener process model, gamma process model, and inverse Gaussian process model, the method of deducing the changing rules of the parameters according to the acceleration factor constant principle was demonstrated. A simulation test was conducted to validate the deduced changing rules of the parameters for the three stochastic process models. An illustrative example involving self‐regulating heating cables was used to illustrate the application of the acceleration factor constant principle under ADT. Results indicate that the acceleration factor constant principle offers an appealing and credible approach to help model accelerated degradation data. Copyright © 2016 John Wiley & Sons, Ltd.

Accelerated degradation testing (ADT) technology for long-life and high-reliability products has become one of the key technologies in life and reliability field. The scientific and reasonable testing program can not only provide correct basis for decision making, but also make full use of resources and reduce the cost of product development. Hence, how to make full use of products’ historical information to develop a short-term efficient pilot program has become a key-problem to be solved in ADT technology. This chaptere proposes the Bayesian optimal design of step-stress accelerated degradation testing (SSADT) based on Gamma process and relative entropy. Firstly, we briefly describe the applicability of Gamma process and the relative entropy in ADT, and the degradation model and relative entropy’s application method are given. Secondly, under the framework of Bayesian theory, we study the Gamma degradation process based SSADT optimal design method by using maximize the relative entropy as the optimization goals and test variables as the optimization design constraints. Finally, we use a 3-steps bulb’s SSADT to verify the effectiveness of the proposed method. The example shows that the method of this chapter is fast and efficient which can comprehensively use the prior information to work out the optimal pilot program.KeywordsPosterior DistributionRelative EntropyDegradation ModelOptimization GoalBayesian TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Super luminescent diode (SLD) is a typical product with long lifetime and high reliability which has great advantages and wide application prospects in many areas. Accelerated degradation testing (ADT) is used to obtain performance parameter data in a short time and extrapolate the lifetime and reliability of the products under normal operation conditions. However, in the application of Super luminescent diode (SLD) in ADT, on one hand, sometimes the sample size may be small for the limited cost, the evaluation accuracy of the lifetime and reliability would be low for the lack of information. On the other hand, with the developing of the SLD, usually a fixed number of samples are put into various tests besides ADT and extra information can be obtained in that process. So if all the available information can be used together in a feasible way, the evaluation accuracy of the lifetime and reliability would be improved. In this paper, Bayesian theory is introduced to solve the problems above for its great capability of data fusion. In this method, feasible degradation data of the SLD from different sources are collected, then processed and tested to make them have the same data format and physical meaning, finally fused to estimate the lifetime and reliability with the established degradation statistical model and reliability evaluation model of SLD. This paper provides a new ADT data evaluation method and the method is also suitable for other similar products.

Space electronic products usually should meet the mission requirements of long life and low cost. Because of insufficient failure data, it is hard to assess the reliability precisely by using traditional reliability testing and statistical method. In this paper, a method of reliability assessment based on integration of highly accelerated life testing (HALT) and accelerated degradation testing (ADT) is proposed. Firstly, based on performance analysis of electronic products, the degradation of performance is modeled. Moreover, the data of drift performance is extracted, fitted and fused into the observation data in ADT. Lastly, the reliability assessment for electronic products is studied based on degradation data. This research provides an effective way for accelerated reliability testing of space electronic products, and it has been applied into practice.

Failure Mode Effect and Critically Analysis(FMECA) is one of the key technologies in testability verification test that based on plenty of failure samples.Line replaceable module(LRM) is the core of the new generation avionics system and military equipment electronic system. Failure data of LRM is difficult to acquire under natural conditions,however,it could be obtained fleetly through accelerated degradation test(ADT).According to the degradation data obtained from the accelerated degradation test and the degradation model, the typical failure modes and the occurrence probability of the LRM could be obtained.