The** ANALYZE** phase is the beginning of the statistical analysis of the
problem. The practical problem was created earlier. This phase
statistically reviews the families of variation to determine which are
significant contributors to the output.

The statistical analysis
is done beginning with a theory, null hypothesis. The analysis
will "fail to reject" or "reject" the theory.

The families of variation and their contributions are quantified and relationships between variables are shown graphically and numerically to provide the direction for improvements.

**For example:**

You may analyze *part-part variation, shift-shift variation, operator-operator variation, machine-machine* variation.

By now the MSA has been accepted and the **Study Variation** has been quantified. The remaining variation is **Process Variation**.**Recall:**

TOTAL VARIATION = PROCESS VARIATION + MEASUREMENT SYSTEM VARIATION

Most of the analysis at this phase is **not** whether the AFTER process performance is different than the BEFORE process performance because none of the improvements have been implemented yet, these improvements are now becoming evident and prioritized.

This phase is about statistically comparing means and variation on all families of variation to drill down and quantitatively explain the critical sources of the dispersion.

By the end of the ANALYZE phase the KPIV's that are creating the most significant effect on "Y" should be identified. Any wastes found by employing Lean tools should be identified and prioritized to improve.

The outputs of ANALYZE lead into the inputs to the IMPROVE phase.

The following links cover topics that are often applied within the ANALYZE phase:

**Hypothesis Testing:**

F-Test

Student's T-Test

Analysis of Variance (ANOVA)

**Analyzing the sources of Process Variation:**

Families of Variation

Multivariate Analysis

**Statistics:**

Power and Sample Size

Alpha and Beta Risks (Type I Error and Type II Error)

P-Value

Confidence Intervals

Pearson's Correlation Coefficient

Spearman's Rho Correlation Coefficient

**Other topics:**

Takt Time

Line Balancing

Value Stream Mapping

Inventory Control

Cellular Flow

Z-score

**Distributions:**

Discrete Distributions

Continuous Distributions

**Shape of the Distribution:**

At this point in the project, and perhaps earlier in the MEASURE phase, there were delays or encounters of adversity. Here are a couple tools as reminders to keep the project on track and charging forward.

Return to the beginning of a DMAIC project

Proceed to the IMPROVE phase

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