Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Statistical Process Control (SPC) 1

Question 1

An Individuals and Moving Range (I-MR) chart is the appropriate control chart choice when:

Accepted Answer

Each inspection yields only a single observation and subgrouping is not feasible

Answer

I-MR charts are designed for situations where only one measurement is produced per time period or rational subgrouping is impractical (e.g., slow processes, destructive testing, or homogeneous batches). The Moving Range between consecutive individuals estimates short-term variation in place of within-subgroup variation.

Question 2

When should a U-chart be used instead of a C-chart for monitoring process defects?

Accepted Answer

When the inspection area, unit size, or opportunity for defects varies between subgroups

Answer

Both C and U charts assume Poisson-distributed count data, but the C-chart requires a constant opportunity area (e.g., fixed unit size). When the inspection unit or sample area varies, defect counts are normalized to a per-unit rate, requiring the U-chart (defects per unit = c/n).

Question 3

What is the fundamental distinction between Ppk and Cpk process capability indices?

Accepted Answer

Ppk is calculated using overall (long-term) standard deviation; Cpk uses within-subgroup (short-term) standard deviation

Answer

Cpk uses σ̂ estimated from within-subgroup variation (via R-bar or S-bar), capturing only short-term, common-cause variation. Ppk uses the overall sample standard deviation, which includes both within- and between-subgroup variation. The ratio Cp/Pp (or Cpk/Ppk) reveals how much long-term drift inflates total variability.

Question 4

Compared to a standard Shewhart X-bar chart, an EWMA (Exponentially Weighted Moving Average) chart offers its greatest advantage when:

Accepted Answer

Small, sustained shifts of ±0.5σ to ±1.5σ in the process mean must be detected

Answer

Shewhart charts are optimal for detecting large, abrupt shifts but are relatively insensitive to small drifts. The EWMA chart applies exponential weighting to historical data, making it far more sensitive to small, persistent mean shifts. The smoothing parameter λ controls the trade-off between responsiveness and stability.

Question 5

In Statistical Process Control, a single point plotting beyond the ±3σ control limits should be interpreted as:

Accepted Answer

A special-cause signal warranting investigation before the next production run

Answer

Control limits are set at ±3σ so that roughly 99.73% of points from a stable process fall within them by chance alone. A point outside these limits has a very low probability (~0.27%) of occurring due to common cause alone, making it a strong signal of a special (assignable) cause that must be investigated and addressed—not a reason to adjust the process arbitrarily.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Statistical Process Control (SPC) 1