Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) 1 — Questions and Answers
Question 1: A Six Sigma Black Belt is monitoring the proportion of defective circuit boards produced each shift. Sample sizes vary from 200 to 400 boards per shift. Which control chart is most appropriate for this situation?
- np-chart
- p-chart (Correct answer)
- c-chart
- u-chart
Correct answer: p-chart
The p-chart monitors fraction (proportion) defective and accommodates variable sample sizes by recalculating control limits as p̄ ± 3√(p̄(1−p̄)/n) for each subgroup. The np-chart requires a constant sample size. The c-chart and u-chart are used for counts of defects per unit, not the proportion of defective items.
Question 2: While monitoring a machining process with X-bar and R charts, a Black Belt finds the R-chart is in statistical control but one point on the X-bar chart falls above the upper control limit. Which action is most appropriate?
- Investigate for a special cause that shifted the process mean (Correct answer)
- Recalculate the control limits to include the new out-of-control point
- Increase the subgroup size to reduce the width of the control limits
- Widen the specification limits to accommodate the observed measurement
Correct answer: Investigate for a special cause that shifted the process mean
A point beyond the control limits on the X-bar chart signals an assignable (special) cause affecting the process mean. Because the R-chart remains in control, process variability is stable, confirming the mean shifted rather than the spread. The correct response is to identify and eliminate the special cause before resuming production—not to adjust the chart or specifications.
Question 3: A Black Belt sets up an Individuals and Moving Range (I-MR) chart for a low-volume chemical process that produces one batch per day. Which assumption is MOST critical to verify before interpreting signals on the I-chart?
- Each batch is produced by a different operator on a rotating schedule
- The process mean has been stable for at least 30 consecutive batches
- The individual measurements are approximately normally distributed (Correct answer)
- The moving range is calculated across at least three consecutive observations
Correct answer: The individual measurements are approximately normally distributed
Unlike X-bar charts—where the Central Limit Theorem causes subgroup averages to be approximately normal regardless of the underlying distribution—an I-chart plots raw individual values. Non-normal data can generate excessive false alarms or mask true signals on an I-chart, making verification of approximate normality essential before interpreting chart signals.
Question 4: A Black Belt is designing a CUSUM chart to detect a 1-sigma shift in a critical machined dimension. Which pair of parameters uniquely defines the CUSUM decision rule and must be specified during chart design?
- Upper control limit (UCL) and lower control limit (LCL)
- Reference value (k) and decision interval (h) (Correct answer)
- Center line (CL) and control limit multiplier (L)
- Subgroup size (n) and sampling frequency (f)
Correct answer: Reference value (k) and decision interval (h)
A CUSUM chart is defined by the reference (slack) value k, which tunes the chart to a target shift magnitude, and the decision interval h, which sets the cumulative sum threshold at which an out-of-control signal is triggered. These two parameters replace the fixed ±3σ boundaries used in Shewhart charts and allow the CUSUM to accumulate evidence of small sustained shifts.
Question 5: After collecting 25 subgroups of n = 5 for an X-bar and R chart baseline study, a Black Belt calculates the within-subgroup standard deviation as σ̂W = 0.40 and the overall standard deviation as σ̂T = 0.85. What does this large discrepancy most likely indicate?
- The measurement system resolution is inadequate for detecting process variation
- The subgroup size of n = 5 is too large for this type of process
- Significant between-subgroup variation exists, indicating the process is not in statistical control (Correct answer)
- The process is capable but is not centered within the specification limits
Correct answer: Significant between-subgroup variation exists, indicating the process is not in statistical control
When σ̂T is substantially larger than σ̂W, the excess variation originates from between-subgroup sources such as shift-to-shift differences, raw material lot changes, or operator variation. This signals that the process is NOT in a state of statistical control—special causes are inflating total variation beyond what within-subgroup (short-term, common-cause) variation alone would predict. Control chart control limits based on σ̂W would be misleadingly narrow under these conditions.
Question 6: A production supervisor asks a Six Sigma Black Belt for a simplified monitoring method that shop-floor operators can use without calculating statistical control limits, primarily to confirm the process remains centered within specification limits during a run. Which tool is BEST suited for this need?
- EWMA chart with a smoothing constant of λ = 0.2
- Multivariate T² (Hotelling) chart for correlated quality characteristics
- Short-run SPC chart with coded (deviation-from-nominal) measurements
- Pre-control chart (Rainbow chart) (Correct answer)
Correct answer: Pre-control chart (Rainbow chart)
Pre-control (Rainbow) charts divide the specification range into color-coded zones and use simple decision rules based on where consecutive measurements fall, requiring no calculation of statistical control limits. They are designed for quick, operator-friendly checks that the process remains centered within specifications during production. They do not replace formal SPC for process improvement or capability analysis, but serve as a practical tool for routine production monitoring.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) 1
A Six Sigma Black Belt is monitoring the proportion of defective circuit boards produced each shift.
Sample sizes vary from 200 to 400 boards per shift.
Which control chart is most appropriate for this situation?