本篇論文主要是以珈碼分配（Gamma Distribution）來擬合軸承之疲勞壽命機率模式，進而經由兩個常用的可靠度衡量指標：平均失效時間(Mean Time To Failure)及第100p百分位數（100p-th percentile）以推估其可靠度。
一直以來，如何找出適當參數估計量是備受爭議的問題，因此本論文中將利用珈碼分配中樣本平均數(sample mean)與樣本變異係數(sample coefficent of variance)近似不偏估計量及其信賴區間。

而且研究結果顯示：本論文之不偏估計量有勝以往估計量的優點，在小樣本時，推估可靠度的誤差最小。

1.研究動機與目的

2.樣本平均數與樣本變異係數之相關定理

3.珈碼分配之參數推估

4.相關文獻之回顧與各估計方法之適用性比較

5.形狀參數的信賴區間之推估

6.軸承之實例探討

參考文獻

附錄一

附錄二

附錄三

[1]J.Lieblein and M.Zelen ( 1956 ) .Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings, Journal of Research of the National Bureau of Standards.
[2]William Q.Meeker and Luis A.Escobar (1998) .Statistical Methods for Reliability Data.
[3] Hwang , T.Y. and Hu , C.Y. ( 1999 ) . On a characterization of the gamma distribution : The independence of the sample mean and the sample coefficient of variation , Annals of the Institute of Statistics Mathematics , 51 , 749-753 , Japan .
[4] Hwang , T.Y. and Hu , C.Y. ( 2000 ) . On some characterization of population distribution , appear in Taiwanese Journal of Mathematics .
[5] H,C.Y. (1990). On Signal to Noise Ratio Statistics , Ph.D.thesis,Institute of Statistics ,National Tsing Hua University ,Taiwan.
[6] Lin, Y.K. (1998) . Further study on the sampling distribution of the coefficient of varaiation under exponential population , Master Hieais , Institute of Statistics , National Tsing Hua University , Taiwan .
[7] H.C.S.Thom ( 1958 ) . A note of the gamma distribution , appear in Monthly Weather Review , Vol.86 ,No.4 ,117-121.
[8] Greenwood ,J.A.and Durand D. ( 1960 ) . Aids for Fitting the Gamma Distribution by Maximum likelihood , Vol.2,55-65.
[9] Wilk et al. ( 1962 ) .Estimation of parameters of gamma distribution using order statistics ,49, 525-545 .
[10]Lawless J.F. ( 1982 ).Statistical models and methods for lifetime data , Canada Wiley .
[11]Bain L.J. and Engelhardt M. ( 1991). Statistical analysis of reliability and life-testing models .
[12] M.Masuyama and Y.Kuroiwa ( 1951). Table of the Likelihood Solutions of Gamma Distribution and its Medical Applications , Statistical Application Research , vol.1, No.1.