Converting DPMO & Sigma Level

07/27/2007

How do you covert DPMO to sigma level and sigma level to DPMO?
Al F.

Generally, you would use a table, such as provided in my Six Sigma Demystified book, or you can calculate sigma level directly in Excel using the formula =(NORMSINV(1-$D2))+1.5, where the data in cell D2 is entered as a decimal (for example, 30% error rate = 300,000 DPMO = 0.3 which would calculate Sigma Level as 2.02).

The conversion is also included in some Six Sigma software, such as our Green Belt XL product.

For a given sigma level, the defects per million opportunities (DPMO) is provided, assuming normality and a 1.5 sigma shift. Note that below approximately 3 sigma defects are included from both tails of the normal distribution.

Sigma	DPMO
1	697672
1.1	660083
1.2	621378
1.3	581815
1.4	541694
1.5	501350
1.6	461140
1.7	421428
1.8	382572
1.9	344915
2	308770
2.1	274412
2.2	242071
2.3	211928
2.4	184108
2.5	158687
2.6	135687
2.7	115083
2.8	96809
2.9	80762
3	66811
3.1	54801
3.2	44567
3.3	35931
3.4	28717
3.5	22750
3.6	17865
3.7	13903
3.8	10724
3.9	8198
4	6210
4.1	4661
4.2	3467
4.3	2555
4.4	1866
4.5	1350
4.6	968
4.7	687
4.8	483
4.9	337
5	233
5.1	159
5.2	108
5.3	72
5.4	48
5.5	32
5.6	21
5.7	13
5.8	9
5.9	5
6	3.4

Learn more about the Lean Six Sigma principles and tools for process excellence in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Lean Six Sigma DMAIC short course ($249), or his online Green Belt certification course ($499).