4.0 Improve

Lean Six Sigma Refresher: The Improve Phase

The Improve Phase is where insights become action. After identifying root causes in the Analyze Phase, practitioners now design, test, and implement solutions that eliminate variation and drive measurable gains. This phase emphasizes experimentation, statistical validation, and practical deployment.

4.1 Simple Linear Regression

4.1.1 Correlation

  • Measures the strength and direction of the relationship between two variables.

  • Correlation coefficients (r) range from -1 to +1.

  • Helps identify whether changes in one variable are associated with changes in another.

4.1.2 Regression Equations

  • Regression models quantify the relationship between inputs (X) and outputs (Y).

  • Provides predictive capability for process outcomes.

4.1.3 Residuals Analysis

  • Residuals are the differences between observed and predicted values.

  • Analysis ensures model validity by checking for randomness and absence of patterns.

  • Detects issues like heteroscedasticity or non-linearity.

4.2 Multiple Regression Analysis

4.2.1 Non-Linear Regression

  • Models relationships that are not straight-line.

  • Useful when processes exhibit curvature or diminishing returns.

4.2.2 Multiple Linear Regression

  • Extends regression to multiple predictors.

  • Identifies the combined impact of several critical inputs.

4.2.3 Confidence & Prediction Intervals

  • Confidence intervals estimate the precision of regression coefficients.

  • Prediction intervals forecast the range of future outcomes.

  • Both provide context for decision-making.

4.2.4 Residuals Analysis

  • Same principles as simple regression, but applied across multiple predictors.

  • Ensures assumptions of linearity, independence, and normality are met.

4.2.5 Data Transformation, Box-Cox

  • Transformations stabilize variance and improve model fit.

  • Box-Cox method identifies optimal power transformations.

4.3 Designed Experiments

4.3.1 Experiment Objectives

  • Define clear goals: optimize performance, reduce variation, or identify key drivers.

  • Objectives guide design and analysis.

4.3.2 Experimental Methods

  • Common methods: factorial designs, response surface methodology, Taguchi methods.

  • Each balances efficiency with insight.

4.3.3 Experiment Design Considerations

  • Factors: number of variables, levels, interactions, and resource constraints.

  • Proper planning ensures meaningful results.

4.4 Full Factorial Experiments

4.4.1 2k Full Factorial Designs

  • Explore all possible combinations of factors at two levels.

  • Efficient for identifying main effects and interactions.

4.4.2 Linear & Quadratic Mathematical Models

  • Linear models capture straight-line relationships.

  • Quadratic models capture curvature and complex interactions.

4.4.3 Balanced & Orthogonal Designs

  • Balanced: equal representation of factor levels.

  • Orthogonal: independent estimation of effects.

  • Both improve statistical validity.

4.4.4 Fit, Diagnose Model and Center Points

  • Model fit assessed via residual plots and R².

  • Center points detect curvature in factor-response relationships.

4.5 Fractional Factorial Experiments

4.5.1 Designs

  • Use a fraction of full factorial combinations.

  • Reduces resource requirements while retaining insight.

4.5.2 Confounding Effects

  • Some factor effects may overlap (confound).

  • Must be carefully managed to avoid misinterpretation.

4.5.3 Experimental Resolution

  • Resolution defines the clarity of main effects vs. interactions.

  • Higher resolution designs provide more precise insights but require more runs.

Final Thoughts

The Improve Phase is the engine of transformation. By applying regression, designed experiments, and factorial methods, practitioners move from analysis to action—testing solutions, validating improvements, and optimizing processes. This phase demands both statistical rigor and creative problem-solving, ensuring that changes are not only effective but sustainable.