How to Convert PPM to CPK

By Brenda Scottsdale; Updated April 24, 2017
Many manufacturing plants use Six Sigma methodology.

PPM and Cpk are Six Sigma quality management terms used in manufacturing. Companies ascribing to a Six Sigma methodology work toward reducing defects to a low rate – six standard deviations away from the mean or 99.99 percent defect-free. PPM and Cpk are both measures of defects. PPM stands for defective parts per million. Cpk is the process capability index. The higher the index, the more closely the process is running to its specifications and the lower the defective parts per million.

Calculate non-defective parts per million. If a process is functioning .002 PPM, there are .002 defective parts for every million parts produced. To calculate how many non-defective parts per million there are, subtract this number from one million. Therefore, 1,000,000-.002 is 999,999.998/1,000,000 non-defective parts.

Convert non-defective parts per million to a percentage. Multiply the numerator by 100 and divide by one million. Therefore (999,999.998 x 100)/1,000,000 is 99.9999998 percent. The more decimal points you keep, the more accurate the calculation will be.

Look up the number of sigma corresponding to the percentage. You can find a sigma conversion table in the back of most statistics books. For our example, 99.9999998 percent corresponds to six sigma.

Look up the Cpk corresponding to the sigma level in a sigma-to-PPM conversion table. The Cpk that corresponds to six sigma is 2.0.

About the Author

Brenda Scottsdale is a licensed psychologist, a six sigma master black belt and a certified aerobics instructor. She has been writing professionally for more than 15 years in scientific journals, including the "Journal of Criminal Justice and Behavior" and various websites.