## Concept

“Sigma" represents the standard deviation from the mean in a normal distribution, and Six Sigma aims at improving the processes to limit defects to a maximum of 3.4 per million opportunities, or to achieve 99.9997% adherence to specified standards. For instance, in a production process that manufactures a million units a month, Six Sigma attempts to limit the manufacturing of defective pieces to 3.4 during the same period.

Six Sigma is the desired state of 3.4 defects per million opportunities.

- 1 sigma denotes 697,602 defects per million opportunities.
- 2 sigma denotes a level of 308,537 defects per million opportunities.
- 3 sigma denotes a level of 66,807 defects per million opportunities.
- 4 sigma denotes a level of 6,210 defects per million opportunities.
- 5 sigma denotes a level of 233 defects per million opportunities.

Six Sigma baselines may lie in any such level, and the objective of Six Sigma intervention is to enhance the process to Six Sigma.

Baselines are measurements that indicate the level at which a process functions. Six Sigma baseline is the level at which the process functions, or the number of defects or variations from the recommended range before applying Six Sigma interventions. It denotes the starting point of Six Sigma interventions. Such measurements take the shape of capability, yield, or Sigma levels.

*Image by N Nayab*

## Calculation

Calculation of the baseline value requires conversion of the defects or variations in a given sample into Defects per Million Opportunities (DPMO).

The formulae for defects per million calculation is:

DPMO = Number of defective items / (Number of Defect Opportunities per Unit x Number of Units) x 1,000,000

In a straightforward example, assuming an assembly line produces a million units of a product, and of these, 691,463 fall within acceptable limits, and the specifications of 308,537 units go beyond the specified limits, in other words the 308,537 units are defective. The baseline measure for the Six Sigma intervention is 308,537 or 2 sigma level. The Six Sigma approach tries to find ways to reduce the number of units not conforming to specifications from 308,537 to 3.4 per million.

In a real life scenario, assume the postal department delivers 378,564 letters a day, and misplaces 17,789 of them, on average. This defect rate of 17,789 for 378,564 needs conversion to one million. (17,789/378,564 x 1,000,000) = 46,990.73. The postal department thereby misplaces 46990.73 letters per million letters delivered, which is the baseline measurement. The sigma level of this baseline value is 3.17.

Now assume the number of possible errors per letter is two, displacement, and wrong delivery. If 17,789 errors fall into any of these two error categories, the defects per million opportunities changes

= 17,789/(2 x 378,564) x 1,000,000 = 23,495.37 defects per million opportunities.

Using any Sigma conversion calculator available online, this translates to a Sigma level of 3.49.

## Data Collection and Analysis

Real life situations with large data for analysis require plotting the mean values of the number of defects or non-compliant units with the total opportunities over different periods in a graph, and plotting the baseline value using a Sigma calculator. Many situations will call for use of sample data instead of all data, and in such situations, identification of the correct baselines depend on the extent of data available or used.

Some pointers to consider when collecting data for calculating the baseline include:

- collecting data from a long period to identify long-term variations
- taking into account known patterns such as monthly, quarterly, or annual cycles, or known occasional problems, to incorporate the full range of circumstances in the data sample

Determining the Six Sigma baseline measurement constitutes the first step in Six Sigma calculations and establishes the exact start point for the Six Sigma project when developing a problem statement.