Asymptotic analysis of estimators for CNp(u, v) based on quantile estimators

Sy Mien Chen; Yu Sheng Hsu

doi:10.1080/1048525031000089338

Asymptotic analysis of estimators for C_Np(u, v) based on quantile estimators

Sy Mien Chen, Yu Sheng Hsu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Pearn and Chen (1997) proposed a class of capability indices C_Np(u, v) which generalize the process capability indices C_p(u, v) (Vännman, 1995) to accommodate cases where the underlying distributions may not be normal. The current indices C_Np(u, v) are functions of quantiles which may not be known. In this article, we apply some existing quantile estimators to estimate the class of indices C_Np(u, v). It is shown that the estimators of C_Np(u, v) we propose are all asymptotically normally distributed and equivalent and can perform better than the estimated C_p(u, v) in some instances.

Original language	English
Pages (from-to)	137-150
Number of pages	14
Journal	Journal of Nonparametric Statistics
Volume	15
Issue number	2
DOIs	https://doi.org/10.1080/1048525031000089338
State	Published - Apr 2003

Keywords

Asymptotic distribution
Process capability index
Quantile estimator
Specification limits

Access to Document

10.1080/1048525031000089338

Cite this

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title = "Asymptotic analysis of estimators for CNp(u, v) based on quantile estimators",

abstract = "Pearn and Chen (1997) proposed a class of capability indices CNp(u, v) which generalize the process capability indices Cp(u, v) (V{\"a}nnman, 1995) to accommodate cases where the underlying distributions may not be normal. The current indices CNp(u, v) are functions of quantiles which may not be known. In this article, we apply some existing quantile estimators to estimate the class of indices CNp(u, v). It is shown that the estimators of CNp(u, v) we propose are all asymptotically normally distributed and equivalent and can perform better than the estimated Cp(u, v) in some instances.",

keywords = "Asymptotic distribution, Process capability index, Quantile estimator, Specification limits",

author = "Chen, {Sy Mien} and Hsu, {Yu Sheng}",

note = "Funding Information: The authors appreciate two referees{\textquoteright} and editor{\textquoteright}s comments from which the presentation of this article is greatly improved. The research of the first author was partially supported by Grant NSC 88-2118-M030-001, National Science Council, Taiwan, Republic of China.",

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T1 - Asymptotic analysis of estimators for CNp(u, v) based on quantile estimators

AU - Chen, Sy Mien

AU - Hsu, Yu Sheng

N1 - Funding Information: The authors appreciate two referees’ and editor’s comments from which the presentation of this article is greatly improved. The research of the first author was partially supported by Grant NSC 88-2118-M030-001, National Science Council, Taiwan, Republic of China.

PY - 2003/4

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N2 - Pearn and Chen (1997) proposed a class of capability indices CNp(u, v) which generalize the process capability indices Cp(u, v) (Vännman, 1995) to accommodate cases where the underlying distributions may not be normal. The current indices CNp(u, v) are functions of quantiles which may not be known. In this article, we apply some existing quantile estimators to estimate the class of indices CNp(u, v). It is shown that the estimators of CNp(u, v) we propose are all asymptotically normally distributed and equivalent and can perform better than the estimated Cp(u, v) in some instances.

AB - Pearn and Chen (1997) proposed a class of capability indices CNp(u, v) which generalize the process capability indices Cp(u, v) (Vännman, 1995) to accommodate cases where the underlying distributions may not be normal. The current indices CNp(u, v) are functions of quantiles which may not be known. In this article, we apply some existing quantile estimators to estimate the class of indices CNp(u, v). It is shown that the estimators of CNp(u, v) we propose are all asymptotically normally distributed and equivalent and can perform better than the estimated Cp(u, v) in some instances.

KW - Asymptotic distribution

KW - Process capability index

KW - Quantile estimator

KW - Specification limits

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U2 - 10.1080/1048525031000089338

DO - 10.1080/1048525031000089338

M3 - 期刊論文

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SN - 1048-5252

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EP - 150

JO - Journal of Nonparametric Statistics

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