本論文主要是探討航空材料的相關壽命推估。就以往經驗來說，統計學家大都利用珈瑪分配來對其參數進行推估，及利用形狀參數(shape parameter)及比率參數(rate parameter)來找出一個適當的估計模式，然以現代高可靠度的產品來說，產品壽命有一定的壽命保證，因此本論文考慮了第三個變數：位置參數（location），來找出一個適當的估計模式。在本論文中，將利用黃提源與胡金源兩位教授所獲得「珈瑪分配之樣本平均數與樣本變異係數具有獨立」的特性，將珈碼分配的模式由兩個參數推廣為三個參數，來推導出上述三個未知參數的估計量，進而獲得先前對航空材料的相關壽命推估有高估或低估的現象。

【1】A.Vasudeva Rao, R.R.L.Kantam and V.L.Narasimham(1991), Linear Estimation Of Location And Scale Parameters In The Generalized Gamma Distribution,Co-
mmunications in Statistics－Theory and Method,20,3823－3848.
【2】Douglas G. Chapman (1953).Estimating the parameters of a truncated gamma distrib-
ution, Annals of Mathematical Statistics, 27, 498－506.
【3】Greenwood, J.A. and Durand D.(1960),Estimation for the three-parameter Weibull,
lognormal, and gamma distributions, Computational Statistics & Data Analysis, 3,11－13.
【4】Hideo Hirose(1995),Maximum likelihood parameter estimation in the three -paramet- er gamma distribution, Computational Statistics & Data Analysis, 20,343-35.
【5】H.Leon Harter and Albert H. Moore(1965),Maximum-likelihood estimation of the parameters of gamma and Weibull populations from complete and from censored sa-
mples,Technometrics,7,639-643.
【6】Hwang, T.Y. and Hu , C.Y. ( 1999 ) . On a characterization of the gamma distribut-
ion : The independence of the sample mean and the sample coefficient of Variation, Annals of the Institute of Statistics Mathematics , 51 , 749-753 , Japan .
【7】Hwang, T.Y. and Hu , C.Y. ( 2000 ) . On some characterization of population distribution , Taiwanese Journal of Mathematics 4 ,3 ,427-437, ROC.
【8】J.F. Lawless(1982) .Statistical models and methods for lifetime data .
【9】Shih-Tai Kao(2000). On the Probability Model of the Failure Time for the Air Conditioning System, Master Thesis, Institute of Statistics , National Tsing Hua University , Taiwan .
【10】Anita Singh(1982).Exact Distribution of Wilks’ L Criterion and Its Percentage Points In The Complex Case,Communications in Statistics simulation and computation,11（2）,217-225.