A Note on the Behavior of C_(pmk) With Asymmetric Specification Limits

摘要

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.