Background: Six Sigma assumes that 1.5 standard deviations is normal variation. So 6 Sigma is calculated using 4.5 standard deviations in the normal distribution (6-1.5=4.5). It also uses the upper tail of the distribution. Knowing this information allows us to manually calculate defects per million opportunities (DPMO), an important statistic that indicates how a business process is performing! In Excel, =normsdist() looks up values in the normal probability distribution, a distribution we will discuss later in the course but one with which you should have some familiarity. =normsdist(4.5) results in 0.999996602326875, meaning that most of the entire area of the curve is within 6 sigma. From this, we calculate that 3.39767E-06 of the area is outside of 6 sigma to the right by subtracting 1- 0.999996602326875 . If we multiply this number by 1,000,000, we get defects per million opportunities (DPMO) of about 3.4. We now can calculate the DPMO for any value of Sigma.

Part 1. Divide your age by 100 and add to 4. For example, my age is 56 / 100 = .56 + 4 = 4.56. Assume that this is the sigma associated with a process. Then calculate the DPMO associated with this value. Post your Excel formula. Example

=(1-NORMSDIST(4.56-1.5))*1000000

1106.685 or about 1107 defects per million opportunities.

Part 2. Now that you are armed with this information, assume that a business ships 100,000 packages. Assume that the number of shipping errors is your own age in years * 5. (For example, I am 56, so the number of errors would be 280). The yield is defined as (opportunities - defects) / opportunities x 100%. For example: =(100000-280)/100000 which equals .9972 or 99.72% yield. Calculate the yield based on the 100,000 packages and your own age in years * 5.

Part 3. From the yield, we can derive the sigma of the process by the following formula: =normsinv(yield) + 1.5. This adds back in the normal variation (or common cause variation) of 1.5 standard deviations. In the example above:

=NORMSINV(.9972)+1.5 = 4.27 Sigma. Calculate the Sigma of the process in #2.

Part 4. Finally, verify that your Sigma calculated in step 3 is correct by calculating the DPMO and then the defects per the 100,000 packages. If you have done this right, you should end up with the number of defects in step 2.

How? In my example, I just use =(1-NORMSDIST(4.27-1.5))*1000000 = 2,800. So if there are 2,800 DPMO, then there are 280 defects per 100,000 opportunities as specified in 2.

Part 5. How might business use 6 Sigma to improve their processes?