Can we calculate sigma level using only ppm ratio?

Logically, yes. Think about this, PPM means parts defective/parts sold, or internal ppm = parts defective/parts produced. your average no. of PPM = a mean of the parts you make that are defective.per million opportunities.since a sigma represents a standard deviation from that mean, you simply need a sigma (standard deviation) formula, You know the calculated mean and the population mean is simple math.Another way to view this is using a ratio of 5000 ppm by division is 50 parts defective per thousand parts made, or 4,950 good parts out of 5000. that's a .05% defect ratio. Rather than drag this out any further, why not just use the long standing, already converted sigma conversion tables? If you are yielding 99.50 (.05dpmo), your sigma level wil be close to 4.08 by interpolation.

When learning about Six Sigma, it may help to consider these charts, which detail how sigma level relates to defects per million opportunities (DPMO)

Here is the table below explaining the conversion of defects per million with Sigma levels,

Sigma Performance Levels – 

Sigma level       Defects Per Million Opportunities (DPMO)

1                                                  ,

2                                                  ,

3                                                    ,

4                                                    6,

5                                                      

6                                                      3.4

This helps a lot to measure what is the sigma level of our manufacturing process defect PPM sigma level accordingly.

Ashok