Many organizations are combining the principles of Lean Manufacturing, Theory of Constraints, and Six Sigma into one program and labeing it as Lean Six Sigma.
The three methodologies are summarized below.
All three of them have a collective goal to improve the process performance towards a target (improve the mean), improve customer satisfaction, and profitability.
You may fall short of satisfying the customer if using anything short of all three. Any of the three are beneficial but may not be enough alone to get the best results.
A successful project will have controllable inputs that provide consistent and accurate output. This type of result requires the collective use of all three methodologies.
The primary difference between Six Sigma and Lean Manufacturing is:
*remember the customer is not only the end-user but may also be your company. These concepts are often combined within organizational structures and call "Lean Six Sigma".
Six Sigma is the most math intensive of the three methodologies and uses statistics to drive and validate ideas and processes. The others use more subjective input but all three require data and math to some extent.
It's hard to balance a line of processes if the output is highly variable and contains yield losses, waste, etc. All three play a role and there is some overlap in each of the methods which is the reason why Lean Six Sigma has become more popular.
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