Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Statistical Process Control (SPC) 1 — Questions and Answers
Question 1: An Individuals and Moving Range (I-MR) chart is the appropriate control chart choice when:
- The process produces continuous data with subgroup sizes of n≥5
- Each inspection yields only a single observation and subgrouping is not feasible (Correct answer)
- The defect rate is below 1% and attribute charts lose sensitivity
- The process mean shifts by more than 2 sigma between subgroups
Correct answer: Each inspection yields only a single observation and subgrouping is not feasible
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?
- When the defect count per unit exceeds the Poisson approximation threshold
- When the inspection area, unit size, or opportunity for defects varies between subgroups (Correct answer)
- When the process is monitored continuously rather than at discrete intervals
- When the proportion defective is expected to remain below 0.10
Correct answer: When the inspection area, unit size, or opportunity for defects varies between subgroups
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?
- Ppk uses specification limits derived from customer requirements; Cpk uses statistically calculated control limits
- Ppk is calculated using overall (long-term) standard deviation; Cpk uses within-subgroup (short-term) standard deviation (Correct answer)
- Ppk applies only to non-normal distributions; Cpk assumes normality
- Ppk requires a minimum of 50 subgroups; Cpk is valid with as few as 20
Correct answer: Ppk is calculated using overall (long-term) standard deviation; Cpk uses within-subgroup (short-term) standard deviation
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:
- Large, sudden shifts of ±3σ or greater must be detected as quickly as possible
- The process produces attribute data with a Poisson defect distribution
- Small, sustained shifts of ±0.5σ to ±1.5σ in the process mean must be detected (Correct answer)
- The within-subgroup variation is highly non-constant across time
Correct answer: Small, sustained shifts of ±0.5σ to ±1.5σ in the process mean must be detected
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:
- Evidence of over-control (tampering) that inflates process variation
- A common-cause signal indicating the control limits should be recalculated
- A special-cause signal warranting investigation before the next production run (Correct answer)
- Confirmation that the process is capable but not centered
Correct answer: A special-cause signal warranting investigation before the next production run
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.
Question 6: An NP-chart is preferred over a P-chart for monitoring fraction nonconforming when:
- The subgroup size varies significantly from sample to sample
- The defect rate is so low that a Laney correction is required
- The subgroup size is constant and plotting the actual count of nonconforming units is more intuitive (Correct answer)
- The data follows a binomial distribution with p > 0.10
Correct answer: The subgroup size is constant and plotting the actual count of nonconforming units is more intuitive
Both the P-chart (proportion nonconforming) and NP-chart (number nonconforming) are valid for binomial attribute data. The NP-chart is specifically suited to constant subgroup sizes because it plots the raw count np rather than the proportion p/n, which operators and technicians often find more natural to interpret directly.
Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Statistical Process Control (SPC) 1
An Individuals and Moving Range (I-MR) chart is the appropriate control chart choice when: