Can Cpk be negative?

Yes, Cpk can be negative. Some quality folks find this hard to believe. In the real world when a negative Cpk appears most people try to check and recheck their calculations or the underlying data. But Cpk can be negative. Let’s try to prove it with 2 scenarios.

Cpk is calculated using the formula…


So we think about this formula, Cpk is the minimum distance of the process average from either specification limits.

Scenario 1
Consider a process as shown in figure 1. The process average is closest to the Lower Specification limit.
In this case, since process average is less than LSL, Cpk is negative.

The area of the histogram or distribution curve in red indicates parts that are below the Lower spec limit. All these parts are rejected.

Scenario 2
Consider another process as shown in figure 2. The process average is closest to the Upper Specification limit. In this case as process average is greater than USL, Cpk in this case is also negative.

The entire area under the distribution curve is red i.e. all parts are rejects as they are above the Upper spec limit.

What does a negative Cpk indicate?
As seen from the examples above, a negative Cpk indicates that the process average is outside the specification limits. Most of the readings are outside the specifications i.e. they are rejects.

Have you come across a negative Cpk? What did you think about it?

Measure Cpk only for stable processes

Cpk and other capability indices should be calculated for stable processes only. This is a critical requirement for calculating capability indices. Sadly, it is the most ignored fact in the real world.

What is a stable process?
A process that does not have any special causes present is a stable process. Such a process has inherent variation due to common causes only. The control chart for a stable process has no 'Out of control' points.

Why is stability important for Capability studies?
The capability indices are designed to determine how capable an ongoing process is for consistently delivering product within customer specifications given the natural variation of the process.
Ongoing processes should typically have only common cause variation i.e. the process is statistically stable.
When assignable causes come into play, the process becomes unstable. Now the control chart has out of control points that need to be watched closely and removed as soon as possible.

When processes are unstable, it is recommended to use performance indices like Pp and Ppk.

For more information on capability indices, please read our White Paper Use of different capability indices.