EXIN LSSA Six Sigma Black Belt cheat sheet

Sigma level maps to DPMO: 1σ ≈ 691,462; 2σ ≈ 308,537; 3σ ≈ 66,807; 4σ ≈ 6,210; 5σ ≈ 233; 6σ ≈ 3.4 DPMO (with the 1.5σ long-term shift applied).

The 1.5σ shift convention reconciles short-term Z (process capability) with long-term observed defect rates; it is a convention, not a physical law.

DMAIC is the improvement roadmap for existing processes; DMADV/DFSS is used when the process or product does not yet exist.

Lean targets the eight wastes (TIMWOODS): Transport, Inventory, Motion, Waiting, Overproduction, Overprocessing, Defects, Skills underused.

The Seven Quality Tools: check sheet, Pareto, cause-and-effect (fishbone), control chart, histogram, scatter diagram, flowchart.

The Seven Management (New) Tools: affinity, interrelationship digraph, tree, matrix, matrix data analysis, process decision program chart, arrow diagram.

Value-added test: the customer would pay for it, it changes form/fit/function, and it is done right the first time; failing any test makes it non-value-added.

Roles: Executive/Champion (resources, project selection), Master Black Belt (coaching, curriculum), Black Belt (full-time project leadership), Green Belt (part-time), Yellow/White Belt (awareness).

Kaizen is continuous incremental improvement by the work team; kaizen event = focused 3-5 day workshop; a kaikaku is radical redesign.

Cost of poor quality categories: internal failure, external failure, appraisal, prevention; prevention spend typically yields the highest return.

Charter elements: business case, problem statement, goal statement, scope (in/out), team, milestones, sponsor, expected benefits.

Problem statement rules: describe the gap, include metric and baseline, state timing and location, avoid cause and solution language.

Goal statement must be SMART and quantified against the baseline; typical target is a 50-70% reduction in the gap, not an arbitrary 6σ claim.

SIPOC: Suppliers, Inputs, Process (5-7 high-level steps), Outputs, Customers - used to set scope and identify CTQs.

VOC → CTQ tree: verbatim customer need → quality driver → measurable CTQ specification with target and tolerance.

Kano model classes: must-be (dissatisfiers), performance (linear), delighter (attractive); differentiates which CTQs drive satisfaction.

Pareto principle: roughly 80% of the effect comes from about 20% of causes; a Pareto chart ranks by frequency, cost, or impact.

RACI clarifies roles: Responsible (does the work), Accountable (one owner, decision), Consulted (two-way input), Informed (one-way update).

Project selection screens use impact/effort or priority matrices; projects should link to strategic objectives and be data-supported.

Measurement System Analysis: repeatability = equipment variation (same operator); reproducibility = appraiser variation; Gage R&R combines both.

Gage R&R acceptance rules (AIAG-style): %GRR < 10% acceptable, 10-30% conditionally acceptable depending on risk/cost, > 30% unacceptable.

Precision vs accuracy: precision is spread (repeatability), accuracy is on-target (bias); a gauge can be precise but biased.

Discrimination (resolution) must be at least 10:1 - the measurement increment should be ≤ 1/10 of the process tolerance or 6σ variation.

Attribute agreement analysis reports within-appraiser and between-appraiser agreement; kappa > 0.75 generally indicates good agreement.

Process capability: Cp = (USL-LSL)/6σ; Cpk = min[(USL-μ)/3σ, (μ-LSL)/3σ]; Ppk uses the overall (long-term) standard deviation.

Cp/Cpk assume stable, approximately normal data; for non-normal data use Box-Cox/Poisson/Weibull capability or percent-defective methods.

Sigma level from yield: Z = NORMSINV(1 - defect rate) for short-term; subtract 1.5 only when converting to the long-term convention.

Data types: continuous (variable) needs smaller samples than discrete (attribute); attribute data requires larger samples for the same confidence.

Sample size for mean confidence: n = (z·s/E)²; for proportion: n = z²·p(1-p)/E².

Baseline data collection plan: operational definitions, data type, stratification factors, sampling method, and who/when/where.

Hypothesis test logic: H0 states no difference/no effect; the p-value is the probability of data at least this extreme if H0 is true; reject H0 when p < α.

Type I error (α) = rejecting a true H0 (producer risk); Type II error (β) = failing to reject a false H0 (consumer risk); power = 1 - β.

Test selection: continuous Y vs continuous X → regression/correlation; continuous Y vs categorical X (2 levels) → 2-sample t; >2 levels → ANOVA.

Attribute Y vs attribute X → chi-square or Fisher's exact; attribute vs continuous → logistic regression or 2-proportion test.

Two-sample t-test assumes independent groups and approximate normality; use the F-test or Levene's test to check equal variances and choose pooled vs Welch.

ANOVA compares k means via F = MSbetween/MSwithin; a significant F requires post-hoc tests (Tukey, Dunnett) to identify which means differ.

Paired t-test is used when the same units are measured twice; it tests the mean of the differences.

Correlation coefficient r measures linear association only; r² is the proportion of variation explained; correlation does not establish causation.

Regression diagnostics: residual normality, constant variance, independence, no influential outliers (Cook's D); check R² adjusted and VIF for multicollinearity.

Multi-vari study stratifies variation into positional, cyclical, and temporal families to narrow the search for dominant causes.

FMEA: RPN = Severity × Occurrence × Detection; prioritize high-severity items even if RPN is moderate; Action Priority tables are an alternative to raw RPN.

DOE sequence: screening (fractional factorial) → characterization (full factorial/RSM) → optimization (steepest ascent, response surface).

Full factorial 2^k runs 2^k combinations; a half-fraction 2^(k-1) uses resolution III/IV/V aliasing; resolution IV means main effects are clear of two-factor interactions.

Randomization, replication, and blocking are the three principles of experimental design; blocking removes nuisance variation.

DOE main effect = change in response mean when a factor moves from low to high; interaction means the effect of one factor depends on the level of another.

Lean improvement tools: 5S (sort, set in order, shine, standardize, sustain), SMED (single-minute exchange of die), kanban, poka-yoke, TPM, standard work.

Poka-yoke types: prevention (contact, fixed-value, motion-step) and detection; aim for prevention at the source.

5 Whys and fishbone drive root-cause identification; verify the root cause with data before implementing countermeasures.

Control plan contents: process step, characteristic, specification, measurement method, sample size/frequency, control method, reaction plan.

SPC chart selection: variable data → X̄-R (small subgroup), X̄-s (larger subgroup), I-MR (individuals); attribute data → p, np, c, u.

Control limits are ±3σ from the process, computed from data, and are not specification limits; specifications come from the customer.

Western Electric/Nelson rules signal special cause: 1 point beyond 3σ, 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, 8 in a row on one side, trends, and cycles.

Control phase handoff: documented standard work, training, control charts owned by the process owner, and a response plan for out-of-control signals.