Bootstrap Confidence Limits for Short-Run Capability Indices

Abstract

The capability indices are widely used by quality professionals as an estimate of process capability. Recently, techniques and tables were developed to construct confidence limits for each index. These techniques are based on the assumption that the underlying process is normally distributed. In industries it may not be possible to get large samples, and, hence, the normality assumption is often violated. For the short-run production processes where sample size is small, appropriate indices can be developed. In this article, the capability indices such as C _p , C _pk , and C _pm are modified, and appropriate capability indices are constructed. A further bootstrap technique is used to define the confidence intervals. A simulation using two distributions (one normal and the other nonnormal) is conducted, and a comparison is made to show the performances of the three nonparametric confidence intervals.

Keywords:

• Process capability indices
• Bootstrap method
• Normal process
• Nonnormal process

Acknowledgments

The author is grateful to Professor B. R. Cho, Department of Industrial Engineering, Clemson University for the constructive comments on the paper. The author is thankful to Professor K. Balachandran, Department of Mathematics, Bharathiar University for his help.