How to calculate and apply Cpk in Six Sigma

Last Updated on 16 September 2023

Cpk is one of the common metrics used for measuring process capability. You use it to measure whether your product is within the limits set by the customer. It is known as the ‘Process Capability Index’.

What is Cpk?

It is a form of grading, in that a larger Cpk number shows a greater capability, and so it is performing better. Each Cpk number is equivalent to a certain process yield and sigma level. It is a measure of how close you are to meeting your customer’s targets, and how consistent your performance is.

The Process Capability Ratio (Cpk) is a statistical measure of your process capability, determining how well your process can meet specification limits, taking both the variability and the process mean into account. It is an extension of the Cp index, which provides a more comprehensive assessment of process performance by analyzing both the process mean’s alignment with the specification limits and process variability.

How is Cpk Calculated?

It is calculated using the following values:

• Lower Specification Limit (LSL) – the lowest value that the customer will accept
• Upper Specification Limit (USL) – the highest value that the customer will accept
• Mean (µ) – the mean average (add up all the measurements and divide by the number of measurements) of the product you are making
• Standard Deviation (σ) – a measure of the variance of the measurements from the mean

Cpk is calculated using the following formula:

Cpk = min [ (USL - μ) / 3σ , (μ - LSL) / 3σ ]

Why is Cpk Important?

While Cp can provide valuable information about process capability potential, we also need to consider the process mean’s alignment with the specification limits. This is where Cpk comes into play, assessing the ability of the process to produce a product that meets customer requirements while taking deviations into account.

A process with a high Cpk score indicates it can consistently meet its specifications. Cpk values ≥ 1.5 are usually considered excellent. In other words, the higher your Cpk score, the better!

Cpk level meanings

There are certain process capability levels that have certain meanings for your process. These are therefore common targets for process improvement and KPIs for your business:

A process capability of at least 1.33 means that the process is ‘capable’ and will meet the customer’s specification limits. It relates to a process yield of 99.99% and a sigma level of 4.0, and so virtually all of the measurements are within the customer requirements.

When do you use it?

As it is useful for calculating how capable a process is, it is most useful during the Measure phase of DMAIC, to see how well the process is currently performing. You will then revisit it in the Improve and Control phases to make sure the improvements have occurred and to monitor it in the future.
The index only works when the data follows a normal distribution.

Difference between cp and cpk

There are two capability indexes with similar names and purposes, which can be confusing. The Cp is the ‘process potential index’ and is calculated with the following formula:

As you can see, this is a lot easier to calculate than the Process Capability Index, and its simplicity is its main advantage.

The main difference is that Cpk also takes into account whether the measurements are off-center, i.e. averaging slightly higher or lower than they should be. Cp only looks at how spread out the figures measurements are.

Cpk: A Practical Example

Let’s revisit our bakery example from the Cp blog post. Our goal remains to bake loaves weighing 950g ± 50g. The USL is 1000g, LSL is 900g, with a standard deviation (σ) of 10g. Let’s assume that the process mean (μ) is 945g.

Calculating Cpk:

Cpk = min [ (1000 - 945) / (3 * 10) , (945 - 900) / (3 * 10) ]Cpk = min [ 1.83, 1.5 ]Cpk = 1.5

With a Cpk of 1.5, our process is in excellent condition, consistently producing loaves within the customer’s specifications.

Having Cp and Cpk metrics in your arsenal can help you paint an accurate picture of your processes’ capabilities and deficiencies. Keep studying these tools, and don’t forget to apply them in real-world situations to see where improvements are required.