A note on the behaviour of the process capability index Cpmk with asymmetric specification limits

The properties of Cpmk in the presence of asymmetric specification limits are discussed. It is shown that Cpmk tends to zero as the process variation increases and vice versa. Furthermore, if the process variation is small, Cpmk has its maximum near the target value but the maximum moves towards the specification midpoint as the variation increases. This is a desirable property as 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. Attention is drawn to the fact that for small process variations there is a shoulder in the graph of Cpmk when the process mean is equal to the specification midpoint.