3.0 Analyze

Lean Six Sigma Refresher: The Analyze Phase

The Analyze Phase is where data transforms into insight. After defining the problem and measuring the process, practitioners now focus on uncovering root causes of variation. This phase blends statistical rigor with practical problem-solving, ensuring improvements target the true drivers of performance.

3.1 Patterns of Variation

3.1.1 Multi-Vari Analysis

  • Examines variation across time, space, and different sources.

  • Useful for identifying whether variation stems from shift-to-shift differences, machine-to-machine differences, or operator-to-operator differences.

  • Provides a structured way to visualize complex variation patterns.

3.1.2 Classes of Distributions

  • Recognizing distribution types (normal, skewed, uniform, exponential) is critical.

  • Different distributions require different statistical approaches.

  • Misclassification can lead to incorrect conclusions about process behavior.

3.2 Inferential Statistics

3.2.1 Understanding Inference

  • Inference allows practitioners to draw conclusions about a population based on sample data.

  • Core principle: sample → estimate → population.

3.2.2 Sampling Techniques & Uses

  • Random sampling ensures unbiased representation.

  • Stratified sampling improves accuracy by accounting for subgroups.

  • Proper sampling prevents misleading results and strengthens conclusions.

3.2.3 Central Limit Theorem

  • States that the distribution of sample means approaches normality as sample size increases.

  • Foundation for many hypothesis tests and confidence intervals.

  • Enables use of parametric methods even with non-normal raw data.

3.3 Hypothesis Testing

3.3.1 General Concepts & Goals

  • Hypothesis testing evaluates whether observed differences are statistically significant.

  • Goal: distinguish between random variation and true process shifts.

3.3.2 Significance: Practical vs. Statistical

  • Statistical significance: Results unlikely due to chance (p-value < α).

  • Practical significance: Results meaningful in real-world terms (impact on cost, quality, customer).

  • Both must be considered to avoid “statistically significant but irrelevant” findings.

3.3.3 Risk: Alpha & Beta

  • Alpha (Type I error): Risk of rejecting a true null hypothesis.

  • Beta (Type II error): Risk of failing to reject a false null hypothesis.

  • Balancing these risks ensures reliable decision-making.

3.3.4 Types of Hypothesis Test

  • Parametric tests: Assume normality (t-tests, ANOVA).

  • Non-parametric tests: Used when data doesn’t meet assumptions (Mann-Whitney, Kruskal-Wallis).

3.4 Hypothesis Testing with Normal Data

3.4.1 1 & 2 Sample t-tests

  • Compare means between one sample and a target, or between two groups.

  • Useful for validating improvements or comparing process conditions.

3.4.2 1 Sample Variance

  • Tests whether process variance matches a target.

  • Ensures consistency in critical quality parameters.

3.4.3 One Way ANOVA

  • Compares means across multiple groups.

  • Identifies whether differences are statistically significant across categories.

3.5 Hypothesis Testing with Non-Normal Data

3.5.1 Mann-Whitney

  • Non-parametric alternative to the two-sample t-test.

  • Compares medians between two groups.

3.5.2 Kruskal-Wallis

  • Non-parametric alternative to ANOVA.

  • Compares medians across multiple groups.

3.5.3 Mood’s Median

  • Tests equality of medians across groups.

  • Robust against outliers.

3.5.4 Friedman

  • Non-parametric test for repeated measures.

  • Useful when data violates ANOVA assumptions.

3.5.5 1 Sample Sign

  • Tests median against a target value.

  • Simple but less powerful than Wilcoxon.

3.5.6 1 Sample Wilcoxon

  • Non-parametric test for median comparison.

  • More sensitive than the sign test.

3.5.7 One and Two Sample Proportion

  • Tests proportions (e.g., defect rates).

  • Critical for attribute data analysis.

3.5.8 Chi-Squared (Contingency Tables)

  • Tests independence between categorical variables.

  • Commonly used in defect classification or survey data.

Final Thoughts

The Analyze Phase is the heart of Lean Six Sigma’s problem-solving journey. By applying statistical tools and hypothesis testing, practitioners move beyond symptoms to uncover true root causes. This phase demands both technical skill and critical thinking—ensuring that improvements in the next phase are not just effective, but sustainable.