Examples — overview

5-Why chain from symptom 'pizza arrives late' down to root cause 'order system without logistics function'.

32 events across 7 weeks — from kickoff to project closure, with a gate review per phase. Dates are remapped to the current week (Monday anchor) on load so the plan always centers on today.

Six customer needs of a delivery service, rated by three customers using Kano — including the importance question and one tie.

5-Why chain from "times vary between 1.5 and 2.3 s under identical configuration" down to the root cause "throwing technique not standardized".

Charter for "Paper Helicopter from the trade-show booth — maximizing flight time with a single prototype". In scope: rotor length and paperclips. Out of scope: rotor width (irreversible, only 1 prototype), throwing technique, paper type, drop height. Target Y: mean flight time ≥ 3.0 s at σ ≤ 0.15 s.

5 follow-up tasks after project close: a workflow note on activating the optimum panel in response-optimization, a second flyer for the wing-width augmentation, drop-height variation for robustness, documenting a throw SOP, and building a throwing fixture.

Kano classification of three helicopter characteristics: must-be "flies at all", performance "flight time", attractive "autorotation (elegant spin, soft landing)". Ships its own VoC/CTQ tree instance (identical to the "Paper Helicopter — VoC/CTQ" example).

SIPOC of the helicopter process: from the raw flyer through cutting, folding, clipping and dropping to the 18-run log table. Highlights the physically forced "trim rotor (between blocks)" step that motivates the later DoE blocking.

Stakeholder matrix with Qprovement Marketing (power high, interest high), trade-show visitor (power medium, interest high), flight instructor as SME (power low, interest medium), and paper supplier (power low, interest low).

VoC "should fly long and glide down gently" translated into three CTQs: flight time ≥ 3.0 s, spread σ ≤ 0.15 s, and autorotation (qualitative). Forms the tree basis for the linked Kano example.

Suppliers, Inputs, Process, Outputs, Customers for the Bella Margherita delivery process — 8 process steps from order intake to handover.

15 tasks for the pizza delivery project across the DMAIC cycle — from kickoff and SIPOC through Ishikawa and hypothesis test to the reaction plan and lessons learned. Status, owner and target dates spread realistically: three done, three in progress, eight open, one blocked (waiting on a sponsor decision). Items with the calendar flag enabled appear in the DMAIC calendar as soon as that module is added to the Define tile.

Teaching case 'Bella Margherita': delivery times too long, cold-pizza complaints rising. Pre-filled with problem statement, three measurable goals, and the project-team org chart.

RACI matrix for 8 activities × 6 roles — who is R(esponsible), A(ccountable), C(onsulted), I(nformed)?

7 stakeholders from CEO to accounting with power/interest ratings and support attitude (supporter / neutral / resistor).

3 Voice-of-Customer quotes (cold pizza, long delivery, address issues) translated into CTQs with measurable requirements.

Mixture of two normal distributions around 9.93 and 10.07 mm. Violates the normality assumption of Cpk.

100 normally distributed measurements around μ ≈ 10.00 mm with σ ≈ 0.05 mm. Textbook capable-process example.

13 parts × 3 appraisers × 2 trials, binary result (pass/fail). Every rating agrees — except appraiser D, who rates part 20 differently on the second trial.

25 repeated measurements of a 10.0 mm reference part (LSL 9.9 / USL 10.1, T = 0.2 mm). Very small spread, negligible bias → Cg ≈ 2.56 and Cgk ≈ 2.51 well above the 1.33 threshold. Textbook capable-gage case.

25 repeated measurements with large spread and noticeable bias. Cg ≈ 0.40 and Cgk ≈ 0.17 — gage clearly fails the capability threshold. Textbook case for a measurement system that must be rejected.

25 repeated measurements with moderate spread and slight positive bias. Cg ≈ 1.01 sits just above the 1.0 threshold, but Cgk ≈ 0.68 falls well below it — bias pulls capability into the not-capable range (overall verdict: not capable). Shows why Cgk must be checked alongside Cg.

Crossed ANOVA study: 10 parts × 3 operators × 3 replicates (90 measurements). Small repeatability and reproducibility variation, dominant part variance → %GRR ≈ 5 % of study variation, ≈ 4 % of tolerance (6–14). Textbook acceptable measurement system.

Crossed ANOVA study with large repeatability and reproducibility variation versus small part variance. 10 parts × 3 operators × 3 replicates → %GRR ≈ 79 % of study variation, ≈ 35 % of tolerance (7–13). Textbook case where the measurement system masks part-to-part variation.

One-way random-effects ANOVA study without operator influence (25 parts × 2 replicates, Bosch convention). Automated CMM measures shaft diameter, within-part variation ≈ 1.5 µm vs. part-to-part variation ≈ 22 µm → %GRR ≈ 8 % of study variation, ≈ 9 % of tolerance, ndc = 16. Textbook acceptable automated measurement system.

Five references (2/4/6/8/10) with 10 repeats each; bias grows from 0 (ref 2) to +1.6 (ref 10). Clear linearity error — %Linearity ≈ 13 %, Q_MS,BI ≈ 27 %, slope highly significant. Both AIAG and VDA 5 turn red. Textbook case for rejecting a measurement system.

Five references (2/4/6/8/10) spanning the measurement range (LSL 0 / USL 12, T = 12) with 10 repeats each. Negligible bias and no slope — %Linearity ≈ 0.07 %, Q_MS,BI ≈ 0.15 %. Textbook linear-gage case across the full range.

3 appraisers × 30 parts × 3 replicates (binary OK/NOK). Fleiss κ ≈ 0.92, effectiveness ≈ 97.8 % per appraiser. Textbook acceptable attribute gage.

3 appraisers × 30 parts × 3 replicates (binary OK/NOK). Fleiss κ ≈ 0.58 and effectiveness 83–88 % alone would be marginal; under AIAG the miss rate (up to 24 %) and false-alarm rate (up to 23 %) decide — the gage is not acceptable. Five parts with unbalanced replicates; removing the reference column triggers ambiguous consensus (W_AMBIGUOUS_CONSENSUS).

3 appraisers × 20 templates × 2 replicates (binary OK/NOK). The classic counting exercise from training: Fleiss κ ≈ 0.79, effectiveness 85–90 %; the AIAG verdict is red because the miss rate (25 %) and false-alarm rate (17 %) are too high. Contains all three teaching cases — an over-strict appraiser, an appraiser who contradicts himself, and one template where everyone agrees and everyone is wrong.

3 appraisers × 25 parts × 2 replicates (nominal A/B/C). Fleiss κ ≈ 0.84, effectiveness 94–96 % per appraiser. Illustrates pairwise Cohen κ, Fleiss κ and confusion heatmaps for unordered categories.

3 appraisers × 20 parts × 2 replicates (ordinal 1–5). Fleiss κ ≈ 0.77, weighted Cohen κ (quadratic) ≈ 0.95 per pair, effectiveness ≈ 90 % per appraiser. Occasional neighbour ratings (±1) — module reports weighted κ as the leading KPI.

50 individual measurements with a linear trend (+0.02 per point). The drift test fires highly significant (p ≈ 0.00009) — the gage or process drifts over time.

50 individual measurements without subgroups. Control chart and drift test unremarkable (p ≈ 0.84) — textbook case of a stable process with no special causes.

25 subgroups of n = 5, baseline limits from only the first 15 subgroups. From subgroup 16 onward the mean shifts by +1.2·σ_x̄ — Nelson rules 5/6 fire, verdict “unstable” (driver: Nelson). Warns because the baseline has fewer than 20 subgroups.

25 subgroups of n = 5. X̄ chart and R chart unremarkable, drift test not significant (p ≈ 0.41) — textbook case of a stable subgrouped process.

25 repeated stopwatch readings against a metronome reference (60 bpm, target value 2.000 s) — Cg ≈ 1.35 / Cgk ≈ 1.15: capable, but borderline. Teaching point: check the clock before running the DoE.

8 process steps from cutting to block change, including exact fold dimensions (rotor 80×47 mm, body 130 mm, fold lines x = 30/47/63 mm) and a rework loop back to the folding step on a fold defect.

8 process steps with value-type classification (VA / BNVA) and input types (parameter x / noise n). Order → kitchen → bake → pack → deliver → handover.

Mean off-center (μ ≈ 10.08 mm) → low Cpk despite small dispersion.

7 steps from capturing a customer inquiry to the order confirmation — 6 activities plus one approval decision whose no-branch opens its own band with a revision step before looping back into the quote calculation.

30 bolt diameters from N(10.000, 0.050) with two seeded outliers at 9.745 and 10.260 (≈ ±5σ). Grubbs (two-sided), generalized ESD and Tukey IQR should flag both.

Inputs (routing, oven, traffic, …) versus outputs (delivery time, temperature, complaint rate) — weighted 0–9 ratings of the dependencies.

Compare cycle time of two machines: difference Δ = 0.5 min at σ ≈ 0.8 min. Two-sided t-test, α = 0.05, power = 80 %. Cohen's d ≈ 0.63 — returns the n per group.

Compare scatter of two suppliers: suspected doubled variance (σ²₁/σ²₂ = 2.0). Two-sided F-test, α = 0.05, power = 80 %. Returns the sample size per group.

Complaints per day across five branches A–E, sample sizes 8/10/12/15/9. Branch D has a clearly elevated mean (6.2 vs. ~5.0) — post-hoc comparisons separate D from the rest.

Delivery times (min) for three drivers A/B/C, 15 each. True means 22/25/28 min at σ ≈ 3 — Cohen's f ≈ 0.82, strong ANOVA signal.

5 steps from order to goods receipt across three lanes — customer, sales, and production — with four hand-offs made visible as lane switches.

After a process improvement, scatter should have dropped from σ₀ = 1.5 to σ₁ = 1.0. One-sided chi-square test, α = 0.05, power = 80 %. Returns the n needed to confirm the improvement statistically.

80 waiting times from Exponential(μ=15 min) — memoryless distribution. Exponential and gamma rank highest.

80 cycle times from Lognormal(μ_log=ln 5, σ_log=0.6) — strongly right-skewed. Distribution-fit should rank lognormal first.

80 values from N(μ=10, σ=2) — clean textbook normal distribution. Shapiro-Wilk / Anderson-Darling should not reject H₀.

80 component lifetimes from Weibull(k=2.5, λ=100 h). Classic wear-out case (β > 1); Weibull should rank as best fit.

4 risks along the delivery process (address entry, oven overload, thermal packaging, traffic) with S/O/D ratings and 2 dated actions each (one already completed, one planned) — burndown shows plan and actual lines.

8 steps across 5 roles (customer, sales, dispatch, warehouse, accounting). Processing ≈ 53 min, waiting time dominates with ca. 2 d 13 h 30 min — PCE below 3 %. Showcases standard issues: inbox idle time, handover waiting, customer-side delays.

Full 6-M example: 6 hypotheses across Man, Method, Machine, Material, Environment, Measurement — rated by three experts — plus 7 supporting facts and 6 experiments (with status, schedule, cost, linked to hypotheses).

Check whether the process mean drifts by Δ = 0.3 from target (σ ≈ 0.5). Two-sided t-test, α = 0.05, power = 80 %. Cohen's d = 0.6 (medium effect).

2 machines × 2 shifts × 2 batches, unequally occupied with one missing combination. Crossed with REML — also shows how the module flags an unbalanced design.

2 shifts × 2 mould cavities × 3 parts, 2 wall-thickness measurements each. Balanced and nested: most of the variation sits between the cavities, not between the shifts.

5 steps from the customer inquiry to the sent quotation — 3 value-added steps on the left, 2 rework steps on the right (chasing missing details, correcting the calculation).

6M fishbone diagram for flight-time variation: throwing technique, clip fit, paper, folding precision, drafts and stopwatch reaction time as candidate causes — throwing technique confirmed as the main driver.

Same 30 pizza deliveries as the regression dataset — here as a correlation matrix over distance, traffic level and delivery time. Highlights the strong pairwise Pearson correlations.

Pre-filled criteria for project selection in the pizza-delivery process: delivery time, pizza quality, price, employee satisfaction, complaint rate. Pairwise comparisons are run inside the module.

9 steps across 4 roles, paper-based workflow from application to system booking. Processing ≈ 22 min, Lead Time > 4 workdays — PCE < 1 %. Classic office lever: one huge idle block in the manager's inbox.

30 batches with batch size and supplier as predictors, complaints as response. Overdispersed count data — negative binomial regression additionally estimates the dispersion parameter θ.

Three continuous factors, quadratic model, 12 runs total — six already measured. The example creates a data sheet with the existing measurements and augments it with six additional D-optimal runs.

Three continuous factors plus one three-level categorical factor (material). Mixed-level optimal designs are a textbook D-optimal use case — classic schemes cannot handle this.

Response-surface model with three continuous factors and a full quadratic polynomial in 12 runs. Classic D-optimal use case.

Five continuous factors with main effects and two-factor interactions in 18 runs. D-optimal alternative to Plackett-Burman when 2FI must stay in the model.

40 shifts with feed rate (mm/s) and tool wear (h) as predictors, defect counts as response. Poisson model with log(λ) = -1 + 0.02·feed + 0.03·wear.

30 vehicle measurements speed → fuel consumption. Two deliberate outliers (rows 6 and 23) drop R² compared to the clean linear fit. Textbook case for residual diagnostics and outlier detection.

30 motor trials with rpm and torque as predictors, power as response. Torque ≈ 0.04·rpm — predictors are highly collinear, VIF spikes. Textbook multicollinearity case.

3² full factorial with 2 replicates (18 runs), blocked by rotor length (L = 8 → 6 → 4 cm, physically forced). Paperclip order randomized within block. True optimum at (L ≈ 7 cm, C = 1) lies between tested lengths — a textbook RSM case.

Goal: optimize the regression model from the DoE Planner "Paper Helicopter" example (18 runs) for "maximize flight time". Predicted optimum at (L ≈ 7 cm, C = 1) → t̂ ≈ 2.80 s, lower desirability bound 2.5 s — lies between the physically tested rotor lengths (6 and 8 cm) and demonstrates the core RSM advantage. This example only loads an empty optimizer state, since response-optimization sources models project-globally from the Regression module. Workflow: open the doe-planner example → action "Transfer to Regression" → "save as model" there → response-optimization then comes alive with data.

30 pizza deliveries with distance (km), traffic level (1–5) and measured delivery time (min). Linear model Time ≈ 5 + 2.5·distance + 1.2·traffic — textbook dataset for multiple linear regression with high R².

50 PCBs with solder temperature (220–255 °C) and pressure (2.0–3.5 bar) as predictors, defect (0/1) as response. Textbook case for binary logistic regression without a trials column.

30 production lines with speed (parts/min) and line age (years) as predictors, surface defect counts as response. Poisson model for predicting the expected defect rate.

3×3 matrix Sub-/System/Super-system × Past/Present/Future — applied to the pizza delivery process.

Classic TRIZ contradiction from the pizza case: deliver faster without sacrificing productivity. Improving = 9 (Speed), worsening = 39 (Productivity).

Eight classical evolution trajectories applied to a passenger-car headlight — from twin-headlight to adaptive LED matrix and beyond.

Three IFR levels for a jamming belt-conveyor transfer chute, with an obstacle list as the task backlog.

Classic textbook case: a wing must be both long (lift) and short (drag). Resolved via separation in time — swing wing.

Resources inventory across 6 categories × 3 system levels for the belt-conveyor case — companion to the IFR example.

Su-Field model for an insufficient mechanical action (drill on concrete). Diagnosis: class 2 — pulsed mode (hammer drilling) selected.

Eight temperature levels with 50 trials each. Binomial response (successes / trials) follows a logistic curve with inflection around 160 °C. Textbook case for binomial GLM with a trials column.

50 lognormally distributed lifetimes. A plain I-MR chart raises false alarms because of the right skew. After Box-Cox transformation (λ ≈ 0) the residuals become approximately normal.

30 inspection units of constant size. Mean defects ≈ 3, units 22–23 spike to ~8 — c-chart triggers.

60 observations: mean stays at μ=10 for the first 30 points, then shifts to μ=10.1 (≈ 1σ). EWMA with λ=0.2 detects the drift; a Shewhart I-chart misses it.

40 bivariate observations with ρ ≈ 0.85. Observations 30 and 31 are multivariate outliers — plausible on each margin but joint deviates from the correlation ellipse.

50 individual measurements with a linear upward drift (+0.6 across the series). Nelson rule 3 (six points in a row trending up) should fire multiple times.

50 individual measurements with a step shift from μ = 10.00 to μ = 10.18 at observation 30. The Nelson rules (especially rule 1 and rule 5) should flag the shift.

4 lessons from the pilot: pre-route planning (success), double-wall thermal boxes (success), Monday standup (improvement), order intake bottleneck (problem).

30 inspection lots with variable sample size (80–120) and varying defect rate. Lots 18–20 at ~10 % — the p-chart should flag them as out-of-control.

I-MR chart from 5 confirmation runs at the optimum (L = 6 cm, C = 1 clip, mean ≈ 2.76 s, σ ≈ 0.12 s). Control limits derived from the baseline spread — the process is in control at the optimum.

5 lessons from the project: sequential blocking resolves the irreversibility of the rotor length (success), MSA before DoE (success), focusing on two factors (success), plus wing width not viable as a third factor (problem) and throwing technique dominating the residual variation (problem).

25 subgroups of 5 measurements each from a stable process (μ = 10.00 mm, σ = 0.05 mm). X̄-R chart shows no Nelson-rule violations.

Three short setups with different means (10, 25, 7.5), 8 measurements each. After nominal centering they form one comparable process (σ ≈ 0.05).

25 intervals from Exponential(μ=35 days). At observations 16–18 the rate doubles (μ=12) — t-chart shows a visible shift.

Bolt diameter measurement series with a few embedded outliers.

80 strongly right-skewed lognormal cycle times. Box-Cox (optimal λ ≈ 0) makes the values approximately normal.

50 Q2 complaints with reason and individual cost. The Pareto analysis sums cost per reason and sorts descending — the 80 % line shows that 'dimensional deviation' alone accounts for most of the cost, even though it is not the most frequent reason. Textbook example: frequency ≠ importance.

248 customer complaints from Q1, split across six reasons. Donut variant (innerRadius = 0.5) with the total shown as the center label — useful when the total itself carries a key message.

45 cycle-time measurements (in seconds) across three shifts (early/late/night) and three production lines (L1/L2/L3) — 5 readings per combination. The heatmap reveals two effects at once: a line effect (L3 ≈ 30 s slower than L1) and a shift effect (night ≈ 10 s slower than early). The (night, L3) cell at 82 s is the clear worst case — a perfect starting point for the Analyze phase.

60 defect events across three shifts (Early/Late/Night) and four defect types (scratches, dimensional, surface, other). The stacked bar chart shows at a glance that the early shift is dominated by dimensional defects while the night shift produces mostly surface defects — a classic anomaly for the Measure phase.

Three boxes showing delivery-time distributions for drivers A/B/C. Same data as the ANOVA example — the boxplot visualizes the ANOVA effect.

Three point clouds of delivery time for drivers A/B/C with connected means — same data as the ANOVA and boxplot examples.

Raw delivery-time data, grouped by driver.

Raw engine-trial data with several collinear predictors.

Raw fuel-consumption data with a few embedded outliers.

Same 30 vehicle measurements as the regression dataset — scatter plot of fuel consumption over speed with stats panel. Two deliberate outliers (rows 6 and 23) are directly visible in the plot.

15-row inspection log that exercises all seven worksheet column types: text (inspection ID, shift), date, time, numeric (diameter in mm), currency (unit cost €), percent (scrap rate) and binary (OK 0/1). Includes a few null cells on purpose to show how missing values are handled.

10 machines with cycle time, scrap rate and daily output. The bubble chart prioritises Six Sigma improvement projects: large bubbles in the upper right (high scrap at high output) are the most expensive problem cases.

Same 30 motor trials as the regression dataset — two scatter plots of power over rpm and power over torque, with stats panel. Visualises the strong predictor correlation before fitting a regression.

10 order rows with quantity, unit price (€), calculated total (=qty·price), discount (%) and final price (=total·(1-discount)). Demonstrates cell-reference formulas and currency/percent columns.

10 baseline runs at (L = 8 cm, C = 0 clips) as an individual value plot — shows the mean and spread of flight time before the DoE.

Scatter plot of the 18 DoE runs (clips vs. flight time) — shows a visibly non-linear relationship across all three rotor lengths, motivating the quadratic clip term in the DoE.

Raw data of the trade-fair project in three sheets: baseline (L = 8 cm, C = 0), 3² full factorial with 2 replicates (18 runs) and confirmation runs (L = 6 cm, C = 1).

Raw MSA type 1 data: repeated stopwatch readings against a 2.000 s metronome reference.

Raw pizza delivery data: delivery time, distance, number of pizzas, driver.

Same 30 pizza deliveries as the regression dataset — scatter plot of delivery time over distance with stats panel. Useful for visual exploration before fitting a regression.

10 production lines with defect rate, repair cost per defect, and monthly defect count. The bubble chart shows the classic frequency ↔ unit-cost trade-off; bubble size reveals which lines carry the largest absolute loss potential — an ideal entry point for DMAIC project selection.

Three sheets (Q1/Q2/Q3) with production data of 10 batches each. Demonstrates the multi-sheet feature of the worksheet — switch via tabs at the bottom.

12 Six Sigma project candidates with effort (person-days), annual benefit (k€) and risk score, grouped by area (Production vs. Quality). The bubble chart prioritises project selection while showing how the two areas position themselves in the effort/benefit/risk landscape: small bubbles in the upper left are quick wins; large bubbles in the lower right should be deferred.

Two shifts of 40 measurements each — shift A ≈ N(μ=9.5, σ=1.5), shift B ≈ N(μ=10.8, σ=2.2). The probability plot shows two lines with different location and slope.

80 bolt diameters measured with a gauge that is too coarse (resolution 0.1 mm versus process σ ≈ 0.15 mm). The probability plot shows clearly visible vertical stripes — a classic indicator of insufficient measurement resolution.

80 Weibull(k=2.5) lifetimes on the normal probability plot — visible curvature in the tails.

I-MR series: observations 1–29 stable at μ=10, from obs. 30 shift to μ=10.18. Western Electric / Nelson rules flag the shift.

395 scrap parts from a production line, split across six mutually exclusive defect types. Textbook pie-chart use case: share of a few categories of a whole. Full-circle variant (innerRadius = 0).

60 approval decisions across three plants and three status levels (OK/conditional/rejected). The mosaic plot reveals two effects at once: the volume differences (column widths — plant A has twice as many decisions as plant B, three times more than plant C) and the quality differences (segment heights — plant C has clearly more rejections per plant).

12 suppliers with price index, on-time delivery rate and annual order volume. The bubble chart visualises the classic price ↔ reliability trade-off; bubble size reveals which suppliers carry the largest strategic weight.

Quadratic model for yield = f(temperature, pressure) with optimum at 180 °C and 3 bar. Shows a classic contour map with a pronounced maximum.

Capability analysis, histogram, control chart and outlier test on one measurement series.

Just the measurement series as a data collection. Analysis is up to you.

Multiple regression with multicollinearity plus a scatter plot of the same data.

Just the trial data as a data collection.

Regression with outlier diagnostics plus a scatter plot of the same data.

Just the consumption data as a data collection.

Complete DMAIC walkthrough of the trade-fair project, from charter through MSA and root-cause analysis to a 3² full factorial with response optimization.

Just the starting point: charter, the flight-time data collection (baseline, DoE, confirmation) and the baseline plot. The analysis is up to you.

Complete DMAIC walkthrough from project charter to lessons learned, including data analysis.

Problem statement, process frame and raw data. You do the analysis; individual examples can be loaded later.

Ideal final result and resource checklist for the same problem.

Only the ideal final result as a starting point.