Estimating percentiles of time-to-failure distribution obtained from a Weibull accelerated degradation model

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We propose a nonparametric kernel estimation method to estimate the percentiles of the time-to-failure distribution under the usual use condition obtained from a Weibull accelerated degradation model. We discuss some of the well-known parametric method that used to estimate the time-to-failure distribution and its percentile under the usual use condition including ordinary least square method and maximum likelihood method. The different exiting methods were compared with the kernel method through simulation by using the mean square error and the bootstrap confidence interval length. In general, when the distributional assumption is available, the maximum likelihood estimator performs better than the other two estimators, while the kernel estimator performs better than the other two estimators when the distributional assumption is not available. Application to real data set was disscuced.