Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) 1

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?

Accepted Answer

p-chart

Answer

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?

Accepted Answer

Investigate for a special cause that shifted the process mean

Answer

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?

Accepted Answer

The individual measurements are approximately normally distributed

Answer

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?

Accepted Answer

Reference value (k) and decision interval (h)

Answer

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?

Accepted Answer

Significant between-subgroup variation exists, indicating the process is not in statistical control

Answer

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.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) 1