EXIN LSSA Black Belt Practical cheat sheet

DMAIC sequence: Define (charter, VOC, CTQ), Measure (baseline capability, MSA), Analyze (root cause verification), Improve (DOE, pilot), Control (SPC, response plan); a project may loop back but each gate needs documented evidence.

Cp = (USL - LSL) / (6 * sigma_within); Cpk = min[(USL - mean), (mean - LSL)] / (3 * sigma_within). Cpk equals Cp only when the process mean is centered on the specification midpoint.

Ppk uses overall sigma (long-term standard deviation) rather than within-subgroup sigma; a large Cp minus Ppk gap signals between-subgroup shift or drift, not just centering error.

Defect metrics: DPMO = (defects / (units * opportunities)) * 1,000,000; process sigma level is derived from DPMO via the standard normal quantile, so 3.4 DPMO corresponds to 6 sigma with the 1.5 sigma shift convention.

Rolled throughput yield RTY = product of each step's first-pass yield; it always falls as step count rises, so a 5-step process at 0.95 yield each gives RTY = 0.95^5 = 0.774, not 95%.

MSA decision rules: %GRR under 10% acceptable, 10-30% conditionally acceptable depending on application and cost, above 30% unacceptable; ndc (number of distinct categories) should be 5 or more.

Hypothesis test selection: continuous Y with 2 groups uses 2-sample t (or Mann-Whitney if normality fails); 3+ groups use ANOVA (or Kruskal-Wallis); categorical Y uses chi-square or Fisher exact for small counts.

Control plan content: characteristic, specification, measurement method, sample size and frequency, control method (SPC chart, poka-yoke, check), reaction plan owner, and revision date; it transfers ownership from Black Belt to process owner.

DOE screening: use fractional factorial resolution IV to separate main effects from two-factor interactions, resolution V when two-factor interactions must be estimable without aliasing with each other.

Sample size for detecting a mean shift: n per group = 2 * (z_alpha/2 + z_beta)^2 * sigma^2 / delta^2; for 80% power and two-sided alpha 0.05 the sum of z terms is about 7.85, so n = 15.7 * sigma^2 / delta^2.

Rational subgrouping requires subgroups to capture only common-cause (short-term) variation; subgroups spanning shifts or batches inflate sigma_within and mask special causes.

Xbar-R chart constants: for n=5, A2=0.577, D3=0, D4=2.114, d2=2.326; UCL_Xbar = Xbar_bar + A2 * Rbar, and sigma_within estimate = Rbar / d2.

Runs rules beyond 3-sigma: 8 consecutive points on one side of centerline, 6 trending points, 2 of 3 beyond 2 sigma, 14 alternating points; each rule trades false-alarm rate against sensitivity to small shifts.

Regression diagnostics: check residual normality (normal probability plot), constant variance (residuals vs fitted), independence (residuals vs order), and leverage; R-squared adjusted penalizes added terms and VIF above 10 signals multicollinearity.

FMEA risk priority number RPN = severity * occurrence * detection, each on 1-10; severity of 9-10 requires action regardless of RPN, and detection ratings drop only when the control detects the failure before it reaches the customer.

Kaizen event scope: one-week focused improvement on a bounded value stream with a pre-defined metric target, daily stand-up, and 30-day follow-up audit; it is not a substitute for a DMAIC project with unknown root cause.

Project charter essentials: business case, problem statement with metric and baseline, goal statement (SMART), scope with start/stop boundaries, team roles, milestone schedule, and expected financial benefit validated by finance.

Problem statement rules: state the gap (observed vs required), where and when it occurs, and its magnitude, without naming a cause or a solution; a cause embedded in the statement biases the Analyze phase.

Stakeholder and tollgate governance: the champion/sponsor approves each DMAIC gate, removes barriers, and owns the business case; the Black Belt leads the technical work and coaches Green Belts.

Voice of customer to CTQ: translate verbatim needs via Kano classification (must-be, performance, delighter) into measurable CTQs with operational definitions and specification limits agreed with the customer.

Financial validation: hard savings change the P&L (labor, material, energy), soft savings are cost avoidance or capacity release; both must be traceable to a documented baseline and signed off before the Control gate.

Team dynamics: Tuckman stages (forming, storming, norming, performing) predict early conflict; RACI assigns decision rights so that the process owner, not the Black Belt, holds final accountability after handover.

Scope creep control: any change to goal, metric, or boundary requires a charter revision with sponsor sign-off; track open issues and parking-lot items so out-of-scope findings become follow-on projects.

Value stream map timing: lead time = sum of process times plus queue and wait times; process cycle efficiency = value-added time / total lead time, typically under 5% in office and service streams.

Little's Law: average work in process = throughput rate * average flow time; if WIP is capped, lead time falls proportionally, which is the basis for limiting WIP in Kanban systems.

Eight wastes: defects, overproduction, waiting, non-utilized talent, transportation, inventory, motion, extra processing; each waste is quantified in the current-state map before countermeasures are chosen.

Takt time = available production time / customer demand; line balancing assigns work elements so each station's cycle time is at or just below takt, with balance efficiency = sum of task times / (stations * bottleneck time).

Standard work documents takt, work sequence, and standard in-process stock; without a documented standard the improvement cannot be sustained or audited in Control.

Poka-yoke levels: prevention (makes error impossible), detection at source, and detection downstream; prevention devices are preferred because they do not depend on operator vigilance.

SMED separates internal from external setup; converting internal to external and simplifying adjustments can cut changeover by 50-90%, enabling smaller lots and lower inventory.

5S audit scoring uses a defined checklist with photo standards per area; scores below target trigger a corrective action with owner and date, otherwise the program decays within months.

Control phase handover: the process owner accepts the control plan, SPC charts, response plan, and training records; the Black Belt's exit is a documented gate, not an informal transfer.

Sustaining gains: monitor the key metric on a control chart with defined reaction plan, audit the standard work at a set frequency, and set a trigger for reopening the project if the metric drifts beyond the control limit.

Mistake-proofing and automation should be preferred over training alone, because training decays; the control plan should show which controls are engineering-based versus administrative.

SPC chart choice: Xbar-R for subgroup size 2-9, Xbar-S for 10 or more, I-MR for individual measurements, p or np for defectives, c or u for defects per unit; attribute charts require constant or tracked opportunity size.

Out-of-control action plan states who responds, what they check first, what containment is applied, and who authorizes stopping the process; it is written before the chart is deployed.

Lessons learned and replication: capture root cause, countermeasure, cost, and results in a standard template so other lines or sites can reuse the solution without repeating the full DMAIC cycle.

Project closure requires baseline versus final capability comparison (Cp/Cpk or Ppk), verified financial benefit, updated documentation and FMEA, and a scheduled follow-up audit at 90 days.

Measurement system discrimination must be finer than the specification tolerance, commonly one-tenth of the tolerance; a gauge that cannot resolve a tenth of tolerance cannot support capability claims.

Bias is the difference between average measured value and a reference standard; linearity tests whether bias changes across the operating range, and stability tests whether bias drifts over time.

Attribute agreement analysis: within-appraiser agreement, between-appraiser agreement, and agreement versus standard; kappa below 0.7 indicates agreement no better than chance-adjusted poor, so the definition needs revision.

Gauge R&R variance model: total observed variance = repeatability (equipment) + reproducibility (appraiser) + part variation; %GRR = 100 * sqrt(GRR variance) / total study variance, but for capability use %GRR relative to tolerance.

Destructive or non-replicable measurement uses nested designs, where parts are nested within appraisers and part-within-appraiser variance substitutes for repeatability.

Sampling plans: for a given AQL and LTPD, the operating characteristic curve gives producer's risk (rejecting good lots) and consumer's risk (accepting bad lots); tightening inspection does not fix an incapable process.

Multi-vari study separates positional, cyclical, and temporal variation before any hypothesis test; it shows where variation lives, so later tests target the right strata.

Components of variation stack: total = within-part (measurement and inherent) + between-part + between-batch + temporal; variance components from ANOVA attribute each source a percentage of total.

Correlation coefficient r measures linear association only; r near zero does not prove independence, and a strong r does not establish causation without a designed experiment or temporal evidence.

Confidence interval for a mean uses t when sigma is unknown: xbar +/- t(alpha/2, n-1) * s / sqrt(n); overlapping intervals are not a formal test of equality between two groups.

Chi-square test of independence requires expected counts of 5 or more in each cell; otherwise combine categories or use Fisher's exact test for 2x2 tables.

Regression prediction intervals are wider than confidence intervals for the mean response, and both widen sharply when extrapolating beyond the observed range of X.

Improve phase prioritization: rank candidate solutions by impact on the verified root cause, effort, and risk; test the highest-leverage countermeasure first with a pilot before full deployment.

Pilot design: define success criteria and sample size before running, use a comparison group or before-after with a control chart, and avoid changing several factors at once so the effect can be attributed.

Full factorial 2^k design estimates all main effects and interactions; a half-fraction (2^(k-1)) confounds the highest-order interaction, and resolution tells you which effects are aliased.

Randomization protects against nuisance factors that vary over time; blocking removes known nuisance variation and increases power without enlarging the experiment.

Response surface methodology (central composite or Box-Behnken) fits curvature to find an optimum; steepest ascent moves from the screening region toward the optimum before fitting the quadratic model.

Confirmation runs at the predicted optimum verify the model; if observed response falls outside the prediction interval, the model is inadequate or a lurking variable changed.

Solution selection matrix weights criteria (impact, cost, risk, time) with agreed weights; the scoring must be set before scoring options to avoid rationalizing a preferred solution.