| Summary: | 碩士 === 國立中央大學 === 統計研究所 === 102 === In order to study the failure time of industrial product of high reliability under normal situation, we usually observe its quality characteristics (QC) degraded over time under some more severe stress conditions which is called an accelerated degradation test. Because the accelerated degradation QC is often non-increasing or non-decreasing, the QC decrement or increment is a nonnegative random variable. Assume that the random variable is distributed according to a generalized gamma distribution, the p quartile failure time (t_p) is of interest at which 100*p% of products reach the threshold value of QC. In addition to obtaining the confidence lower bound of t_p based on its maximum likelihood estimate, we also find the credible lower bound of t_p . A simulation study is conducted to investigate the performance of the proposed lower bounds. The results show that the coverage probability of the confidence lower bound of t_p is not able to maintain its confidence level, while the credible lower bound of t_p holds well its confidence level. Finally, a real data set is illustrated to demonstrate the application of the proposed lower bounds.
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