Analyze Phase

Correlation, regression, hypothesis testing, FMEA, root cause analysis, and waste analysis.

5 minutes 5 Questions

The Analyze Phase is the third phase of the DMAIC methodology in Lean Six Sigma, following the Define and Measure phases. This phase focuses on identifying the root causes of process problems and understanding why defects or variations occur. The primary objective is to transform raw data collected…

Concepts covered
Cause and Effect Diagrams and A3Hypothesis Tests for ProportionsLinear Regression AnalysisHypothesis Tests for RegressionCorrelation Coefficient and Confidence IntervalsCorrelation vs CausationFactor Analysis and Discriminant AnalysisMultiple Analysis of Variance (MANOVA)Sample Size Calculation for Hypothesis TestsTolerance IntervalsHypothesis Tests for VariancesGoodness-of-Fit Chi-Square TestsTypes of Risk (Enterprise, Operational, Supplier)DFMEA vs PFMEARoot Cause AnalysisPareto Charts for Root CauseFault Tree AnalysisResiduals Analysis for Model ValidationSignificance Level, Power, and Error TypesType I Error (Alpha) and Type II Error (Beta)Statistical vs Practical SignificanceAnalysis of Variance (ANOVA)Risk Priority Number (RPN)Gap Analysis5 Whys AnalysisSeven Classic Wastes AnalysisRegression Model Estimation and PredictionConfidence and Prediction IntervalsHypothesis Tests for MeansFailure Mode and Effects Analysis (FMEA)Resource Under-Utilization Waste
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CSSBB - Analyze Phase Example Questions

Test your knowledge of Analyze Phase

Question 1

A team finds a strong positive correlation (r = 0.89) between the number of training hours employees complete and their defect rates on a production line. A manager concludes that increasing training hours will reduce defects and requests budget approval for expanded training. As the Black Belt on this project, what is the most appropriate next step before endorsing this recommendation?

Correct Answer: Conduct a designed experiment or controlled study to test whether training hours actually drive defect reduction

Correlation does not imply causation, so the most appropriate next step is to conduct a designed experiment (DOE) or controlled study to establish whether a true causal relationship exists between training hours and defect rates before committing resources.

Endorsing the recommendation based solely on correlation ignores the fundamental principle that correlation does not equal causation. Performing regression analysis would still only model an associative relationship, not prove causality. Investigating confounding variables and stratifying data is a reasonable analytical step but still falls short of establishing causation, which requires experimental control and manipulation of the independent variable.

The key concept tested is the distinction between correlation and causation in the Analyze phase.

Question 2

A team wants to compare the mean fill weight of two production lines using a two-sample t-test. They need to detect a difference of 0.5 grams, with an estimated standard deviation of 1.2 grams for both lines. They set alpha at 0.05 and want 80% power. Using the formula n = (Zα/2 + Zβ)² × 2σ² / δ², what is the approximate sample size per group?

Correct Answer: Approximately 92 samples per group are needed to meet the specified power and significance requirements

Using the formula n = (Zα/2 + Zβ)² × 2σ² / δ², we substitute Zα/2 = 1.96, Zβ = 0.84, σ = 1.2, and δ = 0.5, giving n = (1.96 + 0.84)² × 2(1.44) / 0.25 = (2.80)² × 2.88 / 0.25 = 7.84 × 11.52 = 90.3, which rounds up to approximately 91 or 92 per group.

The answer of 46 per group incorrectly halves the required size by misapplying pooled variance logic. The answer of 61 per group incorrectly redistributes a total sample size with an unjustified adjustment. The answer of 72 per group incorrectly applies a finite population correction, which is not part of the standard formula.

Key concept tested: sample size determination for a two-sample t-test using power analysis.

Question 3

What does a residual represent in regression analysis?

Correct Answer: The difference between an observed value and the value predicted by the model

A residual is defined as the difference between an observed (actual) value and the corresponding fitted (predicted) value from the regression model, expressed as e = Y - Ŷ. Residuals measure the error or unexplained variation left over after fitting the model.

The difference between the mean and predicted values describes explained deviation, not residuals. The ratio of observed to fitted values is not a standard regression metric. The squared difference between predictor variables and their means relates to sums of squares for the independent variable, not residuals.

Key concept tested: understanding residuals as the unexplained portion of variation in regression analysis.

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