Abstract
Step-stress accelerating life test (SSALT), aiming to predict the failure behavior under use condition by the data collected from elevated test setting, is implemented to specimen with time-varying stress levels. Typical testing protocols in SSALT, such as subsampling, cannot guarantee complete randomization and thus result in correlated observations among groups. To consider the random effects from the group-to-group variation, we build a nonlinear mixed effect model (NLMM) with the assumption of Weibull distribution for life time data analysis from SSALT. Both maximum likelihood estimation (MLE) and Bayesian inference are introduced for the estimation and prediction of model parameters as well as other statistics of interest. Gauss–Hermite (G-H) quadrature is used to obtain an accurate approximation of the likelihood for observations, and different priors of model parameters are applied in Bayesian analysis. A comprehensive simulation study and an analysis for a real data set are conducted to justify the proposed method, suggesting that the incorporation of the random effect from the underlying experimental routine ensures a more solid and practical conclusion when the heterogeneous group effect is statistically significant.
Highlights
In stress accelerating life test (SSALT), the test units experience more than one level of stress progressively; that is, once the units have sustained a prespecified duration under the one stress level, they will be tested under an escalated stress level and so on
SSALT is commonly used in dioxide, electrical cable insulation, insulation fluid, and rear suspension. e advantages from SSALT include the following: it substantially shortens the length of a test without affecting the accuracy of estimation in life time distribution; it is more practical in the sense that fewer test units are required; and it is a flexible strategy in that the stress levels and transition time can be adjusted according to the failure information collected over time
For the tractability in model derivation under the framework of generalized linear mixed effect model (GLMM) or GLM, exponential distribution is usually postulated; under a more general assumption of Weibull distribution, we developed a nonlinear mixed effect model (NLMM) method to analyze failure data from SSALT with random group effects
Summary
Is experimental protocol, called subsampling, assures the stress exerts directly to the test stand other than individual test units and leads to clustered/dependent quality for failure data; besides, different operators or test stands invite heterogeneity as well. Another violation of randomization relates to the raw material produced in batches. For the tractability in model derivation under the framework of GLMM or GLM, exponential distribution is usually postulated; under a more general assumption of Weibull distribution, we developed a NLMM method to analyze failure data from SSALT with random group effects. Two estimation methods are explored: G-H quadrature serves to get an accurate approximation of likelihood in MLE; different priors in the Bayesian method signify the impact of the uncertainty to model parameters. e analysis from both a simulated data set and a real data set proves that when the group-to-group variation is present, the integration of the random effect in modeling ensures a more precise estimation and prediction
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