Lean Six Sigma Black Belt Certification Control Phase: SPC 4

Question 1

A Black Belt observes a trend of 6 consecutive points steadily increasing on an X-bar chart. Per Western Electric rules, this is:

Accepted Answer

A signal of a special cause warranting investigation

Answer

Six consecutive points in a monotonically increasing (or decreasing) trend is a Western Electric rule violation indicating a special cause such as tool wear or process drift.

Question 2

The Ppk index differs from Cpk in that Ppk uses:

Accepted Answer

Overall process standard deviation calculated from all individual measurements

Answer

Ppk uses the overall (long-term) standard deviation from all data, while Cpk uses the within-subgroup (short-term) standard deviation estimated from the control chart.

Question 3

When the process standard deviation σ is known, the control limits for an X-bar chart are set at:

Accepted Answer

X-double-bar ± 3σ/√n

Answer

With known σ, control limits are X-double-bar ± 3σ/√n, where n is the subgroup size, reflecting the standard error of the subgroup mean.

Question 4

Rational subgrouping in SPC means grouping measurements so that:

Accepted Answer

Variation within subgroups is minimized while variation between subgroups captures process changes

Answer

Rational subgrouping minimizes within-subgroup variation (reflecting only short-term random noise) so that between-subgroup differences reveal meaningful process changes.

Question 5

A process producing bolt diameters has been in statistical control for months. Specifications are 10mm ± 0.5mm. The process mean is 10.1mm with σ = 0.12mm. What is Cpk?

Accepted Answer

1.11

Answer

Cpk = min[(USL-μ)/(3σ), (μ-LSL)/(3σ)] = min[(10.5-10.1)/0.36, (10.1-9.5)/0.36] = min[1.11, 1.67] = 1.11.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Control Phase: SPC 4