# How to Calculate Process Capability Index

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When a business process meets customer requirements, whether it's manufacturing or service-based, it’s known as process capability. Measuring the process capability index allows you to see if you have the right combination of materials, equipment, people and methods, by comparing the output of a stable process with the process specifications.

## How It Works

The process capability index is performed by comparing that stable process, which is how the process is supposed to go, with the natural variations that can occur in each outcome. In every process, there will be some variation. Although that variation will always be there, it can be measured, monitored, reduced and controlled. For example, when making a cup of coffee, we can identify the process.

It starts with turning on the coffee maker, measuring out the correct amount of coffee, adding it to the coffee maker and adding the correct amount of water. If these measurements are the same each time, the coffee should taste nearly identical. Still, there are always tiny variations. You want to make sure you use the same brand of coffee each time, keep the coffee maker in good working order and use the same system of measuring.

## Calculating the Index

Calculating the process capability index uses a standard deviation to evaluate an existing process. Process capability measures your process to see if it is capable of making an item within the specifications. On the other hand, process capability index lets you know where your process is in relation to the center of those specifications, kind of like a bell curve. You must make sure all your data is accurate, just like you want to make sure your coffee maker is in good working condition. Otherwise, you could be getting an inaccurate picture of your process capability index.

When your process capability index, abbreviated Cpk in statistical language, is using accurate data, the Cpk can measure the capability of your process to produce a product that meets your customer’s demands. You can measure how close you are to the target, the best-case scenario and how consistent you are compared with the average performance. To go back to the coffee example, you know what you need to make good coffee. But maybe your customer wants to change something about the coffee. The Cpk will allow you to show the customer the ranges within that process that still allows a successful product.

OK, so you have your customer’s specification limits. To arrive at the Cpk, you will use the following abbreviations. Here is the equation: Determine your mean minus your lower specification limit, or LSL. Then calculate your upper specification limit, or USL, minus your mean. Divide both figures by the natural tolerance figure, which is usually three times the standard deviation of the spread of variation. The smaller of the two numbers determine the Cpk.

## Parking the Car Analogy

Here's an example, using the analogy of parking a car. The walls of a garage are like the specification limits. When you go to park your car, you must park between the walls. To do the job to the best of your ability, you will park the car in the center. That’s what you want to work toward with the Cpk. If your Cpk is negative, your process will crash the car into the wall. If your Cpk is 0.5, you may hit the wall. If it is one, you may touch the edge. If it equals two, you're doing well. If it equals three, you have excellent clearance.

## Something to Remember

You need a fair amount of historical data when you are calculating Cpk, so if you have a new process or a short pre-production run, you may not have enough information for an accurate comparison using Cpk. Large enough is generally thought of as about 50 pieces of data to use for comparison purposes.