Burr XII分配產品在逐步型I區間設限下之壽命績效指標之最佳實驗設計

Experimental design for the lifetime performance index of Burr XII lifetime distribution under progressive type I interval censoring

鄭亦彣(Yi-Wen Zheng)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2020年)

https://doi.org/10.6846/TKU.2020.00651

摘要

隨著科技的日新月異，產品的製程逐漸變得繁複且精密。消費者在購買產品時，對於產品品質的要求也變得更為嚴苛。為了達到消費者所需求的品質，生產者在製造產品時，會對製程的要求更加嚴格，如何節省成本及避免造成不必要的浪費，以追求更多的利潤，已是當今生產者所必須重視的問題。
本研究假設產品的壽命服從Burr XII分配時，在逐步型I區間設限下，計算出壽命績效指標C_L之最大概似估計量，並使用此估計量作為檢定統計量進行假設檢定程序，本研究在逐步型I區間設限下決定最佳實驗設計以達到最小的總實驗成本，並以表格形式列出相關值供實際使用。最後，我們用兩個數值實例說明如何使用本研究所提出的最佳實驗設計的檢定程序。

關鍵字

設限樣本 ； Burr XII分配 ； 最大概似估計量 ； 製程能力指標 ； 檢定程序 ； 實驗設計

並列摘要

It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices CL is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Burr XII distribution. Based on the hypothesis testing procedure using the maximum likelihood estimator as testing statistic, the sampling design is determined and the related values are tabulated for practical use to reach the given power level or minimize the total experimental cost under progressive type I interval censoring. Some numerical studies are also given to demonstrate the proposed sampling design. 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

Censored sample ； Burr XII distribution ； Maximum likelihood estimator ； Process capability indices ； Testing algorithmic procedure ； Sampling Design

參考文獻

[1]Boyles, R.A. (1991), The Taguchi capability index, Journal of Quality Technology, 23(1), pp. 17-26

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

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[5]Cohen, A. C. (1991), Truncated and censored sample, Marcel Dekker, New York.