Acceleration Factor Constant Principle and the Application under ADT

The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtained. Therefore, a class of exponential-dispersion processes, named Tweedie exponential-dispersion process (TEDP), is proposed to describe the products’ degradation paths. The TEDP model which comprises the aforementioned stochastic processes as its special cases, is more flexible and applicable for degradation modeling. Considering the nonlinear characteristics of degradation paths and the unit-to-unit variability among the product units, random-effect models are established based on the nonlinear TEDP models with random drift and dispersion parameters. To improve the mathematical tractability of these models, the variational inference, expectation maximization algorithm and differential evolution algorithm are used to estimate the unknown model parameters. Furthermore, two nonlinear TEDP models with accelerated factors and random effects are developed for accelerated degradation analysis. Finally, a simulation study and three real applications are presented to show the effectiveness and superiority of the proposed models and methods.

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.

This paper addresses the optimal design problem for constant-stress accelerated degradation tests using inverse Gaussian (IG) process models. Unlike previous studies that primarily focussed on optimizing stress levels and sample sizes, this research uniquely emphasizes the critical role of measurement timing as a design variable. We investigate D-, A-, and V -optimal designs for IG processes, both with and without random effects. Our study derives analytical solutions for optimal measurement time schedules in IG processes characterized by linear degradation paths and provides numerical solutions for those with nonlinear degradation paths. To streamline the search for optimal time schedules, we employ a lower-dimensional parameterization method that mitigates the substantial computational burden. This approach facilitates the generation of multiple measurement times using only a limited number of design variables. The numerical results highlight the significant impact of optimal time scheduling on enhancing the efficiency and effectiveness of accelerated degradation test designs.

The reliability of circular electrical connectors was usually assessed according to standards like MIL-HDBK-217 (Reliability Prediction of Electronic Equipment). Given to their limitations and mislead results, a new assessment method needs to be presented. Some concerns on the physics of failure (PoF) modeling and reliability assessment of circular electrical connectors are addressed in this paper to overcome this defect. An original approach combining laboratory accelerated degradation testing (ADT) and PoF modeling is proposed for effectively assessing connector reliability. Random vibration and current stress are selected as acceleration factors that affect the contact life of electrical connectors. Then, an appropriate multiple-stresses ADT scheme is derived. The PoF model for electrical connectors under multiple stresses yielded the generalized Eyring relationship. According to the system reliability model for multiposition connectors, connectors' life follows Weibull distribution, which is derived from extreme-value distribution theory. Through ADT and data gained from tests, statistical analysis result yielded the estimated value of reliability character of MIL-C-38999 I series electrical connectors under the action of vibration and current stresses.

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.

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.

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.

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

Degradation is often defined in terms of the change of a key performance characteristic over time. When the degradation is slow, accelerated degradation tests (ADTs) that apply harsh test conditions are often used to obtain reliability information in a timely manner. It is common to see that the initial performance of the test units varies and it is strongly correlated with the degradation rate. Motivated by a real application in the semiconductor sensor industry, this study advocates an allocation strategy in ADT planning by capitalizing on the correlation information. In the proposed strategy, the initial degradation levels of the test units are measured and the measurements are ranked. The ranking information is used to allocate the test units to different factor levels of the accelerating variable. More specifically, we may prefer to allocate units with lower degradation rates to a higher factor level in order to hasten the degradation process. The allocation strategy is first demonstrated using a cumulative-exposure degradation model. Likelihood inference for the model is developed. The optimum test plan is obtained by minimizing the large sample variance of a lifetime quantile at nominal use conditions. Various compromise plans are discussed. A comparison of the results with those from traditional ADTs with random allocation reveals the value of the proposed allocation rule. To demonstrate the broad applicability, we further apply the allocation strategy to two more degradation models which are variants of the cumulative-exposure model.

Motivated by an accelerated degradation test (ADT) on the power gain of microwave power amplifiers, in this article we propose a model-ranking approach for the estimation of some important reliability characteristics. Different degradation models and statistical lifetime distributions are applied to model the data obtained from the ADT. We study the effect of model misspecification in estimating the reliability characteristics when the behavior of the degradation process and the underlying degradation-data-generating mechanism are unknown. We then propose a model-ranking approach with weighted estimation procedures when multiple candidate models are under consideration. Through a Monte Carlo simulation study, we show that the proposed approach is robust and insensitive to model misspecification. Finally, the ADT data from the motivating example are used to illustrate the proposed methodologies.

Statistical methodology for predicting the life of lithium-ion cells via accelerated degradation testing

To solve the problem that the individual differences and the measurement errors affect the accuracy of life estimation in accelerated degradation test, the inverse Gauss process with stochastic parameters is applied in the accelerated degradation test with the consideration of the influence of individual differences, and the analysis of measurement uncertainty is carried out. An inverse Gauss accelerated degradation model considering both individual differences and measurement errors is established. In the maximum likelihood estimation of parameters, Genetic Algorithm and Monte Carlo integral are used to solve the problems caused by complex integral and the unobservable measurement errors in the calculation process. Finally, the proposed method is verified by the Monte Carlo simulation under the constant accelerated stress and step accelerated stress and the illustrative example of electrical connectors under the constant acceleration stress, respectively. The results show that the modeling tool is useful for improving the accuracy of the life prediction and the reliability evaluation.

In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to the traditional stochastic process models, which presumes that the product has experienced some degradation at the beginning of the test. Such a modeling technique can also capture the correlation between the initial degradation and the degradation rate, when the degradation rate of each path does vary from unit to unit. We apply this technique to the three popular stochastic process models, i.e., the Wiener process, the gamma process, and the inverse Gaussian process, and develop the corresponding parameter inference procedures. Monte Carlo simulations are implemented to validate the proposed models and the estimation procedures. Applications to the degradation analysis of block error rates data and GaAs laser data reveal good performance of the proposed models.

Traditional reliability analysis techniques focus on the occurrence of failures over time. Nevertheless, in certain cases where the occurrence of failures is tiny or almost null, the estimation of the quantities that describe the failure process is compromised. In this context, we introduce a reliability model for systems adopting the degradation process using frailty. The evolved degradation model has as experimental data, not the failure, but a quality feature attached to it. Degradation analysis can provide information about the lifetime distribution components without actually observing failures. In this paper, we propose an inverse Gaussian process model with frailty as a possible tool to investigate the effect of unobserved covariates. Moreover, a comparative study with the classical inverse Gaussian process based on simulated data was performed, revealing that the asymptotic properties of the maximum likelihood estimators are compromised when the presence of frailty is ignored. The application was based on two real data sets in the literature, showing that the inverse Gaussian process frailty models are propitious to use; however, gamma and inverse Gaussian distributions for frailty present similar results.

Accelerated degradation testing (ADT) aids the reliability and lifetime evaluations for highly reliable products. In engineering applications, the number of test items is generally small due to finance or testing resource constraints, which leads to the rare knowledge to evaluate reliability and lifetime. Consequently, the epistemic uncertainty is embedded in ADT data and the large-sample based probability theory is no longer appropriate. In this paper, we introduce the uncertainty theory, which is a theory different from the probability theory, to account for such uncertainty due to small samples and build up a framework of ADT modeling. In this framework, an uncertain accelerated degradation model is first proposed based on the arithmetic Liu process. Then, the uncertain statistics for parameter estimations are presented correspondingly, which is completely constructed on objectively observed ADT data. An application case and a simulation case are used to illustrate the proposed methodology. With further comparisons to the Wiener process based accelerated degradation model (WADM) and the Bayesian-WADM, the sensitivities of these models to sample sizes are explored and the results show that the proposed model is superior to the other two probability-based models under the small sample size.