Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC 1 — Questions and Answers
Question 1: A process produces batches of varying sizes and a Black Belt wants to monitor the proportion of defective units per batch. Which control chart is most appropriate?
- np-chart
- p-chart (Correct answer)
- c-chart
- u-chart
Correct answer: p-chart
The p-chart monitors the proportion (fraction) of defective units and accommodates varying subgroup sizes by recalculating control limits for each batch. The np-chart requires a constant subgroup size. The c- and u-charts are used for defect counts, not defective unit proportions.
Question 2: A Black Belt needs to detect a sustained 1-sigma shift in the process mean as rapidly as possible. Which chart type is best suited for this purpose compared to a standard Shewhart X-bar chart?
- np-chart
- I-MR chart
- EWMA chart (Correct answer)
- u-chart
Correct answer: EWMA chart
The Exponentially Weighted Moving Average (EWMA) chart weights recent observations more heavily and is specifically designed to detect small, sustained shifts in the process mean more quickly than a Shewhart chart, which is optimized for large, sudden shifts.
Question 3: An X-bar chart for a stable process shows 9 consecutive points all plotting above the center line. What is the correct conclusion?
- This is normal common cause variation and no action is needed
- A Western Electric run rule has been violated, signaling a probable process shift (Correct answer)
- The control limits must be recalculated before any interpretation can be made
- The subgroup size is too small to draw a valid conclusion
Correct answer: A Western Electric run rule has been violated, signaling a probable process shift
Western Electric Rule 2 states that a run of eight or more consecutive points on the same side of the center line is a special cause signal. Nine points above the center line exceeds this threshold, indicating the process mean has likely shifted upward even though no individual point exceeds the UCL.
Question 4: A Black Belt is monitoring the total number of surface scratches found on a fixed-area aluminum sheet where every sheet is the same size. Which control chart should be used?
- p-chart
- u-chart
- c-chart (Correct answer)
- np-chart
Correct answer: c-chart
The c-chart is used to track the count of defects (not defectives) when the area of opportunity is constant across all units. Because each aluminum sheet is the same size, the opportunity for scratches is equal per unit, making the c-chart appropriate. The u-chart would be used if sheet sizes varied.
Question 5: When applying the principle of rational subgrouping, subgroups should be formed so that:
- Variation between subgroups is minimized while within-subgroup variation is maximized
- All sources of variation are randomly mixed within each subgroup
- Variation within each subgroup reflects only common cause variation (Correct answer)
- Each subgroup contains a minimum of 30 observations for normality
Correct answer: Variation within each subgroup reflects only common cause variation
Rational subgrouping requires that units within a subgroup are produced under essentially the same conditions so that within-subgroup variation represents only common cause (baseline) variation. This maximizes the sensitivity of the chart to detect between-subgroup shifts caused by special causes.
Question 6: On an X-bar and R chart, the R chart is in statistical control but a single point on the X-bar chart exceeds the UCL. What is the correct interpretation?
- Both charts must simultaneously show out-of-control signals before action is warranted
- The out-of-control X-bar point is invalid because the R chart is stable
- The process spread is consistent but the process mean has experienced a shift (Correct answer)
- The control limits should be widened to reduce the rate of false alarms
Correct answer: The process spread is consistent but the process mean has experienced a shift
An in-control R chart means the process variability (spread) is stable and consistent across subgroups. An out-of-control point on the X-bar chart independently indicates that the process mean has shifted. The two charts monitor different process parameters and each signal is interpreted on its own merit.
Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC 1
A process produces batches of varying sizes and a Black Belt wants to monitor the proportion of defective units per batch.
Which control chart is most appropriate?