教師資料查詢 | 類別: 期刊論文 | 教師: 蔡志群CHIH-CHUN TSAI (瀏覽個人網頁)

標題:Mis-specification analyses of gamma and Wiener degradation processes
學年100
學期1
出版(發表)日期2011/12/01
作品名稱Mis-specification analyses of gamma and Wiener degradation processes
作品名稱(其他語言)
著者Tsai, Chih-Chun; Tseng, Sheng-Tsaing; Balakrishnan, N.
單位淡江大學數學學系
出版者Amsterdam: Elsevier BV * North-Holland
著錄名稱、卷期、頁數Journal of Statistical Planning and Inference 141(12), pp.3725-3735
摘要Degradation models are widely used these days to assess the lifetime information of highly reliable products if there exist some quality characteristics (QC) whose degradation over time can be related to the reliability of the product. In this study, motivated by a laser data, we investigate the mis-specification effect on the prediction of product's MTTF (mean-time-to-failure) when the degradation model is wrongly fitted. More specifically, we derive an expression for the asymptotic distribution of quasi-MLE (QMLE) of the product's MTTF when the true model comes from gamma degradation process, but is wrongly assumed to be Wiener degradation process. The penalty for the model mis-specification can then be addressed sequentially. The result demonstrates that the effect on the accuracy of the product's MTTF prediction strongly depends on the ratio of critical value to the scale parameter of the gamma degradation process. The effects on the precision of the product's MTTF prediction are observed to be serious when the shape and scale parameters of the gamma degradation process are large. We then carry out a simulation study to evaluate the penalty of the model mis-specification, using which we show that the simulation results are quite close to the theoretical ones even when the sample size and termination time are not large. For the reverse mis-specification problem, i.e., when the true degradation is a Wiener process, but is wrongly assumed to be a gamma degradation process, we carry out a Monte Carlo simulation study to examine the effect of the corresponding model mis-specification. The obtained results reveal that the effect of this model mis-specification is negligible.
關鍵字Gamma process; Wiener process; Model mis-specification; Mean-time-to-failure; Quasi-maximum likelihood estimate
語言英文
ISSN0378-3758
期刊性質
收錄於SCI
產學合作
通訊作者
審稿制度
國別荷蘭
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