Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 5

Question 1

A Black Belt calculates a process sigma of 4.5 using long-term data. What is the equivalent short-term sigma level assuming the standard 1.5-sigma shift?

Accepted Answer

6.0

Answer

Adding the 1.5-sigma shift to the long-term sigma of 4.5 gives a short-term sigma of 6.0, which represents the process's best-case capability.

Question 2

When should an EWMA (Exponentially Weighted Moving Average) chart be preferred over a standard Shewhart X-bar chart?

Accepted Answer

When the process produces small, sustained shifts that accumulate over time

Answer

EWMA charts give more weight to recent observations and are more sensitive than Shewhart charts for detecting small, gradual process shifts.

Question 3

In hypothesis testing, what does 'power' (1 - beta) represent?

Accepted Answer

The probability of correctly rejecting a false null hypothesis

Answer

Power (1 - beta) is the probability that a statistical test correctly detects a real effect and rejects a false null hypothesis.

Question 4

A stem-and-leaf plot of cycle time data reveals two distinct peaks. What does this bimodal distribution most likely suggest?

Accepted Answer

Two different process streams or populations are mixed in the data

Answer

A bimodal distribution typically indicates that two distinct populations or process streams—such as two machines or shifts—are combined in the dataset.

Question 5

What is the primary risk of using a t-distribution instead of a Z-distribution when the sample size is large (n > 120)?

Accepted Answer

The results are virtually identical, so the risk is negligible

Answer

For large sample sizes, the t-distribution converges to the Z-distribution, making the practical difference between conclusions negligible.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 5