# 6 Sigma Series: Capability index & quantifying the capability of the process to meet specification

In Six Sigma, we use capability indices to directly compare the voice of the process to the voice of the customer. This helps us to quantify the capability of the process to meet specification.

We use the lower specification limit (LSL) and the upper specification limit (USL) as part of this process. More on these can be found in our previous article. So, to define the short-term capability index, we take:

Where **σ** is the result of our Standard Deviation calculation. So, it’s the upper minus the lower limits, divided by 6 * the short term, standard deviation (-3 deviations to +3 deviations).

- Where CP = 1, the voice of the process meets the voice of the customer.
- Where CP < 1, the process has more defects than the VOC allows.
- Where CP >1, the process has fewer defects than the VOC spec.

Sometimes, the distribution isn’t centred. So, let’s say that we have a USL of 10 and an LSL of 5. The CP figure will tell us that it does/doesn’t fit within the range. However, it doesn’t take into account the possibility of the distribution being off-centre.

So, we can calculate the CPU:

And the CPL:

Now, we can calculate the CPK by utilizing the CPL and CPU. The calculation is the MIN of the CPU and the CPL. There are a few outcomes:

- The CP is equal to the CPK, which means the distribution is centred.
- The CPK > 1.33, which means we’re within our variation tolerances.
- The CPK < 1.33 which means the variation is too wide, compared to the spec.

The above assumes that we’ve used the short-term standard deviation calculation. We can also use the long term calculation, with a slightly revised formula.

So, the PPK is:

We can then say that:

- If CP = CPK and PP = PPK then the distribution is centred within specification.
- If CP = PP and CPK = PPK then there is a consistent central offset.
- If CP = PPK then our process is operating at its entitlement level of variation.

Content based on study of the Six Sigma Black Belt course and Six Sigma for Dummies