iSixSigma

Cpk

Definition of Cpk:

Cpk is a common measure used in process capability analysis that allows you to know how well your process is meeting your customers’ expectations and specifications. This article will explain how Cpk is calculated and interpreted. We will explore its application, benefits and provide some tips and best practices so that you can begin assessing how well your process is doing when measured against the requirements specified by your customer. 

Overview: What is Cpk?

Process capability is the quantifiable comparison of the Voice of the Customer (specs, requirements, or expectations of your customer) and the Voice of the Process (control limits). The goal of process capability is to come up with a quantified measure that informs you as to whether you are meeting your customer expectations or not as well as a relative value of how well you are meeting or how badly you are missing.

Besides Cpk or Capability Index, there are a number of other process capability metrics. They are Cp, Pp and Ppk. Since Cp and Cpk are related, we will need to spend a little time talking about Cp before discussing Cpk in order to provide context for Cpk. 

Cp, or capability potential, is a measure of the potential capability with the assumption that the distribution of the sample process data is normally distributed and centered within the customer’s upper specification limit and lower specification limit. It represents the best the process capability can be for the specs and process distribution. If there is only a one-sided spec, then Cp cannot be calculated. The formula is:

Cpk formula

You can say this as Cp is equal to the Customer’s Upper Specification Limit minus the Lower Specification Limit divided by 6 standard deviations. 

We are assuming that the sample distribution is normally distributed, and its width is calculated by adding and subtracting 3 standard deviations on either side of the sample data mean. The standard deviation that is used is called a “pooled standard deviation” or “within variation.”

Cp can take on values equal to 1, greater than 1, or less than 1. Therefore, if we look at the formula above, a value of 1 would mean that the width of the distribution is equal to the width of the specifications or specs. A value greater than 1 would mean that the specs are wider than the distribution of the process, so we are comfortably within spec. If the value is less than 1, it means that the width of the process distribution is wider than the specs, and items will be outside the specs.

However, all of this assumes that the process is centered within the specs. But this is rarely the situation. More often than not, the process mean (x-bar) will not be centered within the specs. Interestingly, if the process mean is off-center, the Cp will still be the same since the Cp does not consider the location of the process. That’s when we need to use the Cpk to assess the process capability.

Cpk is similar to Cp in that it utilizes the customer specs and process variation, as measured by the standard deviation, but it also includes the location of the mean relative to the specs. Since the process mean is now off center, you will report out the minimum condition depending on whether the process has shifted closer to the upper spec or closer to the lower spec. Essentially what you are doing is measuring the distance from the mean to the different specs. Then you divide that distance by half the width of the distribution or 3 standard deviations. Finally, you report out the minimum of the two values since that will be your “worst” condition and lowest process capability. See the formula below.

Cpk formula

The value of the Cpk  ratio can take on any value ranging from 0 to any positive or negative number. A value greater than positive 1 means that the spec limit is far enough away that the process should be capable and be within specs. A value of 0 means that the mean of the distribution sits on the spec so that half the process will be out of spec. A negative value means that the process mean is beyond the spec, resulting in more than 50% of the process being out of spec.

In most business applications, you want the minimum Cpk value be 1.33. This means the closest spec is 4 standard deviations away from the mean. If staying in spec is critical, then the preferred value is 1.67, meaning the closest spec is 5 standard deviations away. Finally, if the value of Cpk is 2, then the closest spec is 6 standard deviations. This is the definition of Six Sigma, and you can then claim that you have a Six Sigma process. 

3 benefits of Cpk 

Cpk is a simple and useful metric for comparing your process with your internal or external specifications, targets, expectations, or any other desired outcome for your process.

1. Simple yet powerful calculation 

To compute your Cpk value, you only need to know the mean and standard deviation of your data and the specs you want to test against. 

2. Can account for a process not centered within the specs 

If the process is centered within the specs, you would use the calculation of Cp to assess the potential of your process capability. But, as it is in most cases, if the process is shifted off center, then the Cpk will account for that shift. 

3. Can be used to compare different processes 

The Cpk allows you to compare the performance of disparate functions since it is a generic measure of the process’s ability to meet specs. If a manufacturing line had a Cpk of 0.82, and a finance department had a Cpk of 1.89, you could say that finance is doing a better job of meeting its customer’s requirements than is manufacturing. 

Why is Cpk important to understand? 

Meeting your customers’ expectations and requirements is vital to your organization staying in business. By understanding how to compute Cpk and interpret its value, you will be able to know what you have to do to meet — and possibly exceed — your customers’ expectations. 

1. Know what variables are needed to calculate Cpk

If you intend to use Cpk for decision-making purposes, you need to know what variables are needed and what their values are so you can do the proper calculations. 

2. Cpk represents your current state process capability

If your Cpk is not high enough to satisfy your customers’ specs, you need to take action so out-of-spec products are not produced and shipped. 

3. You might possibly want to adjust the specs

If you’re not meeting specs, you might want to speak with your customer to see if they can be adjusted without any negative impact. You can use the current Cpk calculation to back into what level of specs you’re able to meet.

An industry example of Cpk 

A plastic extrusion company had contracts with major suppliers of plastic parts to the auto industry. The owner, Norman, was an advocate of Lean Six Sigma and had improved their processes as well as invested in the best equipment available. His customers had rigorous specs because their customers, the auto companies, had rigorous specs for them.

Upon calculating the Cpk for his extrusion process, Norman found that his equipment was capable of achieving a Cpk of 4 on a consistent basis. He was sure that his competitors were nowhere as good. Because he was so tight and centered within the customers’ specs, he decided to launch a two-pronged strategy to improve sales and profits.

The first strategy was to approach the customers and suggest they tighten their specs for his products. Using the Cpk formula he backed into how much tighter the specs could be made and still be well within them. Knowing his competitors, Norman figured that if the specs were made tighter, his competitors would no longer be able to produce products at a competitive price or quality. That meant Norman would get a bigger share of the total business.

His second strategy was based on how tight he was within the specs, even the tighter ones.  He realized that he did not need to stay centered within the specs. Therefore, he adjusted his equipment to produce off center and closer to the lower spec while still staying well within spec. This allowed him to reduce the amount of plastic in each part, therefore saving a small amount of money on each part. Since he was producing parts in the millions, the small increment of savings would add up to a significant increase in profits. A win-win all the way around.

3 key suggestions when thinking about Cpk

Cpk is merely a calculation, but there is a series of hints that can allow you to get the maximum value out of the calculation.  

1. Do both Cp and Cpk calculations

By comparing the potential capability with the actual capability, you will understand what, if anything, you need to do to be sure you remain in spec. 

2. Use the Cpk to compare different parts of the organization

The use of the generic Cpk metric allows you to compare various functions in the organization. It’s a measure of how well each is doing relative to their specs and allows for an apples to oranges comparison. 

3. Use the Cpk to establish strategies to take advantage of a good value

You can consider revising specs or shifting the mean of the process within the specs to take advantage of a good process and high Cpk. 

Frequently Asked Questions (FAQ) about Cpk

What is the difference between Cp and Cpk?

Cp assumes that the process is centered within the specs while Cpk adjusts for a dynamic shift in the mean of the process. 

Can I compare Cpk across different departments of the company? 

Yes. Cpk is a generic measure of how well a department is doing relative to its required specs. You can state that Department A is doing better at meeting specs than Department B if Department A’s Cpk is higher. 

Other than Cpk, are there other common measures of process capability? 

Yes. You can also calculate Cp, Pp and Ppk to measure process capability.

So, what is Cpk again? 

Cpk is a common measure of a process’s ability to meet customer expectations — primarily  specifications. It assumes that the process data is normally distributed but does not require that the mean of the process be centered if there are upper and lower specifications. 

It is calculated by finding the difference between the mean of the process and a spec. That difference is then divided by 3 standard deviations. The higher the value is, the better the process capability. 

The knowledge and understanding of your Cpk value can be a powerful strategy tool for gaining competitive advantage and improved profitability. It can be used for any process with stated specs or qualitative expectations and can be used as a comparative tool across different functional areas.

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