A Modified Definition on the Process Capability Index Cpk Based on Median

Title & Authors
A Modified Definition on the Process Capability Index Cpk Based on Median
Park, Hyo-Il;

Abstract
This study proposes a modified definition about $\small{C_{pk}}$ based on median as the centering parameter in order to more easily control the process since the mean does not represent any quantile of the asymmetric process distribution. Then we consider an estimate and derive the asymptotic normality for the estimate of the modified $\small{C_{pk}}$. In addition, we provide an example with asymmetric distributions and discuss the estimation for the limiting variance that are followed by some concluding remarks.
Keywords
Asymmetric normality;median;process capability index;
Language
English
Cited by
1.
Concept of the One-Sided Variance with Applications,;

Communications for Statistical Applications and Methods, 2012. vol.19. 5, pp.743-750
1.
Concept of the One-Sided Variance with Applications, Communications for Statistical Applications and Methods, 2012, 19, 5, 743
References
1.
Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics-Basic Ideas and Selected Topics, Holden-Day, San Francisco.

2.
Chan, L. K., Xiong, Z. and Zhang, D. (1990). On the asymptotic distribution of some process capability indices, Communications in Statistics - Theory and Methods, 19, 11-18.

3.
Chen, S. M. and Pearn, W. L. (1997). The asymptotic distribution of the estimated process capability index \$C_{pk}\$, Communications in Statistics - Theory and Methods, 26, 2489-2497.

4.
Cho, J. J., Kim, J. S. and Park, B. S. (1999). Better nonparametric bootstrap confidence interval for process capability index \$C_{pk}\$, The Korean Journal of Applied Statistics, 12, 45-65.

5.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife, The Annals of Statistics, 7, 1-26.

6.
Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman and Hall, New York.

7.
Franklin, L. A. andWasserman, G. S. (1992). Bootstrap lower confidence interval limits for capability indices, Journal of Quality Technology, 24, 196-210.

8.
Gunter, B. H. (1989). The use and abuse of \$C_{pk}\$, Part 2, Quality Progress, 22, 108-109.

9.
Juran, J. M. (1974). Quality Control Handbook, 3rd. Ed., McGraw Hill, New York.

10.
Park, H. I. (2009). Median control charts based on bootstrap method, Communications in Statistics - Simulation and Computation, 38, 558-570.

11.
Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics, Wiley, New York.

12.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.

13.
Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap, Springer, New York.