Key Points
- Sigma, DPMO, Yield, and Cpk are interrelated calculations.
- When using the table, assume there is a 1.5 Sigma shift.
- Understanding these calculations can help you iron out defects in your production.
Converting information from Sigma to DPMO and other values can be daunting at first glance. However, you don’t need to waste precious time getting to grips with these calculations. All of these values are vital to understanding where a process might be falling short. This short and informative guide should have you up and running in no time at all.
Sigma to DPMO to Yield to CPK Table
| Sigma | DPMO | Yield | Cpk |
| 1.5 | 500,000 | 50% | 0.50 |
| 3.00 | 66,800 | 93.320% | 1.00 |
| 3.50 | 22,700 | 97.730% | 1.17 |
| 4.00 | 6,210 | 99.3790% | 1.33 |
| 4.50 | 1,350 | 99.8650% | 1.50 |
| 5.00 | 230 | 99.9770% | 1.67 |
| 6.00 | 3.4 | 99.99966% | 2.00 |
Assumptions
No analysis would be complete without properly noting the assumptions made. In the above table, we have assumed that the standard Sigma shift of 1.5 is appropriate (the calculator allows you to specify another value), the data is normally distributed, and the process is stable. In addition, the calculations are made using one-tail values of the normal distribution.
Discussion
If you are starting with DPMO, convert it to a decimal value by dividing by 1,000,000. If you multiply that decimal by 100, that is your Yield (%). If you take the decimal and look it up in a standard normal curve (Z table), you can determine the corresponding Z which is the long-term Z. To convert to short-term Z, which is the Sigma level, use the following formula:
Z(short term) = Z(long term) + 1.5
Then you can determine Cpk using the following formula:
Cpk = Z(short-term) / 3
Why It Matters
So, why would you need all these calculations on hand? When you’re doing data analysis on a given production or process, understanding where things fall short can be helpful. Further, you’re likely using the calculations to seek out errors or defects in production. By striving for a 5 or 6 Sigma, you’re aiming for the best possible production quality your organization can muster.
Other Useful Tools and Concepts
Understanding the minutia behind your Sigma Level can get the best possible products to your customers. As such, understanding a concept like Process Sigma and how it differs from your Sigma Level is crucial.
Further, understanding the differences between Cpk and Sigma can shed some light on your analysis. While we’ve discussed both calculations throughout today’s article, that pales in comparison to our guide exploring these concepts.
Conclusion
Knowing how to do the calculations for Sigma to DPMO and other values is a great ability to have on hand. However, making use of easy tools like the included table makes it so you can get to grips in no time flat. Why waste time when you can focus on what matters? Time is money, after all, so maximize your potential.
