Practical Implementation of the Capability Index C_pk Based on the Control Chart Data

ABSTRACT

Process capability indices are used to measure the ability of the process to manufacture product that meets specification requirement. Since estimated capability index is a random variable with a distribution, most practitioners look at the value of the capability index calculated from the given sample and then make a conclusion on whether the given process as capable or not which will not be reliable. In this paper, based on the theory of statistical hypothesis testing, when the process is in a state of statistical control, we propose a procedure on assessing C _pk index for practitioners to use in determining whether a given process as capable. We consider the case where process measurements are collected from the control chart data, as a sequence of independent samples. Applying Hamaker's approximation, the testing procedure can be adequately derived from a normal distribution approximation and that the more complicated distribution can be avoided. These proposed techniques would be especially applicable when the data are taken from X¯ and R, and X¯ and S control charts.

Keywords:

• Process capability index
• Process mean
• Process standard deviation
• p-value
• Hamaker's approximation.

ACKNOWLEDGEMENTS

The authors would like to thank the referees for helpful comments and suggestions, which significantly improved the paper. The research was partially supported by Grand NSC 92-2213-E-238-014, National Science Council, Taiwan, Republic of China.

Notes

Note: Tables appear in the Appendix B.

Summary statistics: ¯X¯ = 74.0012; R¯ = 0.0232; S¯ = 0.0094.