# How to calculate CPK value

Written by tanya robertson
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In layman's terms, Cpk measures how close you are to your targeted goal along with how consistent you are with your average performance. A real world example is parking a car in a garage. The goal is to park the car perfectly in the middle so there is equal open space on all sides of the car. The Cpk calculation in this scenario would tell you the relationship between the size of the car, the size of the garage, and how far away from the centre of the garage you actually parked the car.

You can calculate Cpk to measure capability and performance for any process. Cpk is a process capability index that consists of a single number that measures the proximity a process is running to its specified limits, relative to the processes natural variability. The larger the index, the better, because this means it's less likely that the process is running outside its specs.

Skill level:
Easy

## Instructions

1. 1

Calculate Cpk using the formula: Cpk = Zmin / 3. In this equation, you find the value for Cpk by calculating the value for Zmin and dividing it by 3. Zmin is calculated by finding the values of Zupper and Zlower and choosing the smaller number between the two. Zupper represents the upper specification limit and Zlower represents the lower specification limit. To put this in the terms of our parked car example, the Zupper and Zlower represent the amount the car can widen before hitting the frame of the garage on any side. The next step is to divide the Zmin value by 3. Three is a standard number in the equation, representing 3 times the apparent process variability. For this example, we will use the given values of: USL = 0.5, Mean = 0.0025, and estimated sigma = 0.15.

2. 2

Calculate Zupper where Zupper = [(USL -- Mean) / Estimated sigma*]. This works out to be Zupper = [(0.5 - 0.0025) / 0.15] = 3.316. Zupper represents the highest process limit that's still within the specified parameters, or the farthest distance between the car and the wall farthest away.

3. 3

Calculate Zlower where Zlower = [(Mean -- LSL) / Estimated sigma*]. This works out to be Zlower = [(0.0025 -- 0) / 0.15] = 0.01667. Zlower represents the lowest process limit that's still within the specified parameters, or the shortest distance between the car and the closest wall.

4. 4

Calculate Zmin where Zmin = smaller of Zupper or Zlower. This works out to be Zmin = 0.01667.

5. 5

Calculate Cpk where Cpk = Zmin / 3. This works out to be Cpk = 0.01667 / 3 = 0.005. If we apply this Cpk value to our parked car scenario, 0.005 tells us the car is crunched against the garage. A Cpk value of 0.5 or lower would indicate you're crunched against the outside parameter. A Cpk value of 1 would mean your barely touching the edge of the parameter. A Cpk value of 2 would mean your distance can double before touching the parameter and so forth.

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