CSSGB formula sheet (free, printable)
Core formulas and references for the ASQ Certified Six Sigma Green Belt exam. Print this page or save to PDF from your browser's print dialog.
1. DMAIC phases — Green Belt scope
| Phase | Green Belt focus |
|---|
| Define | Project charter, SIPOC, VOC/CTQ, stakeholder analysis, problem/goal statement |
| Measure | Data collection plan, MSA/Gage R&R, baseline capability (Cp, Cpk), process mapping |
| Analyze | Root cause tools (fishbone, 5-Why, Pareto), graphical analysis, basic hypothesis tests |
| Improve | Solution selection, mistake-proofing (poka-yoke), kaizen events, piloting |
| Control | Control plan, SPC charts, response plan, sustaining gains |
A GB project is typically 3–6 months, one process owner, one team. BB projects are broader and go deeper into statistics (multiple regression, advanced DOE, multivariate tools).
2. Lean fundamentals
| Takt time | Takt = Available production time / Customer demand rate |
| OEE (Overall Equipment Effectiveness) | OEE = Availability × Performance × Quality |
| Cycle time | CT = Net production time / Units produced |
| Little's Law | L = λ × W (inventory = throughput rate × lead time) |
| Flow efficiency | Value-added time / Total lead time × 100% |
| Process lead time | Sum of all cycle times + wait times in the value stream |
| First-pass yield | FPY = units passing first time / total units started |
| Rolled throughput yield | RTY = FPY₁ × FPY₂ × … × FPYₙ |
3. Process capability
| Cp | (USL − LSL) / 6σ_within (uses σ estimated from R̄/d₂) |
| Cpk | min[ (USL − x̄)/3σ, (x̄ − LSL)/3σ ] |
| Pp | (USL − LSL) / 6σ_overall (uses sample s) |
| Ppk | min[ (USL − x̄)/3σ_overall, (x̄ − LSL)/3σ_overall ] |
| Sigma level → DPMO | With the conventional 1.5σ shift: 3σ ≈ 66,807 DPMO; 4σ ≈ 6,210; 5σ ≈ 233; 6σ ≈ 3.4 |
| DPMO | Defects × 1,000,000 / (Units × Opportunities per unit) |
| Rule | Cp/Cpk require a stable, in-control process. Run a control chart first. |
4. Control charts
I-MR chart (individuals, moving range) — most common at GB level
| I chart center line | x̄ |
| I chart control limits | x̄ ± 2.66 MR̄ (where MR̄ = average of |xᵢ − xᵢ₋₁|) |
| MR chart UCL | 3.267 × MR̄ |
| σ estimate | σ̂ = MR̄ / 1.128 |
X̄-R chart (subgroups, n = 2..10)
| X̄ chart limits | x̿ ± A₂ × R̄ |
| R chart limits | D₃R̄ (LCL) to D₄R̄ (UCL) |
| σ estimate | σ̂ = R̄ / d₂ |
p chart (proportion defective)
| Center line | p̄ = total defectives / total inspected |
| Control limits | p̄ ± 3√[ p̄(1−p̄) / n ] |
| Note | Negative LCL set to 0. Use u chart for defects per unit. |
Control chart constants (n = 2–7)
| n | A₂ | d₂ | D₃ | D₄ |
|---|
| 2 | 1.880 | 1.128 | 0.000 | 3.267 |
| 3 | 1.023 | 1.693 | 0.000 | 2.574 |
| 4 | 0.729 | 2.059 | 0.000 | 2.282 |
| 5 | 0.577 | 2.326 | 0.000 | 2.114 |
| 6 | 0.483 | 2.534 | 0.000 | 2.004 |
| 7 | 0.419 | 2.704 | 0.076 | 1.924 |
5. Basic statistics
| Mean | x̄ = Σx / n |
| Median | Middle value when sorted; average of two middle values if n even |
| Mode | Most frequently occurring value |
| Sample variance | s² = Σ(xᵢ − x̄)² / (n − 1) |
| Sample std dev | s = √s² |
| z-score | z = (x − μ) / σ |
| Standard error | SE = s / √n |
| Range | R = max − min |
6. Hypothesis testing
| Situation | Test | Statistic |
|---|
| 1-sample mean, σ known | z-test | z = (x̄ − μ₀)/(σ/√n) |
| 1-sample mean, σ unknown | t-test | t = (x̄ − μ₀)/(s/√n), df = n−1 |
| 2-sample means | 2-sample t | t = (x̄₁−x̄₂)/√(s₁²/n₁ + s₂²/n₂) |
| Proportions or counts | Chi-square | χ² = Σ(O−E)²/E; df = (r−1)(c−1) for independence, k−1 for goodness of fit |
| Two variances | F-test | F = s₁²/s₂² (larger on top) |
Decision rule: reject H₀ if p-value < α (typically α = 0.05). Type I error (α) = rejecting a true H₀. Type II error (β) = failing to reject a false H₀. Power = 1 − β.
Quick decision guide
| Question | Use |
|---|
| Did the mean shift? | t-test (paired if before/after same units) |
| Are two counts different than expected? | Chi-square goodness of fit |
| Is there a relationship between two categories? | Chi-square test of independence |
| Did variance change? | F-test or Levene's test |
7. DOE at Green Belt level (2² full factorial)
| Runs | 2² = 4 runs (A−B−, A+B−, A−B+, A+B+) |
| Main effect of A | avg(response when A=+) − avg(response when A=−) |
| Main effect of B | avg(response when B=+) − avg(response when B=−) |
| Interaction AB | avg(response when A and B same sign) − avg(response when A and B opposite sign) |
| Coded regression coefficient | effect / 2 |
A GB project typically uses a 2² or 2³ factorial. Fractional factorials and higher-order designs are BB territory.
8. FMEA
| Risk Priority Number | RPN = Severity × Occurrence × Detection (each 1–10) |
| Severity (S) | Impact of the failure mode on the customer (10 = hazardous) |
| Occurrence (O) | Likelihood the cause leads to the failure (10 = almost certain) |
| Detection (D) | Ability of current controls to find the failure before the customer (10 = no detection) |
| Threshold | Avoid fixed RPN thresholds (AIAG discourages them); address high severity first. AIAG-VDA (2019) replaces RPN with Action Priority (AP). |
| Priority | High Severity + High Detection gap is often more critical than a high RPN from high Occurrence alone. |
9. Lean waste — TIMWOODS
| Letter | Waste | Description |
|---|
| T | Transportation | Moving material or people farther than necessary |
| I | Inventory | WIP or finished goods beyond immediate need |
| M | Motion | Unnecessary physical movement by people |
| W | Waiting | Idle time waiting for materials, approvals, or equipment |
| O | Overproduction | Producing more than demand requires (creates other wastes) |
| O | Overprocessing | More work or quality than the customer requires |
| D | Defects | Errors requiring rework or scrap |
| S | Skills | Underutilizing employee knowledge and creativity (8th waste) |
10. VSM symbols — 8 most common
| Symbol name | Shape | Meaning |
|---|
| Process box | Rectangle | A manufacturing or service process step where value is added |
| Inventory triangle | Triangle (I) | Inventory or WIP between two process steps |
| Push arrow | Striped arrow → | Material pushed downstream regardless of demand |
| Pull arrow (supermarket) | Curved arrow with supermarket | Material pulled based on downstream signal |
| Supplier/Customer box | Factory icon | External supplier (top left) or customer (top right) |
| Data box | Rectangle below process | Process metrics: C/T, C/O, uptime, shifts, EPE |
| Kaizen burst | Star/lightning burst | Improvement opportunity identified in the current state |
| Timeline | Jagged line at bottom | Value-added time vs. non-value-added time across the stream |
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