From my research into methodologies I have found that the two most popular methods are (1) PDCA and (2) DMAIC.
PDCA ("Plan-Do-Check-Act") is an iterative four-step problem-solving process typically used in business process improvement. PDCA was made popular by Dr. W. Edwards Deming, who is considered by many to be the father of modern quality control;
Plan – What are you going to do?
Do – Based on analysis, decide on solution.
Check – Verify the solution worked.
Act – Standardize and decide on next PDCA step.
When you are done with PDCA, you do it again. Or, in other words, you are never done because you must practice continuous quality improvements.
DMAIC ("Define-Measure-Analyze-Improve-Control")is a five step process involving the following steps. DMAIC is one of the two key method used in Six Sigma (business management strategy, initially implemented by Motorola).
Define high-level project goals and the current process.
Measure key aspects of the current process and collect relevant data.
Analyze the data to verify cause-and-effect relationships. Determine what the relationships are, and attempt to ensure that all factors have been considered.
Improve or optimize the process based upon data analysis using techniques like Design of experiments.
Control to ensure that any deviations from target are corrected before they result in defects.
PDCA and DMAIC are very similar, but have some differences. PDCA emphasizes more the need to repeat the steps, while DMAIC adds the Control step lacking in PDCA.
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