Fréchet分配產品的壽命績效指標在逐步型II設限下之統計檢定程序

A testing procedure for the lifetime performance index of products with Fréchet distribution under progressive type II censoring

張文瑞(Wen-Jui Chang)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00422

摘要

近年隨著時代的進步，科技產業的快速發展，使得高科技的產品不斷推陳出新，更由於市場的高度競爭，所以對於產品品質的要求也不斷提高，因此，提升產品品質變得相對重要。在實務上，製程能力指標(process capability indices, PCIs)被廣泛應用在評估製程的績效，進而不斷地提升產品品質及製程能力。
本研究假設產品服從Fréchet分配時，在逐步型II設限下，提出一些樞紐量，以對參數做區間估計，並使用壽命績效指標之最大概似估計量，探討其精確分配，在規格下限已知的情況下，發展出一個新的假設檢定程序，以判定壽命績效指標是否達到預定的能力水準。最後，我們用兩個數值實例去說明如何使用本研究提出的區間估計和檢定程序。

關鍵字

逐步型II設限 ； Fréchet分配 ； 最大概似估計量 ； 製程能力指標 ； 檢定程序

並列摘要

In recent years, the development of technology industry is pretty fast, and the high-tech products are also innovated quickly. Due to the highly competitive commercial market, the requirement of high quality products becomes much more important. In practice, process capability indices (PCIs) have been widely used to assess the performance of the process, and then continue to improve the product quality and process capability.

This research is focusing on the lifetime of products which follow the Fréchet distribution. Some pivotal quantities are proposed to construct the interval estimation of parameters. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type II censored sample, and we use this estimator to develop the hypothesis testing algorithmic procedure for the process capability index in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the proposed interval estimation and the testing algorithmic procedure to determine whether the process is capable.

並列關鍵字

progressive type II censoring ； Fréchet distribution ； maximum likelihood estimator ； process capability index ； testing procedure

參考文獻

[1] Balakrishnan, N. and Aggarwala, R. (2000), Progressive Censoring: Theory, Methods and Applications, Birkhauser Publisher, Boston.

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[3] Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), A new measure of process capability: Cpm, Journal of Quality Technology, 20(3), pp.162-175.

[4] Cohen, A. C. (1963), Progressively Censored Samples in Life Testing, Technometrics, 5(3), pp. 327-339.

[5] Fisher, R. A. and Tippett, L. H. C. (1928), Limiting forms of the frequency distribution of the largest or small member of a sample, Proc. Cambridge Phil. Soc., 24, pp.180-190.