Certified Six Sigma Black Belt Exam Process Capability Analysis 1 — Questions and Answers
Question 1: What does the Cp index measure in process capability analysis?
- Process centering relative to specification limits
- Process spread relative to specification width (Correct answer)
- Process mean shift over time
- Number of defects per million opportunities
Correct answer: Process spread relative to specification width
Cp = (USL - LSL) / (6σ) measures the ratio of the specification width to the process spread, indicating potential capability regardless of centering.
Question 2: A process has Cp = 1.5 and Cpk = 0.8. What does this indicate?
- The process is centered and fully capable
- The process has sufficient spread but is significantly off-center (Correct answer)
- The process is incapable due to excessive variation
- Both indices confirm the process is capable
Correct answer: The process has sufficient spread but is significantly off-center
Cp = 1.5 indicates sufficient process spread potential, but Cpk = 0.8 (below 1.0) reveals the process mean is significantly shifted away from the specification center.
Question 3: What is the standard minimum acceptable Cpk value for a process to be considered 'capable' in most Six Sigma guidelines?
- 1.00
- 1.33 (Correct answer)
- 1.67
- 2.00
Correct answer: 1.33
A Cpk of 1.33 corresponds to a 4-sigma process producing approximately 64 DPMO and is the widely accepted minimum threshold for process capability.
Question 4: Which capability index accounts for BOTH process spread AND centering simultaneously?
- Cp
- Pp
- Cpk (Correct answer)
- Cpm (Taguchi index only)
Correct answer: Cpk
Cpk = min[(USL − μ)/3σ, (μ − LSL)/3σ] takes the minimum of both one-sided indices, penalizing any shift of the mean toward either specification limit.
Question 5: What is the key difference between Cpk and Ppk?
- Cpk uses total (long-term) variation; Ppk uses within-subgroup variation
- Cpk uses within-subgroup (short-term) variation; Ppk uses total (long-term) variation (Correct answer)
- They are mathematically identical measures
- Cpk applies to continuous data; Ppk applies to attribute data
Correct answer: Cpk uses within-subgroup (short-term) variation; Ppk uses total (long-term) variation
Cpk uses within-subgroup standard deviation (short-term, potential capability), while Ppk uses overall standard deviation from all data (long-term, actual performance).
Question 6: When Cp equals Cpk for a process, what does this tell you about the process?
- The process has excessive variation
- The process mean is exactly centered between the specification limits (Correct answer)
- The process is out of statistical control
- The specification limits are too wide
Correct answer: The process mean is exactly centered between the specification limits
Cp equals Cpk only when the process mean is exactly at the midpoint of the specification limits, making both one-sided distances equal.
Question 7: Using the relationship Z = 3 × Cpk, what sigma level corresponds to a Cpk of 1.33?
- 3 sigma
- 4 sigma (Correct answer)
- 5 sigma
- 6 sigma
Correct answer: 4 sigma
Applying Z = 3 × Cpk gives Z = 3 × 1.33 = 4, meaning the process operates at the 4 sigma level.
Certified Six Sigma Black Belt Exam Process Capability Analysis 1
What does the Cp index measure in process capability analysis?