CPHQ Statistical Process Control 3 — Questions and Answers
Question 1: Process capability index Cpk differs from Cp in that Cpk:
- Uses specification limits instead of control limits
- Accounts for process centering relative to specification limits (Correct answer)
- Is calculated only for attribute data
- Requires a minimum of 50 data points
Correct answer: Accounts for process centering relative to specification limits
Cpk considers both spread and how well the process mean is centered within specifications, while Cp only measures spread relative to spec width.
Question 2: A healthcare quality team wants to determine if a patient wait-time process is stable before calculating capability. What must they confirm first?
- The data is normally distributed
- The control chart shows the process is in statistical control (Correct answer)
- The sample size exceeds 100
- The specification limits are set by the customer
Correct answer: The control chart shows the process is in statistical control
Process capability indices are only meaningful for stable (in-control) processes; an out-of-control process has unpredictable future performance.
Question 3: Which of the following best explains why using individual (I-MR) charts is appropriate for slow healthcare processes like monthly infection rates?
- Monthly data always follows a normal distribution
- Subgrouping is impractical when data is collected infrequently (Correct answer)
- I-MR charts require no centerline calculation
- Monthly data has no special cause variation
Correct answer: Subgrouping is impractical when data is collected infrequently
When data is collected too infrequently to form rational subgroups, I-MR charts are used with individual measurements.
Question 4: A control chart's UCL for an X-bar chart is calculated as X-double-bar + A₂R-bar. What does the constant A₂ depend on?
- The specification limits
- The subgroup size (Correct answer)
- The process sigma level
- The number of control chart points
Correct answer: The subgroup size
The control chart constant A₂ is derived from the expected value of the relative range and varies with the subgroup sample size n.
Question 5: In SPC, a 'false alarm' (Type I error) occurs when:
- A special cause exists but the chart does not signal it
- The chart signals an out-of-control condition when the process is actually stable (Correct answer)
- The control limits are set too wide
- Common cause variation is misclassified as acceptable
Correct answer: The chart signals an out-of-control condition when the process is actually stable
A Type I error (false alarm) in SPC means the chart signals a special cause when in reality the process has not changed.
Question 6: A hospital's surgical site infection rate is plotted on a p-chart. A new hand-hygiene protocol is implemented. How should the control chart be updated?
- Recalculate control limits using all historical data combined
- Split the chart with new control limits calculated from post-intervention data (Correct answer)
- Remove the pre-intervention data entirely
- Widen the control limits to accommodate the change
Correct answer: Split the chart with new control limits calculated from post-intervention data
After a verified process change, the chart should be split and new control limits calculated from post-intervention data to reflect the new process baseline.
Question 7: Which statement about the u-chart is correct?
- It monitors the number of defectives in a sample of fixed size
- It monitors defects per unit when the area of opportunity varies (Correct answer)
- It requires attribute data with only two outcomes
- It is used exclusively for continuous measurement data
Correct answer: It monitors defects per unit when the area of opportunity varies
The u-chart tracks defects per unit (rate) and is appropriate when the inspection area (e.g., patient-days) varies across samples.
CPHQ Statistical Process Control 3
Process capability index Cpk differs from Cp in that Cpk: