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Simply put, the DEFINE process is where we outline and describe what we want to achieve. Goal setting, target setting, KPIs, desired output, etc.
The ANALYZE process is where start examining the current status while exploring our options and how we're going to achieve the objectives we set.
In the DEFINE process, we answer the WHAT. In the ANALYZE process we deal more with HOW and WHY.
The Define phase focuses on the process selection et goal setting for the LSS improvement project. Once we've chosen wish process we're going to work on and measured all related parameters, in the analyze phase we go more into the details to see what's really ain't working in that process and fine the root cause of potentiel problemes.
In the define phase, you have to define your problem,customers and the current process that you are trying to improve with all details . While in the analyze phase, you have to analyze the problem and determine the root causes of your problem.
It is a very broad question asked, however
1. Identifying a problem and logically explaining it is defining the problem.
2. Collecting the facts, data, Pareto, stratification, scatter, control charts, process capability, MSA etc are all analysis.
In define phase, you would identify your goal and targets specifically in a certain time frame. Further more, you would map your processes in SIPOC, Top Down Charts, Value Stream Mapping, Spaghetti Diagram and non value added, value added and operational value added processes.
KPI would be addressed in MEASURE phase, not define phase.
In analyze phase, you would use different analatical tools on your data collected in measure phase. For instance, for a process you would further probe the sub processes involved and their impact on the desired outcome. This phase is ideally a combination of both, analatical and statictical tools like fish bone diagrams,5WHYs, paretto charts, box plot, histograms, CpK, process capability evaluation.