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My X’s and the Y : Y=f(xi)
By  Arnold Cesar Abaya|Mar 23, 2017|


The Six Sigma methodology provides a systematic approach to solving problems on processes problems. The toolkit related to the DMAIC (Define, Measure, Analysis, Improve and Control) consists of extensive selection of proven tools that, if correctly applied, helps in successfully completing a Six Sigma project. However, easier said than done, six sigma practitioners especially newly trained Green Belts or even  inexperienced Black Belts tends to get lost in their DMAIC story. Most tend to use the tools separately and sequentially rather than in the context of their DMAIC approach. 

In the worst case scenario, Green Belts or even Black Belts do not get the desired outcome of achieving a significantly improved process because they tend to get lost in linking each phase of the D-M-A-I-C. An excellent way of overcoming this problem is to always keep the concept of Y = f(Xi) in mind when applying the specific tools along the DMAIC phase.

Process Outcome Metric is the result of Process Inputs : Y=f(x)

The mathematical formula Y=f(x), which translate simply to “Y is a function of x”, illustrates the concept that the Process’s Important Metric (Y) is a result of the various inputs or causes (X’s) within the process. It is the goal of the DMAIC methodology to identify which of these X’s mainly influence your Y. Having said that, we can simply describe each phase of the DMAIC as follows:

  • DEFINE: Understand your project’s measurable Y
  • MEASURE: Measure your baseline Y and identify/prioritize potential root causes Xs.
  • ANLYZE: Test the relationship between Y and X’s.
  • IMPROVE: Implement solutions to address the X’s and improve the Y.
  • CONTROL: Control the X’s and monitor the Y over time.

Define: Understand Your Project’s Y and How to Measure.

The goal of DEFINE phase is to come up with a Project Charter. It may seem simple but yet many projects have rather a unspecific or undefined business or process problem statement. A poorly described problem will make it difficult to get a clear understanding of what needs to be done. Project may also be poorly scoped and down the road may likely to end up with unresolved problem.

There are a number of tools available during the DEFINE phase to get a clear understanding of your project Y. To understand your project’s Y, you should always start with the Voice of your Customer (VoC) and translate it in a well defined and measurable Critical to Quality (CTQ) elements. The Supplier-Input-Process-Output-Customer (SIPOC) diagram can help clearly link the CTQ to your process output. If there are multiple output Y listed in your output column, a prioritization may be necessary using Pareto analysis or a further verification through the VoC.

The project charter should now be able to link your process Y to the “Big Y” (the CTQ) and should now be stated clearly in your Business Case and Problem Statement. The project charter also states how your Y is measured (Project Metrics) and how the performance should be at the end of your DMAIC process (Project Goal).

Since there is now a clear link of your project Y to your CTQs, it should be now easy to understand how your project contributes the higher-level business objectives such as Customer Satisfaction, Financial Benefits or any relevant goal to the organization’s strategic initiative.

Measure: Prioritize Potential Xs, Validate Measurement System and Measure  your Y

At this point we are still focused on the Project’s Y and we start Measure Phase by identifying all potential causes or X’s through Fishbone Diagram and/or Process Mapping. After coming up with a number of potential X’s, we might now have to reduce to a manageable few using prioritization tools such as Cause & Effect Matrix and FMEA. Note that this point we are still brainstorming based on our experience and expertise of the process and not yet on data. 

The next step is not to validate the measurement system of project’s Y and the identified X’s using Measurement System Analysis (MSA). Use Gage R&R for variable type of data and Attribute Assessment Analysis for attribute type of data. 

The final step of Measure Phase is to determine to baseline process capability of Y either calculating Cpk or Z-score. Take note, however, short-term capability is typically reported both as baseline and as improved process.

Analyze: Determine Significance of X’s to the Y

In the Analyze phase, we now quantify the relationship of X and Y using graphical tools (multi-vars chart, Pareto chart, scatter plots, etc) and statistical tools (such as regression analysis, hypothesis tests, normality tests, ANOVA etc.). There a large numbers of tools available depending on the type of data of the X’s and the Y. So, the Analyze Phase is quite simple and straightforward depending on the type of data and strictly follow the roadmap to determine the right tool to use.


Improve: Implement Solutions to Improve Y, Address Important Xs

Analyze phase brings out the Significant Few X’s based on data and facts. At improve phase, we come up with potential solutions by addressing these Significant X. Solution formulation will  require brainstorming and creativity. In order to find the best solution, the team need to assess the solution based on (1) impact of solution to Y, (2) cost-effectiveness of solution, (3) easiness of implementation or timeframe needed. Risks involved in implementing the solutions also needs to be assessed so as to avoid creating another problem. FMEA can help the team identify the risks and put additional necessary controls.

It is also necessary at this point to determine the effectiveness of solution/s be determining the process capability of the improved process through a pilot run.

Control: Monitor the Y and Important Xs Over Time

Control Phase locks in the gains and sustains the performance of your process overtime. This is where we employ Statistical Process Charts with the corresponding Out-of-Control-Action Plan (OCAP) on the critical X’s. When a control plan have been throughly documented (training plan, documentations, response plan etc), the project can now be handed over to the process owner.


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