Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Assessment 1

Question 1

A control chart for a packaging line shows 8 consecutive data points all falling above the centerline, yet none exceed the upper or lower control limits. What should the Black Belt conclude?

Accepted Answer

The process exhibits special cause variation

Answer

A run of 8 or more consecutive points on the same side of the centerline is a recognized non-random pattern (per Nelson/Western Electric rules), signaling special cause variation even when no individual point breaches the control limits. The Black Belt should investigate the assignable cause.

Question 2

Which document, created during the Define phase of DMAIC, formally authorizes a Six Sigma project by establishing the business case, scope, goals, timeline, and team roles?

Accepted Answer

Project charter

Answer

The project charter is the governing document of the Define phase. It provides the team's formal mandate, sets scope boundaries to prevent scope creep, and aligns stakeholders before data collection begins. SIPOC and fishbone diagrams are analytical tools used later in the project.

Question 3

A Black Belt sets α = 0.05 and runs a hypothesis test. The null hypothesis is not rejected — but the null hypothesis is actually false. What statistical error has been committed?

Accepted Answer

Type II error (β error)

Answer

A Type II error (beta error) occurs when the test fails to reject a null hypothesis that is in fact false — the analyst misses a real effect. Type I error is the opposite: rejecting a true null. Reducing β requires increasing sample size or raising α.

Question 4

A multiple regression model built in the Analyze phase yields an R² of 0.82. How should the Black Belt interpret this value?

Accepted Answer

82% of the variation in the response variable is explained by the predictors in the model

Answer

R² (coefficient of determination) quantifies the proportion of total variability in the dependent variable (Y) that is accounted for by the independent variables in the model. An R² of 0.82 means the model explains 82% of Y's variation; the remaining 18% is unexplained noise or unmodeled factors.

Question 5

A process is measured and found to produce 250 defects per million opportunities (DPMO). Approximately what sigma level does this represent?

Accepted Answer

5 sigma

Answer

Using the standard sigma conversion table (which incorporates the 1.5-sigma long-term shift), approximately 233 DPMO corresponds to 5 sigma, while 6,210 DPMO corresponds to 4 sigma. A DPMO of 250 falls closest to the 5-sigma level. For reference, 6 sigma = 3.4 DPMO.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Assessment 1