CSSGB cheat sheet

Six Sigma is a data-driven methodology that reduces variation so a process produces no more than 3.4 defects per million opportunities (DPMO), equal to a 6-sigma long-term level after the 1.5-sigma shift.

Sigma-to-DPMO reference (1.5-sigma shift applied): 3 sigma ~ 66,807; 4 sigma ~ 6,210; 5 sigma ~ 233; 6 sigma ~ 3.4 DPMO.

DMAIC (Define, Measure, Analyze, Improve, Control) improves existing processes; DMADV or DFSS (Define, Measure, Analyze, Design, Verify) creates new processes or products.

Core model Y = f(x): Y is the output or CTQ, and the x's are the input process variables that must be found, controlled, or optimized.

Roles: Champion/Sponsor funds the project and removes barriers; Master Black Belt is the technical coach; Black Belt leads full time; Green Belt leads part time; Process Owner owns the process after handoff.

Cost of poor quality (COPQ) = internal failure + external failure + appraisal + prevention costs; a 3-4 sigma organization typically spends 15-25% of revenue on COPQ versus under 1% near 6 sigma.

Lean targets speed and the eight wastes: defects, overproduction, waiting, non-utilized talent, transportation, inventory, motion, excess processing (DOWNTIME).

Quality pioneers: Shewhart (control charts), Deming (PDCA, 14 points), Juran (quality trilogy, Pareto principle), Crosby (zero defects, cost of nonconformance), Ishikawa (fishbone, quality circles), Taguchi (robust design, loss function).

Theory of Constraints sequence: identify the constraint, exploit it, subordinate everything else to it, elevate it, then repeat; system throughput is set by the constraint.

A project charter contains the business case, problem statement, goal statement, scope (in and out), team and roles, milestones/schedule, expected benefits and costs, and approvals.

A problem statement states what, where, when, and how much (a measurable gap and its impact) with no stated cause and no stated solution.

A goal statement must be SMART (Specific, Measurable, Achievable, Relevant, Time-bound) and should quantify the target improvement in the same metric as the baseline.

SIPOC maps Suppliers, Inputs, Process (5-7 high-level steps), Outputs, and Customers; it is used to set and communicate project scope boundaries.

VOC to CTQ flow: collect voice of the customer, translate to needs, then to measurable CTQs with operational definitions; Kano classifies needs as dissatisfiers, satisfiers, or delighters.

Team development stages are forming, storming, norming, performing, and adjourning; conflict during storming is a normal phase, not a defect.

RACI assigns each task one Accountable owner, plus Responsible doers, Consulted contributors, and Informed recipients.

Project selection criteria: linkage to strategic goals, COPQ or revenue impact, feasibility, availability of data, and duration (a Green Belt project is typically 3-6 months).

RUMBA test for objectives: Reasonable, Understandable, Measurable, Believable, Achievable.

Continuous (variable) data carries more information per observation than discrete (attribute) data; measure continuous whenever the process permits it.

Gage R&R %study variation: under 10% acceptable; 10-30% marginal and judged against risk and cost; over 30% unacceptable - fix the measurement system before measuring the process.

Repeatability is equipment variation (one appraiser, same parts, repeated trials); reproducibility is appraiser variation (different appraisers, same parts).

Attribute agreement: Kappa above 0.90 excellent, 0.70-0.90 acceptable, below 0.70 needs improvement; within-appraiser agreement should approach 100%.

Sample size for a mean: n = (z x sigma / E)^2, where E is the desired margin of error; halving the margin of error requires four times the sample.

Cp = (USL - LSL) / (6 sigma) measures potential capability; Cpk = min[(USL - mean)/(3 sigma), (mean - LSL)/(3 sigma)] measures actual capability and penalizes off-centering.

Cp/Cpk use within-subgroup (short-term) sigma; Pp/Ppk use overall (long-term) sigma, so Ppk is generally less than or equal to Cpk on the same data.

Yield metrics: DPU = defects / units; DPMO = (defects / opportunities) x 1,000,000; RTY = the product of the first-pass yields of all process steps.

Sampling methods: random, systematic (every kth unit), stratified (random within strata), and cluster (whole groups); convenience sampling is biased and should be avoided.

Hypothesis testing: H0 states no difference or no effect; the alternative H1 is the claim the data must support, and the burden of proof lies with H1.

Type I error (alpha) rejects a true H0 (producer risk); Type II error (beta) fails to reject a false H0 (consumer risk); power = 1 - beta.

Decision rule with p-values: reject H0 when p < alpha; otherwise fail to reject H0 (never 'accept' H0).

Test selection: continuous Y with two levels uses a t-test; three or more levels uses ANOVA; count/categorical data uses chi-square; equal-variance checks use F, Levene, or Bartlett tests.

A paired t-test handles two related measurements on the same units (before/after); a two-sample t-test handles independent groups.

ANOVA splits total variation into between-group and within-group components; a small F-test p-value indicates at least one group mean differs from the others.

Correlation coefficient r ranges from -1 to +1 and measures linear association only; r-squared is the proportion of variation in Y explained by X.

Regression assumptions are checked with residuals: independence, normality, constant variance, and no influential outliers (high leverage or large Cook's D).

Chi-square goodness-of-fit and test of independence require attribute data with expected counts of at least five per cell.

Designed experiments (DOE) estimate main effects and interactions efficiently, whereas one-factor-at-a-time (OFAT) testing cannot detect interactions at all.

Full factorial 2^k design: k factors at two levels require 2^k runs; resolution III confounds main effects with two-factor interactions, resolution IV confounds two-factor interactions with each other, resolution V confounds two-factor with three-factor interactions.

Randomization protects against nuisance variables, replication provides an independent error estimate, and blocking removes known sources of variation such as shift, operator, or batch.

A main effect is the average response change as one factor moves from low to high level; an interaction exists when the effect of one factor depends on the level of another.

FMEA ranks failure modes by RPN = Severity x Occurrence x Detection; higher RPN gets earlier corrective action, and severity alone can override the ranking.

Poka-yoke (mistake proofing) prevents an error at its source and is preferred over detection-based controls because detection still allows defects to be produced.

Lean improvement tools: 5S (sort, set in order, shine, standardize, sustain), kaizen events, value stream mapping, SMED setup reduction, TPM, kanban, standard work, and cellular layout.

Pilot the change on a limited scale and confirm statistically that the effect is real and practical before full deployment; verify the improvement against the original baseline capability.

A control plan lists, per process step: the characteristic and specification, measurement method, sample size and frequency, control method, and the reaction plan (OCAP).

Control limits are computed from process data at plus/minus three sigma around the center line; specification limits are customer tolerances and are never plotted as control limits.

Chart selection: continuous data uses X-bar and R (subgroup n of 2-8), X-bar and S (n of 9 or more), or I-MR (n = 1); attribute defectives use p or np; attribute defects use c or u.

Out-of-control signals include: one point beyond 3 sigma, two of three consecutive points beyond 2 sigma, four of five beyond 1 sigma, eight consecutive points on one side of the center line, trends, and too little variation.

Control limits are reliable only after about 20-25 subgroups of rational-subgroup data collected while the process is stable.

Capability must be re-verified after improvement; ongoing tracking of Cpk/Ppk and DPMO demonstrates that the gain is sustained.

Standardization sustains gains through documented procedures, revised work instructions, training, visual controls, and mistake-proofing devices.

Project closure requires handoff to the process owner, documentation of the new method, lessons learned, and a defined audit or follow-up schedule.