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

np-chart

Answer

c-chart

Answer

u-chart

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

Recalculate the control limits to include the new out-of-control point

Answer

Increase the subgroup size to reduce the width of the control limits

Answer

Widen the specification limits to accommodate the observed measurement

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

Each batch is produced by a different operator on a rotating schedule

Answer

The process mean has been stable for at least 30 consecutive batches

Answer

The moving range is calculated across at least three consecutive observations

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

Upper control limit (UCL) and lower control limit (LCL)

Answer

Center line (CL) and control limit multiplier (L)

Answer

Subgroup size (n) and sampling frequency (f)

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

The measurement system resolution is inadequate for detecting process variation

Answer

The subgroup size of n = 5 is too large for this type of process

Answer

The process is capable but is not centered within the specification limits

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?

Accepted Answer

Pre-control chart (Rainbow chart)

Answer

EWMA chart with a smoothing constant of λ = 0.2

Answer

Multivariate T² (Hotelling) chart for correlated quality characteristics

Answer

Short-run SPC chart with coded (deviation-from-nominal) measurements