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Significance of Y=f(X) in Lean Six Sigma

If you are new to Lean Six Sigma then Y=f(X) is one amongst many jargons that you will have to familiarize yourself.

The objective of Lean Six Sigma philosophy and DMAIC improvement methodology is to identify the root causes to any problem and control/manage them so that the problem can be alleviated.

Six Sigma is process oriented approach which considers every task as a process. Even the simplest of the tasks, such as performing your morning workout or getting ready to office is considered as a process. The implication of such a view point is to identify what is the output of that process, its desired level of performance and what inputs are needed to produce the desired results.

Y is usually used to denote the Output and X for the inputs.

Y is also known as dependent variable as it is dependent on the Xs. Usually Y represents the symptoms or the effect of any problem.

On the other hand, X is known as independent variable as it is not dependent on Y or any other X. Usually Xs represents the problem itself or the cause.

As you will agree that any process will have at least one output but most likely to have several inputs. As managers, we all are expected to deliver results and achieve a new level of performance of the process such as Service Levels, Production Levels, Quality Levels, etc., or sustain the current level of performance.

In order to achieve this objective, we focus our efforts on the output performance measure.  However a smart process manager will focus on identifying Xs that impact the output performance measure in order to achieve the desired level of performance.

How does one identify the input performance measures or Xs?

Six Sigma DMAIC methodology aims to identify the inputs(Xs) that have significant impact on output (Y). After that the strength and nature of the relationship between Y and Xs are also established.

Six Sigma uses a variety of qualitative and quantitative tools & techniques listed below to identify the statistical validation of the inputs (or root causes), their strength and nature of relationship with Y:

  • Cause and Effect Diagram/Fish Bone diagram
  • 5 Why Analysis
  • Process Maps
  • Histogram
  • Descriptive Statistics
  • Run Charts
  • Normal Distribution Plots
  • Box plots
  • Stem and Leaf Plots
  • Hypothesis Testing
  • ANOVA (Analysis of Variance)
  • Chi-Square Test
  • 1-t Test
  • 2-t Test
  • Paired t Test
  • Correlation
  • Regression
  • Scatter Plots
  • Statistical Process Control (SPC)/Control Charts

What does f in Y= f(X) mean?

‘f’ represents the nature and strength of the relationship that exists between Y and X. On one hand, this equation can be used for a generic interpretation that symbolizes the fact that Y is impacted by X and nature of relationship can be quantified. On the other hand, such a mathematical expression can be created provided we have sufficient data using the above mentioned analytical tools such as regression and other hypothesis tests.

The mathematical expression that we obtain is nothing but an equation such as:

TAT = 13.3 – 7.4*Waiting Time + 1.8*No. of Counters – 24*Time to Approve

Once such an equation is established, it can be easily used to proactively identify the Y for various values of X. Thus Y= f(X) is the basis for predictive modeling. All the newer analytical concepts such as Big Data, etc are based on this foundation principles.

Criteria for Successful Lean Six Sigma Project

In a recent Lean Six Sigma Project kick-off meeting of one of my clients, after the teams presented their project charters, the business leader made an extempore announcement that the best and most successful Lean Six Sigma project will receive a special recognition and the team members will be lucratively rewarded.

Immediately few of them wanted to know what criteria will be used for selection. The business leader indicated that I will be the one who will define the criteria for successful Lean Six Sigma Project.

Factors that I consider among the criteria for success of Lean Six Sigma Projects are arranged in the descending order of their importance in the below list:

  • Project Scope – Lean Six Sigma projects without well defined scope are bound to fail, but they end up creating a lot of mess around.  Scope usually refers to the boundaries of any project. A poorly defined project is one which hasn’t balanced the Project Goal, Scope and Timelines. Also, poorly communicated scope and not defining what is out of scope are equally important and to be addressed.
  • Retains interest and commitment of the resources – Improvement projects are successful when its team members contribute their best. Lean Six Sigma projects usually challenge the existing paradigm. Hence without whole hearted and continued participation of the team members, no project will be successful. The sponsor/champion and the Green Belt/Black Belt are entrusted to retain the interest and commitment of the resources.
  • Attracts adequate buy-in from key stakeholders – Stakeholders of any project could either be the decision makers, important players who influence the decisions or even impacted parties. Successful Lean Six Sigma projects will have to manage the expectations of all the above stakeholders from time to time and create adequate buy-in. Rather than focusing too much on technical root cause analysis, the emphasis should be on how Lean Six Sigma project can bring about mid-to-large scale change in the organization.
  • Flawless execution– Immaterial of the breadth and depth of the analysis done in any Lean Six Sigma project, what sticks out is execution. Well led and implemented project is bound to be successful, as even the quality of data collected and analysis is a function of the flawless execution. Adherence to weekly team meetings, project milestones and tollgates reviews are some simple and easy signs to evaluate execution. Further unbiased data collection and analysis, open minded assessment of solutions, in depth piloting and sustained monitoring are additional measures of flawless execution.
  • Identifiable impact on customers – As the proof of the pudding is in the eating, so is the success of any Lean Six Sigma in positive impact it creates on customers. Usually organizations evaluate the success of projects based on the performance of the CTQ (before-after studies). While this is definitely a good way to assess the impact, more often than not, such movements in CTQs aren’t felt by the customers. Considering several other business parameters to validate the impact of the CTQ, including post improvement Voice of Customer may be a very good method. For example, a reduction in defects certainly will reduce the rework effort, increase productivity, reduce complaints, apart from increasing customer satisfaction.
  • Making a discovery – Any successful Lean Six Sigma project should un-earth something new, make a discovery about the problem. A project without a discovery could mean we are fixing obvious things. In order to ensure the project team makes a discovery, the quality of work done in the Measure and Analyze phase have to be evaluated. Have the teams identified all possible causes to the problem? Have they collected data of good quality and quantity? Have they holistically analyzed the data to make the discovery? And finally what is the discovery?

Based on my experience with Lean Six Sigma in the last 2 decades, I would consider these 6 factors as significant elements of successful project.