良率的信賴區間估計

Confidence Interval for Proportion of Conformance

李宗翰

指導教授 ： 王秀瑛

國立交通大學/理學院/統計學研究所/碩士(2012年)

https://doi.org/10.6842/NCTU.2012.00238

摘要

在工業上，良率為生產產品之品質特性落在規格界限內的比例。當我們假設良品的個數服從二項分配時，那麼建造良率的信賴區間是一個在工業應用中很重要的過程。在這項研究中，我們提出了一個方法，以改善現有良率之信賴區間估計。我們設法建立了一個程序來計算所提出的區間之覆蓋率下界。而模擬研究則提供了在不同的區間下去比較各種區間的優點與缺點。

關鍵字

良率 ； 信賴區間 ； 二項分配 ； 覆蓋率

並列摘要

Proportion of conformance is defined as the proportion of products with quality characteristic inside the specification limits. The construction of confidence interval for proportion of conformance is an important problem in industrial applications, especially when the number of conforming units follows a binomial distribution. In this study, we propose an approach to improve the existing confidence intervals for proportion of conformance. We establish a procedure to calculate the lower bound for the coverage probability of proposed the intervals. A simulation study is provided to compare the performance of different intervals.

並列關鍵字

proportion of conformance ； confidence interval ； binomial distribution ； coverage probability

參考文獻

Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. American Statistical Association, 52, 119-126.

Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals. Journal of the American Statistical Association, 78, 108-116.

Brown, L. D., Cai, T. T., and DasGupta, A. (2001). Interval Estimation for a Binomial Proportion (with discussion). Statistical Science, 16, 101–133.

Chou, Y. and Owen, D.B. (1984). One-Sided Confidence Regions on the Upper and Lower Tail Areas of Normal Distribution. Journal of Quality Technology 16, 150-158.

Frey, J. (2010). Fixed-width sequential confidence intervals for a proportion. The American Statistician 64, 242–249.