Lean Six Sigma Black Belt Control Phase: SPC 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?

Accepted Answer

p-chart

Answer

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?

Accepted Answer

The process is exhibiting special cause variation and requires investigation.

Answer

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?

Accepted Answer

The control limits (voice of the process) are wider than the specification limits (voice of the customer).

Answer

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?

Accepted Answer

Collecting 5-7 consecutive units at a specific point in time, with this sampling repeated periodically.

Answer

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?

Accepted Answer

CUSUM chart

Answer

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.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Control Phase: SPC Questions and Answers