On the Asymptotic Confidence Intervals of Multiple-Stream Yield Index S_pk^M

Author： Wang Dja-Shin Chou Chao-Yu Lin Yu-Chang

ISSN： 0361-0926

Source： Communications in Statistics: Theory and Methods, Vol.40, Iss.22, 2011-11, pp. : 3948-3958

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Abstract

The process capability index is a simple quantitative way to assess the capability of a process. To measure the overall yield of a multiple-stream process, Wang et al. (2009) proposed a yield index, denoted by , and then provided a point estimator of for practical industrial applications. In addition to point estimation, interval estimation plays an important role in statistical inference on the process index. In the present paper, we consider the problem of constructing the confidence interval for . First, the sampling distribution of is derived by applying Central Limit Theorem and the method of cumulative distribution functions. Then, the confidence intervals for are obtained using numerical integration by coding a MATLAB computer program. Several useful tables are provided for the purpose of constructing the confidence intervals of . A numerical example is presented to show how these tables may be applied for interval estimation of in a real production process.