使用衰變與設限資料對壽命分配之推論

Inference for the Lifetime Distribution from Degradation and Censored Data

孫正文(Cheng-Wen Sun)

指導教授 ： 唐正 ； 黃榮臣

國立清華大學/理學院/統計學研究所/博士(2009年)

https://doi.org/10.6843/NTHU.2009.00562

摘要

The purpose of this dissertation is to study four statistical inference problems for the lifetime distribution based on censored Wiener degradation data. We first propose an effective method for collecting intermediate, non-failure threshold-crossing data from a highly reliable product and prove the asymptotic properties of our proposed estimators of the parameters for the inverse Gaussian lifetime distribution. A numerical study shows our method performs well as compared to two other traditional methods. As an alternative to the Kolmo-gorov-Smirnov test, we propose a model selection method and a goodness-of-fit test proce-dure to choose a better-fitted distribution to a censored lifetime dataset. We show our method has the same performance with traditional goodness-of-fit test by efficiency of Bahadur (1960). We obtain some sufficient conditions for the existence of an almost unbiased estima-tor (under the definition of Haldane) when an unbiased estimator does not exist under a gen-eral setting. We then demonstrate that some existing results in the Binomial case are special cases. Finally we show that, for the complete data case, unbiased estimators and almost unbi-ased estimators of the percentiles of the inverse Gaussian distribution do not exist, and, con-sequently, propose asymptotically unbiased estimators for complete and Type 2 censored sample cases.

關鍵字

衰變試驗 ； 模型選取 ； 適合度檢定 ； 幾乎不偏估計 ； 反高斯分布 ； 設限樣本

並列摘要

無資料

並列關鍵字

Degradation test ； Model selection ； Goodness-of-fit test ； Almost unbiased estimator ； Inverse Gaussian distribution ； Censored samples

參考文獻

[1]Abrahamson, I.G. (1967), “Exact Bahadur Efficiencies for the Kolmogorov- Smirnov and Kuiper One- and Two-Sample Statistics,” Annals of Mathematical Statistics, 38, 1475-1490.

[2]Anderson, T.W., and Darling, D.A. (1952), “Asymptotic Theory of Certain Goodness of Fit Criteria Based on Stochastic Processes,” Annals of Mathematical Statistics, 26, 193-213.

[3]Anscombe, F.J. (1956), “On Estimating and Significance of the Logarithm of a Ratio of Frequencies,” Biometrika, 43, 461-464.

[5]Bahadur, R.R. (1960), “Stochastic Comparison of Tests,” Annals of Mathematical Statis-tics, 31, 276-295.

[6]Balakrishnan, N., and Aggarwala, R. (2000), Progressive Censoring: Theory, Method, and Application, Boston: Birkhäuser.