Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC 1

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?

Accepted Answer

p-chart

Answer

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?

Accepted Answer

EWMA chart

Answer

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?

Accepted Answer

A Western Electric run rule has been violated, signaling a probable process shift

Answer

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?

Accepted Answer

c-chart

Answer

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:

Accepted Answer

Variation within each subgroup reflects only common cause variation

Answer

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.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC 1