Estimating and Testing Quantile-based Process Capability Indices for Processes with Skewed Distributions

This article extends the recent work of Vannman and Albing (2007) regarding the new family of quantile based process capability in- dices (qPCI) CM A(τ, v). We develop both asymptotic parametric and non- parametric confidence limits and testing procedures of CM A(τ, v). The ker- nel density estimator of process was proposed to find the consistent estima- tor of the variance of the nonparametric consistent estimator of CM A(τ, v). Therefore, the proposed procedure is ready for practical implementation to any processes. Illustrative examples are also provided to show the steps of implementing the proposed methods directly on the real-life problems. We also present a simulation study on the sample size required for using asymptotic results.

[1]  Joseph Moses Juran,et al.  Quality-control handbook , 1951 .

[2]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[3]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[4]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[5]  Kerstin Vännman,et al.  A uniformed approach to capability indices , 1995 .

[6]  Rob J Hyndman,et al.  Sample Quantiles in Statistical Packages , 1996 .

[7]  Taiwan Roc,et al.  AN APPLICATION OF NON-NORMAL PROCESS CAPABILITY INDICES , 1997 .

[8]  W. Pearn,et al.  Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing , 1997 .

[9]  Lora S. Zimmer,et al.  Process Capability Indices in Theory and Practice , 2000, Technometrics.

[10]  배도선,et al.  비대칭 모집단에 대한 공정능력지수의 개발 ( Process Capability Indices for Skewed Populations ) , 2000 .

[11]  Do Sun Bai,et al.  Control charts for positively‐skewed populations with weighted standard deviations , 2001 .

[12]  Do Sun Bai,et al.  Process capability indices for skewed populations , 2002 .

[13]  Gerry Leversha,et al.  Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press). , 2003, The Mathematical Gazette.

[14]  Yu-Sheng Hsu,et al.  Asymptotic analysis of estimators for C Np (u, v) based on quantile estimators , 2003 .

[15]  Fred A. Spiring,et al.  A Bibliography of Process Capability Papers , 2003 .

[16]  Hung-Chin Lin,et al.  The measurement of a process capability for folded normal process data , 2004 .

[17]  P. C. Lin.  Application of the generalized folded-normal distribution to the process capability measures , 2005 .

[18]  Dennis K. J. Lin,et al.  Another Look at the Process Capability Index , 2006, Qual. Reliab. Eng. Int..

[19]  Kerstin Vännman,et al.  Process capability indices for one-sided specification intervals and skewed distributions , 2007, Qual. Reliab. Eng. Int..