Abstract
When optimizing an accelerated degradation testing (ADT) plan, the initial values of unknown model parameters must be pre-specified. However, it is usually difficult to obtain the exact values, since many uncertainties are embedded in these parameters. Bayesian ADT optimal design was presented to address this problem by using prior distributions to capture these uncertainties. Nevertheless, when the difference between a prior distribution and actual situation is large, the existing Bayesian optimal design might cause some over-testing or under-testing issues. For example, the implemented ADT following the optimal ADT plan consumes too much testing resources or few accelerated degradation data are obtained during the ADT. To overcome these obstacles, a Bayesian sequential step-down-stress ADT design is proposed in this article. During the sequential ADT, the test under the highest stress level is firstly conducted based on the initial prior information to quickly generate degradation data. Then, the data collected under higher stress levels are employed to construct the prior distributions for the test design under lower stress levels by using the Bayesian inference. In the process of optimization, the inverse Gaussian (IG) process is assumed to describe the degradation paths, and the Bayesian D-optimality is selected as the optimal objective. A case study on an electrical connector’s ADT plan is provided to illustrate the application of the proposed Bayesian sequential ADT design method. Compared with the results from a typical static Bayesian ADT plan, the proposed design could guarantee more stable and precise estimations of different reliability measures.
Highlights
Acceleration degradation testing (ADT) is commonly used to obtain degradation data of products over a short time period, to help extrapolate lifetime and reliability under usage conditions [1].In an accelerated degradation testing (ADT), products are exposed to higher-than-use conditions to get the degradation data in a short time [2,3]
To capture the uncertainties embedded in these parameters, Bayesian ADT design is utilized, and this method treats model parameters as random variables by assigning prior distributions based on the available historical data and expert’s knowledge
In order to illustrate the proposed method, we assume that a sequential ADT is conduct on the electric connectors given in Yang [28], and their stress relaxation data are used to build up the initial prior distributions in this case study
Summary
Acceleration degradation testing (ADT) is commonly used to obtain degradation data of products over a short time period, to help extrapolate lifetime and reliability under usage conditions [1]. Proposed a Bayesian design method for ADT, with physically-based statistical models. Entropy 2017, 19, 325 power-law statistical degradation model with nonlinear stress life relationships is developed Based on this model, the optimal objective is to minimize the expected pre-posterior variance of the quantile life at the use condition. When the difference between prior information and the actual situation is large, the optimal plan designed by the static Bayesian design method might lead to the over-testing or under-testing problems, which means the test resources have been consumed more or the collected ADT data are insufficient. Using the information obtained at the highest stress level, a Bayesian framework was proposed to optimally determine both the sample allocation and stress combination at lower stress levels of subsequent accelerated tests.
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