Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Measure Phase: Data Analysis 1

Question 1

A Black Belt plots a histogram of process output data and observes two distinct peaks. What does this bimodal distribution most likely indicate?

Accepted Answer

Two different process conditions or input streams are mixed in the data

Answer

A bimodal distribution typically signals that the data is drawn from two distinct subpopulations or process conditions (e.g., two shifts, two machines, two operators). Stratifying the data by the suspected factor is the correct next step.

Question 2

A Black Belt calculates a Cp of 1.45 and a Cpk of 0.72 for a critical dimension. What does this combination most likely indicate?

Accepted Answer

The process spread is acceptable but the process is significantly off-center

Answer

Cp measures potential capability (spread relative to spec width) while Cpk accounts for centering. A high Cp with a low Cpk indicates the process has adequate spread but is poorly centered — the mean is shifted significantly toward one specification limit.

Question 3

During the Measure phase, a Black Belt needs to detect a 1.5-sigma shift in the process mean with 90% power using a two-sided t-test. Which action will most directly increase the statistical power of the test?

Accepted Answer

Increase the sample size

Answer

Statistical power increases with larger sample sizes because larger samples reduce the standard error, making it easier to detect true differences. While loosening alpha also increases power, increasing sample size is the most direct and statistically sound approach.

Question 4

A Black Belt finds that 68% of the total variation in a Gage R&R study is attributable to reproducibility (operator-to-operator variation). What is the most appropriate corrective action?

Accepted Answer

Standardize the measurement procedure and provide operator training

Answer

Reproducibility variation reflects differences between operators using the same gauge on the same parts. High reproducibility error points to inconsistent technique or unclear measurement procedures, so standardizing the method and training operators addresses the root cause directly.

Question 5

A Black Belt uses a box plot to compare defect counts across four production lines. Line C shows several data points plotted as individual dots beyond the box plot whiskers. What do these points represent?

Accepted Answer

Data points that fall outside 1.5 times the interquartile range and are flagged as potential outliers

Answer

In a standard box plot, whiskers extend to 1.5 times the IQR from the quartiles. Individual points plotted beyond the whiskers are flagged as potential outliers — they warrant investigation but should not be automatically discarded without cause.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Measure Phase: Data Analysis 1