Certified Six Sigma Black Belt Exam Process Capability Analysis 2 — Questions and Answers
Question 1: Which prerequisite must be verified BEFORE conducting a process capability analysis?
- The dataset must contain at least 200 observations
- The process must be in statistical control (Correct answer)
- The data must follow a Poisson distribution
- Specification limits must be symmetric around a nominal value
Correct answer: The process must be in statistical control
Process capability analysis is only meaningful when the process is in statistical control, ensuring that variation is random, stable, and predictable over time.
Question 2: What does DPMO stand for in the context of Six Sigma process capability?
- Defects Per Manufacturing Operation
- Defective Parts Manufacturing Output
- Defects Per Million Opportunities (Correct answer)
- Defective Products in Monthly Output
Correct answer: Defects Per Million Opportunities
DPMO (Defects Per Million Opportunities) normalizes defect rates to one million opportunities, enabling comparison across processes with different complexities.
Question 3: How many DPMO does a true Six Sigma process produce when accounting for the standard 1.5 sigma long-term shift?
- 3.4 (Correct answer)
- 6.8
- 2,700
- 66,807
Correct answer: 3.4
With the 1.5 sigma long-term drift applied, a six sigma process produces 3.4 DPMO — the defining benchmark of Six Sigma quality.
Question 4: Which graphical tool is most appropriate for verifying the normality assumption before performing standard capability analysis?
- Pareto chart
- Normal probability plot (Correct answer)
- Scatter diagram
- Cause-and-effect diagram
Correct answer: Normal probability plot
A normal probability plot (or Anderson-Darling test) graphically assesses whether data follows a normal distribution, which is required for valid Cp and Cpk calculations.
Question 5: What happens to the Cpk value when the process mean shifts closer to a specification limit?
- Cpk increases because the process becomes more efficient
- Cpk remains unchanged since it only reflects spread
- Cpk decreases because the distance to the nearest limit shrinks (Correct answer)
- Cpk becomes negative only after the mean exceeds the specification
Correct answer: Cpk decreases because the distance to the nearest limit shrinks
Cpk uses the minimum distance from the mean to either specification limit; as the mean shifts toward a limit, that minimum distance shrinks, reducing Cpk.
Question 6: Which capability approach is most appropriate when process data follows a non-normal distribution?
- Apply standard Cp and Cpk with no modification
- Use percentile-based or distribution-specific capability indices (Correct answer)
- Increase the sample size until normality emerges
- Use only control charts without capability indices
Correct answer: Use percentile-based or distribution-specific capability indices
Percentile-based capability indices use actual data percentiles to define process boundaries, avoiding the invalid normality assumption for skewed or non-normal distributions.
Question 7: The Taguchi Capability Index (Cpm) differs from Cpk primarily because it:
- Uses the range instead of standard deviation
- Penalizes deviation of the process mean from the target value T (Correct answer)
- Applies only to bilateral (two-sided) tolerances
- Requires at least 500 data points to be valid
Correct answer: Penalizes deviation of the process mean from the target value T
Cpm incorporates a target value T in its denominator, penalizing the process whenever the mean deviates from the target — even when still within specification.
Certified Six Sigma Black Belt Exam Process Capability Analysis 2
Which prerequisite must be verified BEFORE conducting a process capability analysis?