Advanced SearchSearch Tips
On the Plug-in Estimator and its Asymptotic Distribution Results for Vector-Valued Process Capability Index Cpmk
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
On the Plug-in Estimator and its Asymptotic Distribution Results for Vector-Valued Process Capability Index Cpmk
Cho, Joong-Jae; Park, Byoung-Sun;
  PDF(new window)
A higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The third generation index is more powerful than two useful indices and that have been widely used in six sigma industries to assess process performance. In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent the variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, we consider more powerful vector-valued process capability index = (, ) that consider the univariate process capability index . First, we examine the process capability index and plug-in estimator . In addition, we derive its asymptotic distribution and variance-covariance matrix for the vector valued process capability index . Under the assumption of bivariate normal distribution, we study asymptotic confidence regions of our vector-valued process capability index = (, ).
Vector-valued process capability index;plug-in estimator;limiting distribution;variance covariance matrix;asymptotic confidence region;
 Cited by
Alt, F. B. and Smith, N. D. (1988). Multivariate Process Control, In P.R. Krishnaiah and C.R.Rao, Editors, Handbook of Statistics, 7, North-Holland, Amsterdam, 333-351.

Chan, L. K., Xiong, Z. and Zhang, D. (1990). On the asymptotic distributions of some process capability indices, Communications in Statistics: Theory and Methods, 19, 11-18. crossref(new window)

Cho, J. J., Kim, J. S. and Park, B. S. (1999). Better nonparametric bootstrap confidence interval for process capability index $C_{pk}$, Korean Journal of Applied Statistics, 12, 45-65.

Franklin, L. A. and Wasserman, G. S. (1992). Bootstrap lower confidence interval limits for capability indices, Journal of Quality Technology, 24, 196-210.

Hubele, N. F., Shahriari, H. and Cheng, C. S. (1991). A bivariate process capability vector, Statistical Process Control in Manufacturing(J.B. Keats and D.C. Montgomery, eds.), New York, 299-310.

Kocherlakota, S. and Kocherlakota, K. (1991). Process capability indices: Bivariate Normal distribution, Communication in Statistics: Theory and Methods, 20, 2529-2547. crossref(new window)

Kotz, S. and Johnson, N. L. (1993). Process Capability Indices, 1st ed., Chapman & Hall.

Niverthi, M. and Dey, D. K. (2000). Multivariate process capability, a Bayesian perspective, Communication in Statistics: Simulation and Computation, 29, 667-687. crossref(new window)

Park, B. S., Lee, C. H. and Cho, J. J. (2002). On the confidence region of vector-valued process capability indices $C_p$ and $C_{pk}$, Journal of the Korean Society for Quality Management, 30, 44-57.

Pearn, W. L., Kotz, S. and Johnson, N. L. (1992). Distributional and inferential properties of process capability indices, Journal of Quality Technology, 24, 216-231.

Pearn, W. L., Wang, F. K. and Yen, C. H. (2007). Multivariate capability indices: Distributional and inferential properties, Journal of Applied Statistics, 34, 941-962. crossref(new window)

Shahriari, H. and Abdollahzadeh, M. (2009). A new multivariate process capability vector, Quality Engineering, 21, 290-299. crossref(new window)

Taam, W., Subbaiah, P. and Liddy, J. W. (1993). A note on multivariate capability indices, Journal of Applied Statistics, 20, 339-351. crossref(new window)