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.
In order to predict the reliability of the product with high reliability and long life, the accelerated degradation test (ADT) is commonly applied. However, in the studies of optimizing the ADT plans, there is nearly no researches on how to select the test stress levels. In this paper, the drift Brownian motion is selected as the degradation model. The optimization of the selection of the stress levels in a step stress accelerated degradation test (SSADT) is studied. The objective is to minimize the mean square error (MSE) of the prediction of the product operation reliability under the cost constraints. Through a Monte Carlo simulation method, the optimal stress levels and related sample size and test time are obtained. At last, the robustness of the results is shown through the sensitive analysis. INTRODUCTIONIn the reliability prediction of the product with long life and high reliability, since the accelerated degradation test (ADT) is able to utilize the information of the product performance degradation to make more sense of the prediction, it is widely applied.Relatively, as the step stress accelerated degradation test (SSADT) uses a small sample size and short test time, it is commonly performed in the practice. With the motivation of predicting the product reliability more precisely under certain constraints, the problem of the test plan optimization has drawn a lot of attentions.In this century, a lot of researchers have studied the optimization of ADT plans all over the world. With the test cost as the constraint and minimizing the asymptotic variance of the product p percentile life prediction as the objective, references [1] to [6] have optimized the plans of the ADTs, though the degradation processes are not modeled all the same in these references. And reference [6] has considered the optimization of the test stress levels.Using the mean time to failure (MTTF) as the minimizing criteria, in order to minimize the asymptotic variance, reference [7] developed an optimal plan for the design of ADT with a reciprocal Weibull degradation data. Reference [8] introduced the SSADT model when the degradation path follows a gamma process and optimized the test plan.Using the asymptotic variance of the product mean life at the use stress as a constraint, reference [9] optimized a SSADT with the product degradation process characterized by the appropriate stochastic model to minimizing the test cost.Reference [10] presented a novelty method of Monte Carlo simulation based optimal design for degradation test. And in order to minimize the mean square error (MSE) of the product p percentile life prediction, the authors in references [11] and [12] optimized the ADT with the degradation process modeled by a nonlinear mix-effect model.In practice, predicting the reliability of the product at a certain operation time has drawn a lot of concern. Therefore, in this paper, the optimal objective is selected to be minimizing the MSE of the prediction of the product operation reliability. While using the drift Brownian moti...
Aimed at the quantitative analysis for the run risk of dam, an evaluation method based on grey-stochastic risk analysis and its engineering application was put forward. According to the disposal of regarding the complicated uncertainty relationship in the run of dam as a grey-stochastic complex uncertainty, the analysis method of grey-stochastic risk probability was set up. By ascertaining the functional function, the grey-stochastic risk probability was transformed into commonly stochastic risk probability. Finally, the amended firstorder second-moment method was utilized to calculate quantitatively the failure risk of reservoir dam and the risk value obtained falls in a grey space, which satisfactorily reflects the uncertainty of the run risk of dam.
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