Definitions
Understanding The Basic And Advanced Modes
The Basic Mode of the Sigma Calculator automatically adds a 1.5 Sigma shift to the process Sigma value that is calculated. Why is this done? It's done because it is the "standard" way that Sigma is reported (note: this may be different in your company, but it is done in this manner by Motorola, GE and many other companies). By doing so, the calculator result assumes that you are providing long-term data and it is providing short-term Sigma. The 1.5 Sigma shift is based on the assumption that over time, and with a sufficiently large number of samples, a realistic Sigma value is 1.5 Sigma less than that calculated to show the success of your project (i.e. that shown in this calculator and in reports to your company).
If you want to calculate the process Sigma using data other than long-term, you should switch to the Advanced Mode where you can change the process Sigma shift value from 1.5 to whatever you feel is appropriate.
Here are a couple of examples to help illustrate the calculations. A long-term 93% yield (e.g. 100 opportunities, 7 defects) equates to a process Sigma long-term value of 1.48 (with no Sigma shift) or a process Sigma short-term value of 2.98 (with a 1.5 Sigma shift). A long-term 99.7% yield (e.g. 1,000 opportunities, 3 defects) equates to a process Sigma long-term value of 2.75 (with no Sigma shift) or a process Sigma short-term value of 4.25 (with the 1.5 sigma shift).
Final Thought: When we talk about a Six Sigma process, we are referring to the process short-term (now). When we talk about DPMO of the process, we are referring to long-term (the future). We refer to 3.4 defects per million opportunities as our goal. This means that we will have a 6 sigma process now in order to have in the future (with the correction of 1.5) a 4.5 sigma process -- which produces 3.4 defects per million opportunities.
Notice: Sigma with a capital "S" is used above to denote the process Sigma, which is different than the typical statistical reference to sigma with a small "s" which denotes the standard deviation.
Understanding The Formula
Defects Per Million Opportunities (DPMO) = ((Total Defects) / (Total Opportunities)) * 1,000,000
Defects (%) = ((Total Defects) / (Total Opportunities)) * 100
Yield (%) = 100 - (Defects Percentage)
process Sigma = NORMSINV(1-((Total Defects) / (Total Opportunities))) + 1.5
Alternatively,
process Sigma = 0.8406 + SQRT(29.37 - 2.221 * (ln(DPMO))).
Reference: Breyfogle, F., 1999. Implementing Six Sigma: Smarter Solutions Using Statistical Methods. 2nd ed. John Wiley & Sons.
Understanding Negative Sigma
Sigma value is simply a modified Z score (Table of the Standard Normal (z) Distribution). Sigma (with a capital "S") is not the same thing as the standard deviation of a process, referred to as sigma (with a lower case "s" or as the greek letter s). Consequently, it is quite possible to get a negative sigma value. A negative sigma value means that most of your product or service (process) is completely outside your customer's specification range. A full discussion can be found on negative Sigma.
