Lean Six Sigma Black Belt Control Phase: SPC Questions and Answers — Questions and Answers
Question 1: A quality team is monitoring the number of non-conforming units from a production line. Due to fluctuating daily production schedules, the number of units inspected each day varies. Which control chart is the most appropriate for monitoring the process performance under these conditions?
- np-chart
- c-chart
- u-chart
- p-chart (Correct answer)
Correct answer: p-chart
A p-chart is used for attribute data (e.g., conforming/non-conforming) and tracks the proportion of defective items. It is specifically designed to handle situations where the subgroup (sample) size is not constant, as the control limits are recalculated for each subgroup based on its size. An np-chart requires a constant sample size, while c-charts and u-charts are used for counting the number of defects, not the number of defective units.
Question 2: An Xbar-R chart for a stable process shows eight consecutive points trending steadily downwards, although all points remain within the upper and lower control limits. According to the Western Electric rules for identifying special cause variation, what is the correct interpretation?
- The process is exhibiting special cause variation and requires investigation. (Correct answer)
- Since no points are outside the control limits, the process is considered in control.
- The control limits are too wide and should be recalculated immediately.
- The process is showing natural, common cause variation and no action is needed.
Correct answer: The process is exhibiting special cause variation and requires investigation.
A run of seven or more consecutive points trending in the same direction (up or down) is one of the key Western Electric rules for detecting a non-random pattern. This indicates a process shift or trend, which is a sign of special cause variation that must be investigated, even if no points have breached the 3-sigma control limits.
Question 3: A process is being monitored with an Xbar chart and is determined to be in a state of statistical control. Despite this, a high percentage of the output is being rejected for failing to meet customer requirements. What is the most likely cause of this issue?
- The measurement system is flawed.
- The control limits (voice of the process) are wider than the specification limits (voice of the customer). (Correct answer)
- The process has too much special cause variation.
- The specification limits are wider than the control limits.
Correct answer: The control limits (voice of the process) are wider than the specification limits (voice of the customer).
A process can be stable and predictable (in control) but not capable of meeting customer needs. This occurs when the natural variation of the process, represented by the control limits, is greater than the tolerance allowed by the customer, defined by the specification limits. The process is consistent, but consistently producing non-conforming product.
Question 4: A Black Belt is establishing an Xbar-S chart to monitor the fill weight of a product. To ensure the chart is sensitive to shifts in the process average, data must be collected in rational subgroups. Which of the following data collection strategies best represents rational subgrouping?
- Collecting 50 consecutive units once at the end of each shift.
- Mixing units from three different production lines to form one subgroup.
- Collecting 5-7 consecutive units at a specific point in time, with this sampling repeated periodically. (Correct answer)
- Collecting one unit every hour over an 8-hour shift to form a subgroup of 8.
Correct answer: Collecting 5-7 consecutive units at a specific point in time, with this sampling repeated periodically.
The principle of rational subgrouping is to minimize the variation *within* a subgroup while maximizing the chance to see variation *between* subgroups. Collecting a small number of consecutive units provides a 'snapshot' of the process's common cause variation at that moment. The other methods improperly mix potential special cause variation (like time-based or machine-based differences) into the within-subgroup calculation, which inflates the control limits and makes the chart less sensitive.
Question 5: For a critical process characteristic, a team needs a control chart that is more sensitive to detecting small, sustained shifts in the process mean than a standard Shewhart chart (like an Xbar chart). Which of the following charts is specifically designed for this purpose?
- p-chart
- I-MR chart
- CUSUM chart (Correct answer)
- Pareto chart
Correct answer: CUSUM chart
The CUSUM (Cumulative Sum) chart is designed to detect small but persistent shifts in the process mean, often less than 1.5 sigma. It achieves this by plotting the cumulative sum of deviations from a target value, which makes it more sensitive to small changes over time compared to Shewhart charts that treat each subgroup independently.
Question 6: Which of the following BEST describes the primary purpose of a Control Plan developed during the Control phase of a DMAIC project?
- To provide a detailed, documented plan for monitoring process inputs and outputs to ensure that project gains are sustained. (Correct answer)
- To serve as the final project report summarizing the financial benefits and lessons learned for executive leadership.
- To outline the statistical analysis and hypothesis tests that were performed in the Analyze phase.
- To document the brainstorming and solution-selection activities from the Improve phase.
Correct answer: To provide a detailed, documented plan for monitoring process inputs and outputs to ensure that project gains are sustained.
The primary purpose of a Control Plan is to create a system for sustaining the improvements made during the project. It is a living document that specifies which variables (inputs and outputs) will be monitored, the methods and frequency of measurement, and the reaction plan to follow if the process goes out of control.
Lean Six Sigma Black Belt Control Phase: SPC Questions and Answers
A quality team is monitoring the number of non-conforming units from a production line.
Due to fluctuating daily production schedules, the number of units inspected each day varies.
Which control chart is the most appropriate for monitoring the process performance under these conditions?