Remember "The Little Engine That Could," the children's story about self-confidence in the face of huge challenges? In it, a train engine keeps telling itself "I think I can" while carrying a very heavy load up a big mountain. Next thing you know, the little engine has done it...but until that moment, the outcome was uncertain.

It's a wonderful story for teaching kids about self-confidence. But from a quality and customer service viewpoint, it's a horror story: if your business depends on taking the load up the hill, you want to know you can do it.

That's where capability analysis comes in.

When customers ask if you're able to meet their requirements, process capability analysis lets you reply, "I know we can."

## How Do You Prove Your Process Is Capable?

You want to determine if your part-making process can meet a customer's specification limits—in other words, can you produce good parts?  Statistically speaking, we assess the capability to make good parts by comparing the width of the variation in your process with the width of the specification limits.

The first step in capability analysis is to make sure your process is in statistical control, or producing consistently. If it's not, any estimates of process capability you make won't be reliable.

The results of a capability analysis usually include capability histograms and capability plots that help you visually assess the distribution of your data and verify that the process is in control.

It also includes capability indices, which are ratios of the specification tolerance to the natural process variation. Once you understand them, capability indices are a simple way of assessing process capability. Because they reduce process information to a single number, you can also use capability indices to compare the capability of one process with another.

This video offers a quick demonstration of a simple capability analysis:

## Selecting the Right Type of Capability Analysis

You need to select the right capability analysis for your data based on its distribution. Depending on the nature and the distribution of your process data, you can perform capability analysis for:

• normal or nonnormal probability models (for measurement data)
• normal data that might have a strong source of between-subgroup variation
• binomial or Poisson probability models (for attributes or count data)

Capability analysis using a normal probability model provides a more complete set of statistics, but it assumes that the data follow an approximately normal distribution, and come from a stable process.

If you apply normal capability analysis to badly skewed data, you may drastically over- or underestimate the defects a process will produce. In this case, it's better to select a probability model based on a nonnormal distribution that best fits your data.

Alternatively, you might transform the data to better approximate the normal distribution. Minitab can transform your data using the Johnson transformation or Box-Cox power transformation.

The important thing to keep in mind is that in both normal and nonnormal capability analysis, the validity of the results depends on the validity of the assumed distribution.

## Additional Considerations in Capability Analysis

Typically, data for a capability analysis consists of groups of samples, produced over a short period, that are representative of the output from the process. Collecting small subgroups of samples under the same conditions, and then analyzing the variation within these subgroups, lets you estimate natural variation in the process. You can also use individual item data to assess capability, as long as it's been collected over a long enough time to account for different sources of variation.

Guidelines typically recommend getting at least 100 total data points—such as 25 subgroups of size 4—to obtain reasonably precise capability estimates.

Process data also may have random variation between subgroups. If you think strong between-subgroup variation exists in your process, use Minitab's Capability Analysis (Between/Within) or Capability Sixpack (Between/Within) options, which calculate both within- and between-subgroup standard deviations, then pool them to calculate the total standard deviation. Accounting for both sources of subgroup variation can give you a more complete estimate of the your process' potential capability.

If you have attribute (count) data, you can perform capability analyses based on the binomial and Poisson probability models. For example, with Capability Analysis (Binomial) you can compare products against a standard and classify them as defective or not. Capability Analysis (Poisson) lets you classify products based on the number of defects.

## Accessing Capability Analysis Tools

The full range of capability tools in Minitab are found in the Stat > Quality Tools > Capability Analysis menu, including:

• Normal and Non-normal Capability Analysis
• Between/Within Capability Analysis
• Normal and Nonnormal Capability Analysis with Multiple Variables
• Binomial Capability Analysis
• Poisson Capability Analysis

You should also check out the Capability SixpackTM for Normal, Nonnormal, or Between-Within capability analyses, which combines the following charts into a single display, with a subset of the capability statistics:

• Chart to verify that the process is in control.
• Capability histogram and probability plot to verify the data follow the specified distribution.
• Capability plot that displays process variability compared to the specifications.

## Take Guesswork Out of Capability Analysis with the Assistant

If capability analysis seems complicated, there's no denying that it can be. However, the Assistant in Minitab Statistical Software can take a lot of the labor and uncertainty out of doing capability analysis, especially if its a method you're new to. I'll cover how to use the Assistant for capability analysis in detail in my next post.