Capability Indices Key Points

• Cpk is useful for a variety of different use cases.
• You can calculate capability indices with minimal inputs if necessary.
• It is preferred to have three values available when calculating your Cpk.

How do you calculate capability indices? Capability analysis is an essential tool for statistical process control (SPC) and process improvement, applicable to a variety of environments from hospitals and labs to assembly and manufacturing.

How to Calculate Capability Indices

The formula for calculating a C_pk index is easily found:

USL, upper specification limit; LSL, lower specification limit.
*Estimated sigma = average range/d2

Common understanding includes the fact that C_pk climbs as a process improves – the higher the C_pk, the better the product or process. Using the formula above, it’s easy to calculate C_pk once the mean, standard deviation, and upper and lower specification limits are known.

Only One Specification or Tolerance

But what if you have only one specification or tolerance – for example, an upper, but no lower, tolerance? Is C_pk advisable under these circumstances?

When faced with a missing specification, consider one of the following three options:

1. Not calculating C_pk, since all the variables are not known
2. Entering an arbitrary specification
3. Ignoring the missing specification and calculating C_pk on the only Z-value available

Example: Plastic Pellet Manufacturer

Examining a specific situation may clarify the outcome of each of these possibilities. A customer of a plastic pellet manufacturer has specified that the pellets should have a low amount of moisture content. The lower the moisture content, the better, but no more than 0.5 units is allowed; too much moisture will create manufacturing problems for the customer. The process is in statistical control.

This customer would undoubtedly not be satisfied with option 1 as C_pk has been specifically requested. With option 2, it could be argued that the LSL is 0 since moisture levels below zero are impossible. As such, with a USL at 0.5 and LSL at 0, the C_pk calculation would be as follows.

Assume the X-bar = 0.0025 and the estimated sigma is 0.15.

The customer is not likely to be satisfied with a C_pk of 0.005, and that number does not represent the process capability accurately.

Option 3 assumes that the lower specification is missing. Without an LSL, Z_lower is missing or nonexistent. Z_min becomes Z_upper and C_pk becomes Z_upper / 3.

Z_upper = 3.316 (from above)

C_pk = 3.316 / 3 = 1.10

A C_pk of 1.10 is more realistic than one of 0.005 for the data given in this example and is more representative of the process itself.

A Misleading C_pk

As the example demonstrates, setting the lower specification to 0 results in a lower, misleading C_pk. As the process improves (here, moisture content decreases), the C_pk should have increased. If 0 was used as the LSL. However, the C_pk would have decreased. This is one clue that entering an arbitrary specification is not advised.

Why Do Capability Indices Matter?

Cpk is a great way of seeing how well a process is performing. Further, given that you’ve got three main data points when calculating it, it allows you to see if any outstanding variations need addressing. Additionally, you might be given a capability index from your customer, especially if you’re doing any contract work on parts.

Other Useful Tools

While we’ve discussed these concepts in depth, Cpk isn’t the only calculation to keep track of when looking at the data from your processes. Understanding how your Process Sigma relates to your standard deviations is a vital tool. Our comprehensive guide details why this matters and how to calculate it.

If you’re looking to integrate Six Sigma into your workflow, it might be worth understanding the training and certification processes. Our handy guide will have you well on your way to becoming a Six Sigma practitioner.

Summary

What should be done when only one specification exists? The (only) specification you have should be used, and the other specification should be left out of consideration or treated as missing. In these cases, use only Z_upper or Z_lower.

C_pk can and should be calculated when only one specification exists, provided only the remaining valid specification is used. Further, as the example demonstrates, the missing specification should remain missing and not be artificially inserted into the calculation.