- Define: Start with a Pareto chart to prioritise which problem category to focus on.
- Measure: Use a run chart or control chart to establish a baseline and confirm the process is stable.
- Measure: Calculate process capability (Cp, Cpk) to see if you're meeting spec — but only after confirming stability.
- Analyse: Run hypothesis tests to verify which root causes are statistically significant.
- Analyse: Use correlation analysis to identify which input variables (Xs) drive your output (Y).
- Improve: Complete an FMEA to anticipate failure modes in your improved process.
- Control: Re-establish control charts on the improved process to monitor sustainment.
The 10 Core Statistical Tools
Each tool below answers a specific question at a specific point in DMAIC. Click through to the free calculator or template for any tool to start using it immediately — no login required.
Control Charts
Measure & Control phases
Is my process stable over time? Are the variations I'm seeing normal or a signal that something changed?
Inputs: Continuous or attribute data collected over time (20+ subgroups). Type depends on data: X-bar R for means, I-MR for individuals, p-chart for proportions, c-chart for counts.
Common mistake: Reacting to every point as if it's special cause. Only points outside control limits or showing non-random patterns (Western Electric rules) indicate instability.
Pareto Analysis
Define & Analyse phases
Which defect types or problem categories should I focus on first? Which 20% of causes drive 80% of the impact?
Inputs: Frequency counts for each defect or problem category, collected over a representative period.
Common mistake: Stopping at the first Pareto chart. Run a second-level Pareto on the top category to drill into root causes.
Process Capability (Cp, Cpk)
Measure & Control phases
Can my process consistently meet specification limits? How much of my output falls within acceptable range?
Inputs: Upper and lower specification limits (USL, LSL), process mean and standard deviation from 20+ data points.
Common mistake: Calculating capability before confirming the process is stable. Run a control chart first — capability from an unstable process is meaningless.
Hypothesis Testing
Analyse phase
Is the difference I'm seeing real or just random variation? Which root cause actually drives the outcome?
Inputs: Two or more datasets to compare. Test selection depends on data type: t-test for means, chi-square for proportions, ANOVA for 3+ groups.
Common mistake: Confusing statistical significance with practical significance. A p-value below 0.05 doesn't mean the difference matters — check effect size too.
Regression & Correlation
Analyse phase
Which input variables (Xs) drive my process output (Y)? How strong is the relationship and is it statistically significant?
Inputs: Paired data points for the input variable and output variable. Minimum 20 data pairs for meaningful correlation.
Common mistake: Assuming correlation means causation. A strong correlation identifies a relationship to investigate, not proof that one variable causes the other.
Histogram
Measure phase
What does the distribution of my process data look like? Is it normal, skewed, bimodal? Where do most outputs cluster?
Inputs: 50+ continuous data points. Bin selection affects interpretation — too few bins hide patterns, too many create noise.
Common mistake: Using too few data points. A histogram from 10 observations tells you almost nothing about the true distribution.
Run Chart
Measure phase
Is my process trending up, down, or staying stable? Are there obvious shifts or cycles in the data over time?
Inputs: 15+ time-ordered data points. Simpler than a control chart — no control limits calculated, but shows trends and shifts.
Common mistake: Treating a run chart as a substitute for a control chart. Run charts show trends; control charts add statistical limits to distinguish signal from noise.
Scatter Plot
Analyse phase
Is there a visible relationship between two variables? Does increasing X appear to affect Y?
Inputs: Paired (X, Y) data points. Plot 20+ points to see a meaningful pattern.
Common mistake: Forcing a linear interpretation on data that has a curved or threshold relationship. Always look at the scatter before fitting a line.
FMEA
Improve & Control phases
What could go wrong in my process, how bad would it be, and how likely is it? Which failure modes need controls first?
Inputs: Process steps, potential failure modes for each, severity (1-10), occurrence (1-10), detection (1-10) ratings.
Common mistake: Assigning scores individually rather than with a cross-functional team. FMEA scores should reflect consensus from people who know the process.
Measurement System Analysis (MSA)
Measure phase
Can I trust my measurement data? How much of the variation I'm seeing comes from the measurement process itself?
Inputs: Multiple operators, multiple parts, multiple trials. A Gage R&R study typically uses 2-3 operators, 10 parts, 2-3 trials.
Common mistake: Skipping MSA and blaming the process for variation that actually comes from inconsistent measurements. Always validate the measurement system first.