SIX SIGMA (6σ) | Calculation of Six Sigma and Sigma Level | DMAIC and DMADV

 SIX SIGMA (6σ)

• Six sigma is a methodology for improving business processes by identifying and eliminating the defects and reducing the variations in processes. 

• The business processes can be related to design, manufacturing or administrative functions. 

• The failure of business process or product is considered as defects.

• Six sigma is achieved only when a process produces 3.4 defects per million opportunities (DPMO) i.e. only 3.4 defects are allowed in 1000000 (ten lakhs) products, sales, services or opportunities in any business processes. 

• The sign of sigma is denoted as "σ" used in statistics to represent the standard deviation. 

• Six sigma was first introduced at Motorola Company by Engineer Bill Smith in 1986 in America.

• It is a continuous improvement process which enables the organization to provide better products and services to customers.

• Customer satisfaction and business processes improvement are the main objectives of Six Sigma.

• DMAIC and DMADV are the main methodologies of Six Sigma.

• As sigma level increases from 1 to 6, defect level decreases as shown in below Sigma Performance Table. 

• The term Six Sigma is based on a Statistical Concept in which defective items can be minimized by maintaining 6 standard deviations (6σ) between the process mean and its upper & lower specifications limit as shown in below graph.

Calculation of Six Sigma

As we know, to achieve six sigma the number of defects must be 3.4 in 1 million opportunities. 

So, 1 Million Opportunities = 1000000

Defect Per Million Opportunities (DPMO) = 3.4

Therefore, Yield = 1 Million Opportunities − DPMO = 1000000 − 3.4 = 999996.6

Yield%  = (Yield ÷ 1 Million Opportunities) × 100%

              = (999996.6 ÷ 1000000) × 100%

              = 99.99966% (Defect Free) 

Defect% = 100% − 99.99966%

                = 0.00034%

Theoretically six sigma works on zero defect. 

Calculation of Sigma Level

Example: A manufacturing industry produces 12000 parts out of which 80 found defective. There were 3 opportunities to get the product defective. Calculate sigma level of the industry? 

Solution: 

Given

No. of Unit Produced = 12000

No. of Defects = 80

No. of Defect Opportunities = 3

As we know,

DPMO = 2222.22

Yield (Defect Free) = 1000000 − 2222.22 = 997777.78

Yield% = (997777.78 ÷ 1000000) × 100% = 99.7777%

Now using Sigma Performance Table, we see value of DPMO and Yield% lies between 4 and 5 sigma level. Hence this industry is working between 4 and 5 Sigma. 

DMAIC

This methodology is used for improving the existing business processes like existing design, product or service. It has 5 phases:-

(1)- Define: Define the problem or issue and process that needs improvement like project, product or service.

(2)- Measure: Measure and collect the data from existing process.

(3)- Analyze: Analyze the data to find the root cause of problem.

(4)- Improve: Improve the whole process by eliminating the problem.

(5)- Control: Control the process in order to keep the improvement for long lasting.

DMADV

This methodology is used for creating a new design, product, or service. It has 5 phases:-

(1)- Define: Define the process and set the goals to meet the customer's requirement.

(2)- Measure: Measure all the data including critical components of process and product capabilities.

(3)- Analyze: Analyze the data and develop various designs of a process and select the best one.

(4)- Design: Design and test the product, service or process.

(5)- Verify: Verify that the process designed meets the customer's requirement and make sure the designed product, service or process performs well under actual conditions.