To calculate the Sigma Level:
$$\text{DPMO} = \left(\frac{D}{O}\right) \times 1,000,000$$
$$\text{Sigma Level} = 1.5 + 0.8406 \times \log(\text{DPMO})$$
Where:
A sigma level is a term used in both statistics and manufacturing to describe the rate of defects per million opportunities as a function of the number of standard deviations from a mean of a sample. For example, in a standard mean data set of 1 million objects, only 3.4 out of a million would fall within the sixth standard deviation.
Let's assume the following values:
Using the formula:
$$\text{DPMO} = \left(\frac{50}{1,000,000}\right) \times 1,000,000 = 50$$
$$\text{Sigma Level} = 1.5 + 0.8406 \times \log(50) ≈ 4.79$$
The Sigma Level is approximately 3.91.
Let's assume the following values:
Using the formula:
$$\text{DPMO} = \left(\frac{100}{500,000}\right) \times 1,000,000 = 200$$
$$\text{Sigma Level} = 1.5 + 0.8406 \times \log(200) ≈ 5.95$$
The Sigma Level is approximately 3.50.
