A Note on the Behavior of C_pmk with Asymmetric Specification Limits

Abstract

The properties of C_pmk in the presence of asymmetric specification limits are discussed. It is shown that C_pmk tends to zero as the process variation increases and vice versa. Furthermore, if the process variation is small, C_pmk has its maximum near the target value but the maximum moves towards the specification midpoint as the variation increases. This may be a desirable property because for large variation the percentage of items inside the specification limits is larger if the process mean is equal to the specification midpoint than if it is equal to the target value. Considering C_pmk as a mixture of C_pk and C_pm, C_pmk behaves more like C_pm if the process variation is small, whereas C_pmk behaves more like C_pk if the process variation is large. Attention is drawn to the fact that for small process variations there is a shoulder in the graph of C_pmk when the process mean is equal to the specification midpoint.

• Process Capability Indices
• Statistical Process Control

Additional information

Notes on contributors

Jutta Jessenberger

Ms. Jessenberger is an external member of the Department of Statistics. Her email address is [email protected].

Claus Weihs

Dr. Weihs is a Professor in the Department of Statistics.