Free Lean Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers — Questions and Answers
Question 1: A quality team is monitoring the number of nonconforming units produced on an assembly line. Each hour, they inspect a different number of units based on production volume. Which type of control chart is most appropriate for monitoring the proportion of nonconforming units in this scenario?
- np-chart
- c-chart
- p-chart (Correct answer)
- I-MR chart
Correct answer: p-chart
A p-chart is used for attribute data (go/no-go, pass/fail) and is designed to monitor the proportion of defective items. It is specifically suited for situations where the subgroup (sample) size varies over time. An np-chart requires a constant sample size. A c-chart tracks the number of defects, not defective units, and assumes a constant sample size. An I-MR chart is for continuous data, not attribute data.
Question 2: Which of the following statements most accurately describes the fundamental difference between control limits and specification limits?
- Control limits are set by management, while specification limits are calculated from process data.
- Specification limits are used for attribute data, while control limits are used for variable data.
- Control limits are wider than specification limits to allow for normal process variation.
- Control limits represent the voice of the process, while specification limits represent the voice of the customer. (Correct answer)
Correct answer: Control limits represent the voice of the process, while specification limits represent the voice of the customer.
Control limits are calculated statistically from the process's own data and represent its inherent, natural variation (the voice of the process). Specification limits are determined by external requirements, such as engineering designs or customer needs (the voice of the customer). A process can be in control but still not meet specifications, and vice versa.
Question 3: An operator running a stable process notices a measurement that is slightly above the process average but still well within the control limits. To be proactive, the operator makes a small adjustment to the machine settings to bring the next output closer to the average. What is the most likely result of this type of action over time?
- A gradual reduction in process variation.
- An increase in overall process variation. (Correct answer)
- The process mean will shift significantly lower.
- No significant change in the process output.
Correct answer: An increase in overall process variation.
Adjusting a stable process based on common cause variation (random fluctuations within the control limits) is known as tampering or overcontrol. As demonstrated by Deming's Funnel Experiment, such actions do not reduce variation but actually add to it, making the process less stable and predictable over time.
Question 4: A process control plan requires taking a sample of five consecutive parts from a machine every hour to form a subgroup for an Xbar-R chart. What is the primary principle behind this sampling strategy, known as rational subgrouping?
- To capture the maximum amount of variation within each subgroup.
- To ensure that special cause variation is included within each subgroup.
- To minimize within-subgroup variation and maximize the opportunity to see variation between subgroups. (Correct answer)
- To simplify data collection by spreading it evenly across a shift.
Correct answer: To minimize within-subgroup variation and maximize the opportunity to see variation between subgroups.
The core principle of rational subgrouping is to collect data for a subgroup over a short period under consistent conditions. This minimizes the chance for special causes to influence the measurements within the subgroup, making the within-subgroup variation representative of only common cause variation. This then makes any significant variation between subgroups more likely to be due to a special cause, which is what control charts are designed to detect.
Question 5: An analysis of a manufacturing process shows that its output is highly predictable and exhibits only common cause variation. However, a process capability study (Cpk) reveals a value of 0.75. Which of the following best describes this process?
- Capable but not in control.
- In control and capable.
- Out of control and not capable.
- In control but not capable. (Correct answer)
Correct answer: In control but not capable.
A process that is predictable and exhibits only common cause variation is considered 'in statistical control.' However, a Cpk value less than 1.0 (and certainly below the common target of 1.33) indicates that the process is not capable of consistently producing output that meets customer specification limits. Therefore, the process is stable but not able to meet requirements.
Question 6: When interpreting a control chart, which of the following is the most direct and universally recognized signal of a special cause of variation?
- Seven consecutive points trending in one direction.
- Fourteen points in a row alternating up and down.
- A single point falling outside the upper or lower control limits. (Correct answer)
- Two out of three consecutive points in Zone A on the same side of the centerline.
Correct answer: A single point falling outside the upper or lower control limits.
According to the most common sets of rules for detecting special causes (like the Western Electric or Nelson rules), a single point falling outside the 3-sigma control limits is the strongest and most basic indicator of an out-of-control condition that requires immediate investigation. While the other options are also valid rules for detecting non-random patterns, a point outside the limits is the most definitive signal.
Free Lean Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers
A quality team is monitoring the number of nonconforming units produced on an assembly line.
Each hour, they inspect a different number of units based on production volume.
Which type of control chart is most appropriate for monitoring the proportion of nonconforming units in this scenario?