Certified Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers

Question 1

A Black Belt is analyzing process data where the number of surface blemishes is counted on manufactured panels. The size of the panels inspected varies from one subgroup to the next. Which type of control chart is most appropriate for monitoring this process?

Accepted Answer

u-chart

Answer

A u-chart is used to monitor the average number of defects per unit (or area of opportunity) when the sample size varies. [20, 27] A c-chart is used for the number of defects when the sample size is constant. [28] p-charts and np-charts are used for tracking the proportion or number of defective units, not the number of defects per unit.

Question 2

While reviewing a control chart, a quality analyst observes seven consecutive data points trending downwards. What does this pattern most likely indicate?

Accepted Answer

A special cause of variation is present, suggesting a gradual process shift.

Answer

A run of seven or more consecutive points trending in one direction is a standard rule for detecting a special cause of variation. [15] This non-random pattern, known as a 'trend', suggests a systematic, gradual change in the process mean, such as tool wear or machine degradation.

Question 3

A process capability analysis yields a Cp value of 1.67 and a Cpk value of 0.85. Which of the following is the most accurate interpretation of these results?

Accepted Answer

The process is not centered within the specification limits.

Answer

A high Cp value (typically > 1.33) indicates that the process has low inherent variation relative to the specification width, meaning it has good potential capability. [2] However, a Cpk value less than 1.0 indicates that the process is not actually capable of meeting specifications. The significant difference between Cp and Cpk reveals that the process mean is shifted away from the center of the specification limits. [4, 12]

Question 4

A manufacturing process producing specialty bolts is monitored by taking a sample of 5 consecutive bolts every hour. This data is then plotted on an X-bar & R chart. This method of sampling is an application of which fundamental SPC concept?

Accepted Answer

Rational Subgrouping

Answer

Rational subgrouping is the practice of organizing data into subgroups where the items are produced under essentially the same conditions. [13, 17, 24] The goal is to minimize the variation *within* a subgroup to properly estimate common cause variation, which then allows the variation *between* subgroups to reveal special causes. Taking 5 consecutive parts ensures they were made under very similar conditions.

Question 5

A chemical process has a long cycle time, and a critical quality characteristic can only be measured once when each batch is completed. Which control chart is the most suitable for monitoring this process characteristic?

Accepted Answer

I-MR (Individuals and Moving Range) chart

Answer

The I-MR chart is designed for continuous data where measurements are taken one at a time (subgroup size n=1). [5, 7] It is appropriate for situations like this, where subgrouping is not practical due to long cycle times, infrequent data collection, or destructive testing. [31]

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers