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Optimal Design for Degradation Tests Based on Gamma Process with Random Effects
【2012.11.07 10:00-11:00am,S309】

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 2012-10-31  

  Colloquia & Seminars 

  Speaker

  Sheng-Tsaing Tseng,台湾清华大学

  Title

  Optimal Design for Degradation Tests Based on Gamma Process with Random Effects

  Time

  2012.11.07 10:00-11:00am

  Venue

  S309

  Abstract

  Degradation models are usually used to provide information on the reliability of highly reliable products that are not likely to fail within a reasonable period of time under the traditional life tests or accelerated life tests. Gamma process is a natural model for describing degradation paths which exhibit a monotone increasing pattern, while the commonly used Wiener process is not appropriate in such a case. In this talk, we discuss the problem of optimal design for degradation tests based on a gamma degradation process with random effect. In order to conduct a degradation experiment efficiently, several decision variables (such as the sample size, inspection frequency, and measurement numbers) need to be determined carefully. These decision variables affect not only the experimental cost, but also the precision of the estimates of lifetime parameters of interest. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal decision variables are found by minimizing the asymptotic variance of the estimate of the 100p-th percentile of the lifetime distribution of the product. A laser data is used to illustrate the proposed method. Moreover, the effect of model mis-specification that occurs when the random effects are not taken into consideration in the gamma degradation model are assessed analytically. The numerical results of these effect reveal that the impact of model mis-specification on the accuracy and precision of the prediction of percentiles of the lifetimes of products are somewhat serious for the tail probabilities. A simulation study also shows that the simulated values are quite close to the asymptotic values.

  Affiliation

  Dr. Tseng received the B. S. degree in Business Mathematics from Soochow University, the M. S. degree in Applied Mathematics from Tsing-Hua University, and the Ph.D. degree in Management Science from Tamkang University, Taiwan. Currently, he is a chair professor in the Institute of Statistics at Tsing-Hua University, Taiwan. His research interests include reliability lifetime analysis, quality & productivity improvement, and statistical decision methodology. His articles have appeared in numerous technical journals such as Technometrics, Journal of Quality Technology, IIE Transactions, IEEE Transactions on Reliability, EJOR, NRL, JSPI, SS, IEEE Transactions on Semiconductor Manufacturing, and others. He has received the outstanding research award from the National Science Council of the ROC, Taiwan in 1993, 1999, and 2004. He is an elected member of ISI, and a member of the IEEE and a senior member of ASQ. 

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