#### Sigma Level

Sigma level indicates the compliance rate of the process i.e. how effective process in avoiding defect or in other words is meeting client’s expectation. It is considered to be the positive way of representing the process capability

**Short Term Sigma Level (Z _{st})**

Short term sigma level is calculated using within standard deviation of the process. Z_{st} represents the potential capability of the process i.e. how the process will perform if all short term variations are constant which is an ideal scenario.

**Long Term Sigma Level (Z _{st})**

Long term sigma level is calculated using the overall process standard deviation, hence representing the actual capability of the process. It is considered that over the period because of natural variation the short term sigma level is shifted by 1.5σ. Thus Z_{LT} can also be calculated as

Sigma level can be calculated for both attribute data as well as continuous data.

#### Sigma Level for Attribute data

The sigma level for discrete data is calculated using DPU and DPMO.

The standard normal distribution (Z-distribution) is the tool referred to calculate the sigma level using DPMO.

At 6σ level, the process is expected to make only 3.4 defects per million opportunities.

To calculate sigma level in Minitab, calculate compliance rate:

In Minitab, go to Calc -> Probability Distribution -> Normal, as we use standard normal distribution to calculate sigma level

Now, select ‘Inverse cumulative probability’ and updated compliance rate in ‘Input Constant.’ The ‘x’ value in the session window is the short term sigma level of the process if short-term attribute data is collected.

#### Sigma Level for Continuous data

Sigma level for continuous data is represented as the number of standard deviations (σ) can fit between the Mean and closest specification limit (SL). If Zst is six, that means six standard deviations (σ) can be accommodated between mean and SL. Higher Zst means lower the variation hence lower the DPMOs.