Lean Six Sigma Black Belt Certification Control Phase: SPC 4 — Questions and Answers
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:
- Normal variation requiring no action
- A signal of a special cause warranting investigation (Correct answer)
- Acceptable if points remain within control limits
- Only significant if points cross the centerline
Correct answer: A signal of a special cause warranting investigation
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:
- Control chart estimates of within-subgroup sigma
- Specification limits instead of control limits
- Overall process standard deviation calculated from all individual measurements (Correct answer)
- A minimum sample of 30 subgroups
Correct answer: Overall process standard deviation calculated from all individual measurements
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:
- X-double-bar ± 2σ
- X-double-bar ± 3σ/√n (Correct answer)
- X-double-bar ± A2 × R-bar
- X-double-bar ± 3 × MR-bar/d2
Correct answer: X-double-bar ± 3σ/√n
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:
- Each subgroup spans the widest possible time window to capture all variation
- Variation within subgroups is minimized while variation between subgroups captures process changes (Correct answer)
- All subgroups contain exactly 5 observations
- Subgroups are formed randomly without regard to time order
Correct answer: Variation within subgroups is minimized while variation between subgroups captures process changes
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?
- 1.11 (Correct answer)
- 1.39
- 1.25
- 0.93
Correct answer: 1.11
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.
Question 6: Which of the following is a key limitation of using only Cp and Cpk to assess process capability?
- They cannot be used with X-bar charts
- They assume the process data is normally distributed (Correct answer)
- They require at least 200 subgroups
- They do not account for specification limits
Correct answer: They assume the process data is normally distributed
Traditional Cp and Cpk calculations assume process data follows a normal distribution; non-normal data requires transformation or non-parametric capability methods.
Question 7: In SPC, tampering (also called over-adjustment) occurs when an operator:
- Ignores out-of-control signals on a control chart
- Adjusts the process in response to common cause variation (Correct answer)
- Increases the subgroup sample size during unstable periods
- Recalculates control limits after removing outliers
Correct answer: Adjusts the process in response to common cause variation
Tampering is adjusting a process in reaction to common cause variation (random noise), which actually increases overall process variability — a concept illustrated by Deming's funnel experiment.
Lean Six Sigma Black Belt Certification Control Phase: SPC 4
A Black Belt observes a trend of 6 consecutive points steadily increasing on an X-bar chart.
Per Western Electric rules, this is: