Six Sigma Fundamentals and Lean Concepts
Domain 1 tests the vocabulary that every later phase depends on: the statistical meaning of sigma level and the Lean view of waste and flow. Questions ask you to convert a defect rate into a sigma level, classify a tool as Lean or Six Sigma, and catch misuse of DPMO or capability claims.
Sigma level and the 1.5 shift
- Sigma level is the distance from the process mean to the nearer specification limit, expressed in standard deviations.
- DPMO = defects / (units × opportunities) × 1,000,000. Benchmark values with the conventional 1.5σ long-term shift: 3σ ≈ 66,807; 4σ ≈ 6,210; 5σ ≈ 233; 6σ = 3.4 DPMO.
- Y = f(x): Y is the CTQ output; the Xs are process inputs. Projects change Xs and prove the effect on Y.
- DMAIC improves existing processes; DMADV/DFSS designs new ones.
Lean concepts that pair with Six Sigma
- The customer defines value; a value stream map separates value-added steps from waste.
- Eight wastes (DOWNTIME): Defects, Overproduction, Waiting, Non-utilized talent, Transportation, Inventory, Motion, Extra processing.
- Takt time = available work time ÷ customer demand. Flow, pull (kanban) and level scheduling (heijunka) follow from it.
- Poka-yoke prevents errors, SMED cuts changeover time, 5S and standard work stabilize the workplace.
- Lean attacks lead time and waste; Six Sigma attacks variation. Lean Six Sigma deploys both.
Worked example
A billing centre handles 40,000 invoices per quarter, each with 3 defect opportunities, and records 240 defects. DPMO = 240 / (40,000 × 3) × 1,000,000 = 2,000. The standard normal z for a 0.002 tail is 2.88; adding the 1.5σ shift gives about 4.4σ. The reasoning matters: dividing by units instead of opportunities gives 6,000 DPMO and a wrong answer near 3.9σ.
Traps that cost marks
Reporting DPU as DPMO; dropping the opportunity count; quoting a short-term Z from a long-term study (or the reverse); calling 5S or a value stream map a statistical Six Sigma tool; assuming Lean means headcount reduction.