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標題: 損壞個數之貝氏預測區間--以指數分配之設限資料為例
Bayesian Prediction Intervals for a Future Number of Failures Based on Censored Data from Exponential Population
作者: 陳衍成
Chen, Yen-Cheng
關鍵字: 設限資料;Censored data;貝氏預測區間;覆蓋機率;指數分配;within-sample;Bayesian prediction interval;coverage probability;exponential distribution
出版社: 應用數學系所
引用: References [1] Cox, D. R. (1953), Some Simple Approximate Tests for Poisson Variates, Biometrika, 40, 354-360. [2] Escobar, L. A. and Meeker, W. Q. (1999), Statistical Prediction Based on Censored Life Data, Technometrics, 41, 113-124. [3] Hahn, G. J. and Nelson, W. (1973), A Survey of Prediction Intervals and Their Applications, Journal of Quality Technology, 5, 178-188. [4] Lawless, J. B. (2003), Statistical Model and Methods for Lifetime Data, John Wiley & Sons, Inc. New York. [5] Nelson, W. (1972), Statistical Methods for the Ratio of Two Multinomial Proportions, The American Statistician, 26, 22-27. [6] Nelson, W. (2000), Weibull Prediction of a Future Number of Failures, Quality and Reliability Enginerring International, 16, 23-26. [7] Nordam J. D. and Meeker, W. Q. (2002), Weibull Prediction Intervals for a Future Number of Failures, Technometrics, 44, 15-24. [8] Patel, J. K. (1989), Prediction Intervals—A Review, Communications in Statistic—Theory and Methods, 18, 2393-2465. [9] Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods For Reliability Data, John Wiley & Sons, Inc. New York.
此篇論文使用貝氏(Bayesian)方法去預測未來某期間內,某物件損壞個數。本人假設物件之生命長度依循指數分配。而取得之資料為設限資料(censored data)。我們提供了一個基於靴拔(Bootstrap)理論的計算法來處理繁瑣的貝氏方法中的積分。最後我們將貝氏方法所得之預測結果與一些其他預測方法做比較。我們使用覆蓋機率的概念去衡量預測方法的精準與否。結果顯示出貝氏預測方法在預測損壞個數的區間比其他方法精準。

In this paper Bayesian method is used to find prediction intervals of the future number of failures based on censored data. The failure time of such units is assumed to follow an exponential distribution. A bootstrap-based algorithm is proposed to work out the tedious computation of Bayesian integration. Comparisons are made among the results obtained by Bayesian method and some other available prediction methods based on within sample. We use coverage probability concepts for evaluating the appropriateness of prediction intervals. The results suggest that the Bayesian method performs better than all other alternatives.
其他識別: U0005-2606200615543500
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