On C_pk Assessment in the Presence of Tool Wear

Abstract

Process capability indices are routinely used in manufacturing industries for process monitoring. A basic assumption while using process capability indices is that there are no assignable causes of variation present. However, when variation due to an assignable cause is present and is tolerated, the conventional methods of capability measurement become inaccurate. In this article, we suggest an estimate of C_pk assuming that the process capability changes dynamically. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. We discuss the problem of testing whether a given process is capable. The critical values for different sample sizes are obtained based on the sampling distribution. An example involving tool wear problem is presented.

Keywords:

• Critical value
• Dynamic capability
• Instantaneous capability
• Process capability
• Replacement time
• Systematic assignable cause

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62F03

Acknowledgments

Thanks are due to the Editor and the anonymous reviewer for their constructive comments which has lead to considerable improvement in the presentation.