Cp and Pp

Capability indices that measure whether a process is capable of meeting specifications by calculating a ratio between the specification spread and the process spread. In general, the higher your Cp and Pp values, the more capable your process. To calculate Cp and Pp, you must know both the upper and lower specification limits.

Cp indices recognize the fact that your samples represent rational subgroups, which indicate how the process would perform if the shift and drift between subgroups could be eliminated. Therefore, it calculates process spread using within-subgroup variation.

Pp, on the other hand, ignores subgroups and considers the overall variation of the entire process. This overall variation accounts for the shift and drift that can occur between subgroups; therefore, it is useful in measuring capability over time. If your Pp value differs greatly from your Cp value, you conclude that there is significant variation from one subgroup to another.

Compare your Cp and Pp values to benchmark values to determine whether to improve your process; many industries use benchmark values of 1.33. If the values of your indices are less than the benchmark values, you must take steps to improve your process.

For example, a butter manufacturer uses an automatic filling machine to make 500 gm containers of butter. The manager wants to ensure that the filling process meets specifications of 498 gm to 502 gm of butter in each container. To assess the capability of this process, the manager randomly collects and weighs five containers per day for twenty days: each day's collection is a subgroup for this analysis. Further inspection reveals a leak in the machine, so the manager fixes this problem and collects another twenty subgroups of 5 containers after the improvement takes effect. The following graphs illustrate Cp and Pp values of this filling process before and after improvement.

A disadvantage of the Cp and Pp indices is that they compare only the process spread with the specification spread, but not their locations. In other words, they do not describe how far the process is running from the target region. For example, both processes below have the same Cp and Pp values, although one is clearly not capable.  To avoid mistakes, use graphs in combination with other capability indices (such as Cpk, Ppk, etc.) to draw meaningful conclusions from your data.