在逐步型I區間設限下對單參數柏拉圖分配的壽命績效指標之檢定程序

A testing procedure for the lifetime performance index of products with one-parameter pareto distribution under progressive type I interval censoring

盧錦洋(Jin-Yang Lu)

指導教授 ： 吳淑妃

淡江大學/管理學院/統計學系碩士班/碩士(2012年)

https://doi.org/10.6846/TKU.2012.00477

摘要

近年來,由於科技的進步,許多高科技產品像是電腦，手機等等，使得消費者對於產品品質要求更加嚴格，在實務上，已經發展了很多種方法來評估產品的品質能力，製程能力指標(process capability indices, PCIs)就是其中一種方法。
製程能力指標已經被廣泛地用於評估製程的績效以及不斷地提升產品品質及製程能力。當產品的壽命服從單參數柏拉圖分配時，望大型的壽命績效指標應該是被考慮的。在逐步型I區間設限下，我們求出壽命績效指標之最大概似估計量並探討其漸近分配。在規格下限已知的情形下，我們使用此估計量發展出一個新的假設檢定程序以判定壽命績效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所提出的檢定程序。

關鍵字

逐步型I區間設限 ； 柏拉圖分配 ； 最大概似估計量 ； 製程能力指標 ； 檢定程序

並列摘要

In recent years, consumers are in the pursuit of more stringent product quality requirements for many high-tech products such as computers, mobile phones, etc. In practice, many researchers have developed a variety of methods to assess the quality of the product and the method of process capability indices (PCIs) is one of them.
Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. When the lifetime of products possesses a one-parameter pareto distribution, the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

並列關鍵字

progressive type I interval censored ； one-parameter pareto distribution ； maximum likelihood estimator ； process capability index ； a testing procedure

參考文獻

[1] Aggarwala, R. (2001), Progressive interval censoring: some mathematical results with applications to inference, Communications in Statistics - Theory and Methods 30 ,1921–1935.

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

[3] Boyles, R.A. (1991). The Taguchi capability index, Journal of Quality Technology, 23, 17-26.

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

[6] Cohen, A. C. (1963), Progressively censored samples in the life testing, Technometrics, 5, 327-339.