壽命的統計分析對於各個嶺域的統計學家及工作者都引起相當大的興趣，
例如:生物科技、醫藥醫學方面的倖存分析、工業工程的可靠度分析等。其

中這方面的研究，在最近這幾年來其延伸的速度非常的快，而且有關這方

面的相關刊物更是層出不窮。在這篇論文□，我們主要是利用樣本變異係數

去導出空調系統壽命之機率模型，以便在空調系統的例行性維修方面獲得較

可靠的可靠度預測。而其所得之結論為：在不同的樣本數下，使用不同的參

數估計式對於可靠度的預測會造成高估或低估的現象。

The statistical analysis of lifetime has become a topic of considerable interest to statisticians and workers in areas such as engineering, medicine, and the biological sciences. The field has expanded rapidly in recent years, and publications on the subject can be found in the literatures of several other disciplines besides statistics. In this paper, the sample coefficient of variation is used to derive the probability model of the lifetime for the air conditioning system, and the prediction of reliability would be more reliable and available for scheduling maintenance. The conclusion would be drawn as: some predictions of reliability are overestimate and are underestimate by using different estimators for different sample size.
1. Introduction …..………………………………………………….. …1

2. The Related Theorems of Sample Coefficient of Variation ….… ………3

3. The Estimation of the Parameters for Gamma Distribution……. ……...6

4. Comparisons With the Previous Estimates…………………… ……...9

5. Confidence Interval for Shape Parameter..……………………… …..11

6. Application to Boeing Scientific Research…………..…………….. …..13

References ………….…………………………………………… 18

Appendix I…………..……………………………………………….20

Appendix II.………………………………………………………….32

Appendix III ……………………………………………………….…33

Appendix IV………………………………………………………..….34

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[2] Bain Lee J. and Engelhadt Max, Statistical Analysis of Reliability and Life-Testing Models, 1991, p300.
[3] Cramer H., Mathematical Methods of statistics , Princeton University Press ,1946, p.348.
[4] Fisher R.A.," On the Mathematical Foundations of Theoretical Statistics ,"Philosophical Transactions Royal society ,Series A, vol. 222, 1941,pp.309-368.(1941).
[5] Greenwood, J. A. and Durand, D. (1960). Aids for fitting the gamma distribution by maximum likelihood, Technometrics, 2, 55-65.
[6] Hastings C., Jr; J. T. Hayward; AND J. P. Wong, JR. (1955) Approximations for digital computers.p155-163 Princeton Univ. Press, etc.