Certified Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers — Questions and Answers
Question 1: A Black Belt is analyzing process data where the number of surface blemishes is counted on manufactured panels. The size of the panels inspected varies from one subgroup to the next. Which type of control chart is most appropriate for monitoring this process?
- p-chart
- c-chart
- u-chart (Correct answer)
- np-chart
Correct answer: u-chart
A u-chart is used to monitor the average number of defects per unit (or area of opportunity) when the sample size varies. [20, 27] A c-chart is used for the number of defects when the sample size is constant. [28] p-charts and np-charts are used for tracking the proportion or number of defective units, not the number of defects per unit.
Question 2: While reviewing a control chart, a quality analyst observes seven consecutive data points trending downwards. What does this pattern most likely indicate?
- The process has become more stable and predictable.
- A special cause of variation is present, suggesting a gradual process shift. (Correct answer)
- The measurement system has an issue with reproducibility.
- This is common cause variation and no action is required.
Correct answer: A special cause of variation is present, suggesting a gradual process shift.
A run of seven or more consecutive points trending in one direction is a standard rule for detecting a special cause of variation. [15] This non-random pattern, known as a 'trend', suggests a systematic, gradual change in the process mean, such as tool wear or machine degradation.
Question 3: A process capability analysis yields a Cp value of 1.67 and a Cpk value of 0.85. Which of the following is the most accurate interpretation of these results?
- The process variation is too large relative to the specification limits.
- The measurement system is not capable of assessing the process.
- The process is not centered within the specification limits. (Correct answer)
- The process is both capable and centered.
Correct answer: The process is not centered within the specification limits.
A high Cp value (typically > 1.33) indicates that the process has low inherent variation relative to the specification width, meaning it has good potential capability. [2] However, a Cpk value less than 1.0 indicates that the process is not actually capable of meeting specifications. The significant difference between Cp and Cpk reveals that the process mean is shifted away from the center of the specification limits. [4, 12]
Question 4: A manufacturing process producing specialty bolts is monitored by taking a sample of 5 consecutive bolts every hour. This data is then plotted on an X-bar & R chart. This method of sampling is an application of which fundamental SPC concept?
- Process Centering
- Rational Subgrouping (Correct answer)
- Attribute Data Collection
- Random Sampling
Correct answer: Rational Subgrouping
Rational subgrouping is the practice of organizing data into subgroups where the items are produced under essentially the same conditions. [13, 17, 24] The goal is to minimize the variation *within* a subgroup to properly estimate common cause variation, which then allows the variation *between* subgroups to reveal special causes. Taking 5 consecutive parts ensures they were made under very similar conditions.
Question 5: A chemical process has a long cycle time, and a critical quality characteristic can only be measured once when each batch is completed. Which control chart is the most suitable for monitoring this process characteristic?
- p-chart
- X-bar and S chart
- c-chart
- I-MR (Individuals and Moving Range) chart (Correct answer)
Correct answer: I-MR (Individuals and Moving Range) chart
The I-MR chart is designed for continuous data where measurements are taken one at a time (subgroup size n=1). [5, 7] It is appropriate for situations like this, where subgrouping is not practical due to long cycle times, infrequent data collection, or destructive testing. [31]
Question 6: Which of the following statements best distinguishes between common cause and special cause variation?
- Common cause variation is predictable and inherent to the process, while special cause variation is unpredictable and arises from specific, identifiable events. (Correct answer)
- Special cause variation is always undesirable and must be eliminated, while common cause variation is always acceptable.
- Common cause variation is identified when a point falls outside the control limits, while special cause variation is the noise within the limits.
- Reducing common cause variation is the responsibility of operators, while addressing special cause variation is the responsibility of management.
Correct answer: Common cause variation is predictable and inherent to the process, while special cause variation is unpredictable and arises from specific, identifiable events.
Common cause variation is the natural, random 'noise' inherent in a stable process. [25] Special cause variation is due to specific, assignable events (e.g., a machine malfunction, a new operator) that make the process unstable and unpredictable. [14, 26] Control charts are used to distinguish between the two.
