CSSC Black Belt cheat sheet

DMAIC phases and core deliverables: Define (project charter, VOC/CTQ, SIPOC, stakeholder analysis), Measure (operational definitions, MSA, baseline capability), Analyze (root-cause verification, hypothesis tests), Improve (DOE, pilot, solution selection), Control (SPC, control plan, standard work, poka-yoke).

Project charter elements: business case, problem statement (with magnitude, location, timing), goal statement (SMART, no solution embedded), scope/in-scope-out-of-scope, team and roles, milestones, expected financial benefit.

Y = f(X1...Xn): Y is the output/CTQ; Xs are process inputs. Six Sigma projects reduce variation in Y by identifying and controlling the vital few Xs (typically 20% of Xs drive 80% of Y variation).

VOC to CTQ translation: collect voice of customer (interviews, complaints, Kano survey), translate to needs, then to measurable CTQ characteristics with operational definitions and specification limits.

SIPOC maps Suppliers, Inputs, Process (4-7 high-level steps), Outputs, Customers; used in Define to set scope and in Measure to identify measurement points.

Lean wastes (TIMWOODS): Transport, Inventory, Motion, Waiting, Overproduction, Overprocessing, Defects, Skills unused. Value-added work is defined by the customer and must transform the product/service.

Six Sigma belt roles: Champion (sponsor, removes barriers), Master Black Belt (technical coach, curriculum), Black Belt (full-time project leader), Green Belt (part-time leader), Yellow/White Belt (awareness, team member).

Cost of poor quality (COPQ): internal failure, external failure, appraisal, prevention. Six Sigma projects should target the failure categories, which are typically 60-90% of total quality cost.

Descriptive statistics: mean = Σx/n; sample standard deviation s = sqrt(Σ(x-x̄)²/(n-1)); median resistant to outliers; range = max - min. Report n, mean, s, and shape together.

Measurement system analysis: repeatability (equipment variation, EV) and reproducibility (appraiser variation, AV). Gage R&R %GRR = 100 × GRR/TV, where GRR = sqrt(EV² + AV²) and TV = sqrt(GRR² + PV²).

Gage R&R decision rule: %GRR < 10% acceptable; 10-30% conditionally acceptable depending on cost/risk; > 30% unacceptable - improve the measurement system before collecting process data.

Number of distinct categories (ndc) = 1.41 × (PV/GRR); require ndc ≥ 5 for the gage to discriminate parts.

Attribute agreement: kappa = (Po - Pe)/(1 - Pe), where Po = observed agreement and Pe = chance agreement. Kappa ≥ 0.75 is generally good; ≥ 0.90 excellent.

Process capability for stable normal data: Cp = (USL - LSL)/(6σ); Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]. Cpk accounts for centering; Cp does not.

Ppk uses overall sample standard deviation (long-term); Cpk uses within-subgroup σ estimated from R-bar/d2 or s-bar/c4. Compare Cpk vs Ppk to detect between-subgroup shifts.

Sigma level from Cpk (centered, short-term): Z = 3 × Cpk; DPMO conversion via normal table, e.g., Cpk = 1.0 → 3σ → ~2,700 DPMO (long-term 1.5σ shift convention).

Data types: continuous (variable) vs discrete (attribute: defectives vs defects). Attribute capability: p = d/n; for defects per unit, u = c/n; use p-charts for proportion defective, c/u charts for counts.

Hypothesis test logic: H0 (no difference/no effect) vs H1; α = P(Type I error, reject true H0); β = P(Type II error, fail to reject false H0); power = 1 - β.

p-value decision rule: reject H0 if p-value < α. The p-value is P(data at least this extreme | H0 true), not P(H0 true).

Test selection: 1-sample t (mean vs target, σ unknown); 2-sample t (two independent means); paired t (before/after on same units); 1-proportion/2-proportion Z (attribute); chi-square (independence, homogeneity); ANOVA/F-test (3+ means).

ANOVA: F = MSbetween/MSwithin. Significant F means at least one mean differs; follow with Tukey or Dunnett post-hoc to identify which.

Variance tests: F-test (2 variances, normal data); Levene's or Bartlett's test (3+ variances). Equal-variance assumption precedes pooled t and ANOVA.

Regression: y = b0 + b1x; R² = proportion of variation explained; adjusted R² penalizes extra predictors. Check residual plots for normality, constant variance, independence, and lack of fit.

Correlation coefficient r ranges -1 to +1; r² is the shared variance. Correlation does not establish causation - require temporal order, mechanism, and elimination of confounders.

Multi-vari study: stratify variation into within-piece, piece-to-piece, and time-to-time to locate dominant variation source before formal testing.

Root-cause tools: 5 Whys, fishbone (Ishikawa) 6M categories (Man, Machine, Material, Method, Measurement, Environment), fault tree, FMEA (RPN = Severity × Occurrence × Detection).

DOE terminology: factors (Xs), levels (settings), response (Y), runs (treatment combinations), replicates, blocking, randomization, confounding. Randomize run order to protect against nuisance effects.

Full factorial: 2^k runs for k factors at 2 levels; main effects plus all interactions estimable. Fractional factorial 2^(k-p) uses resolution: III (main effects confounded with 2-factor interactions), IV (main effects clear, 2FIs confounded with each other), V (main effects and 2FIs clear).

Main effect = change in mean response as a factor moves from low to high level; interaction = difference in effect of one factor across levels of another (non-parallel lines).

Taguchi: orthogonal arrays, signal-to-noise ratios - smaller-is-better SN = -10 log10(mean of y²); larger-is-better SN = -10 log10(mean of 1/y²); nominal-is-best SN = 10 log10(μ²/σ²).

Response surface methodology: steepest ascent to move toward the optimum, then central composite or Box-Behnken design to fit a quadratic model and locate the stationary point.

Poka-yoke (error-proofing): prevention (impossible to err) preferred over detection (alerts/catches the error). Examples: fixtures, limit switches, color-coding, forced sequencing.

5S workplace discipline: Sort (seiri), Set in order (seiton), Shine (seiso), Standardize (seiketsu), Sustain (shitsuke). SMED reduces changeover by separating internal and external setup.

Kaizen event (rapid improvement workshop) targets a bounded process in days; PDCA/PDSA cycles iterate plan, do, study/check, act.

Solution selection criteria: impact on CTQ, cost, risk, ease of implementation, sustainability. Pilot before full deployment; verify improvement with a hypothesis test on before/after data.

Control chart anatomy: center line (process mean or p̄, c̄, ū), upper and lower control limits at ±3σ of the plotted statistic, plotted points in time order. Control limits are not specification limits.

Variable charts: X̄-R (small subgroups, n ≤ 9), X̄-s (n ≥ 10), individuals I-MR (n = 1). Attribute charts: p (proportion defective, variable n), np (constant n), c (count of defects, constant area), u (defects per unit, variable area).

Western Electric / Nelson rules: 1 point beyond 3σ; 2 of 3 beyond 2σ same side; 4 of 5 beyond 1σ same side; 8 consecutive on one side; trend of 6-7; 14 alternating; 15 within 1σ. Any pattern signals special cause.

Process state: common-cause variation (stable, inherent) vs special-cause variation (assignable, from a specific source). Do not adjust a stable process in response to common-cause variation (tampering/overadjustment increases variation).

Control plan contents: process step, characteristic and specification, measurement method and frequency, sample size, control method (chart, poka-yoke, check), reaction plan and owner, revision history.

Reaction plan: what action to take, who takes it, and what to do with nonconforming product when a control chart signals an out-of-control point.

Standard work: documented current best method with takt time, work sequence, and standard in-process inventory. Without standard work there is no baseline for improvement.

Ongoing capability monitoring: recalculate control limits only after a verified process change; track Cp/Cpk and Ppk over time; audit the control plan at defined intervals.

Project closure: verify results against the goal statement, document lessons learned, transfer ownership to the process owner, and confirm financial benefit with finance.

DFSS is used for new products/processes where no baseline exists; common roadmaps: DMADV (Define, Measure, Analyze, Design, Verify) and IDOV (Identify, Design, Optimize, Verify).

QFD house of quality: customer requirements (Whats) vs engineering characteristics (Hows), relationship matrix (strong/medium/weak), competitive assessment, correlation roof, and importance weights to prioritize design characteristics.

CTQ flowdown: customer CTQs → design requirements → subsystem specifications → component tolerances → process capability requirements. Each level must be verifiable.

Tolerance design: worst-case stack-up sums tolerances arithmetically; statistical (RSS) stack-up = sqrt(t1² + t2² + ... + tn²), which is tighter and requires capable processes.

Robust design: minimize sensitivity to noise factors (environment, usage, deterioration) by selecting factor levels at a flat response region rather than chasing a peak.

FMEA in design (DFMEA) vs process (PFMEA): identify failure modes, effects, causes, and controls; RPN = Severity × Occurrence × Detection; act on high severity first regardless of RPN.

Reliability basics: R(t) = e^(-λt) for constant failure rate; MTBF = 1/λ; series system reliability = product of component reliabilities; parallel (redundant) systems increase reliability.

Design verification vs validation: verification confirms the design meets specified requirements; validation confirms the product meets customer needs in actual use.

Team stages (Tuckman): Forming (orientation, dependence), Storming (conflict, roles contested), Norming (cohesion, agreed norms), Performing (task focus, high output), Adjourning (closure).

Team roles: Champion/sponsor, Black Belt (leader/facilitator), process owner (sustains gains), subject-matter experts, finance representative (validates benefits), Green Belt team members.

Meeting discipline: agenda, roles (facilitator, scribe, timekeeper), action items with owner and due date, minutes distributed, decisions documented.

Conflict handling modes (Thomas-Kilmann): competing, collaborating, compromising, avoiding, accommodating. Collaborating is preferred for win-win on important issues.

RACI matrix assigns Responsibility, Accountability (one per task), Consulted, Informed for project deliverables and decisions.

Gate reviews: tollgate at each DMAIC phase end; deliverables reviewed by champion/MBB; project can be continued, redirected, or closed.

Resistance to change: identify stakeholders, assess impact and influence, communicate the why, involve affected staff in design, provide training, and make the new method the default.

Project risk: maintain a risk register with probability, impact, mitigation owner; escalate cross-functional barriers to the champion.