CPHQ Statistical Process Control 2 — Questions and Answers
Question 1: A quality manager notices that 8 consecutive data points on a control chart all fall on the same side of the centerline. What does this pattern indicate?
- Random variation within control limits
- A run rule violation suggesting a process shift (Correct answer)
- A trend toward the control limit
- Normal seasonal fluctuation
Correct answer: A run rule violation suggesting a process shift
Eight consecutive points on one side of the centerline is a classic run rule (Nelson Rule 2) indicating the process mean has likely shifted.
Question 2: Which type of control chart is most appropriate for monitoring the proportion of defective items in a healthcare process when the sample size varies?
- p-chart (Correct answer)
- np-chart
- c-chart
- u-chart
Correct answer: p-chart
The p-chart monitors proportion defective and accommodates variable sample sizes, unlike the np-chart which requires constant sample sizes.
Question 3: In a healthcare setting, the standard deviation of a process is estimated from control chart data as 2.5. What is the width of the ±3σ control limits around a centerline of 50?
- 42.5 to 57.5 (Correct answer)
- 45 to 55
- 47.5 to 52.5
- 40 to 60
Correct answer: 42.5 to 57.5
Control limits are centerline ± 3σ = 50 ± 3(2.5) = 50 ± 7.5, giving limits of 42.5 and 57.5.
Question 4: A hospital tracks medication errors per 1,000 patient-days. Which SPC chart is best suited for this rare-event count data?
- X-bar and R chart
- c-chart or u-chart (Correct answer)
- p-chart
- I-MR chart
Correct answer: c-chart or u-chart
The c-chart (constant area of opportunity) or u-chart (variable area) is appropriate for count data like errors per patient-days.
Question 5: What is the primary purpose of the R chart used alongside an X-bar chart?
- Monitor the process average over time
- Monitor process variability within subgroups (Correct answer)
- Detect rare events
- Calculate process capability
Correct answer: Monitor process variability within subgroups
The R chart monitors within-subgroup variability (range), complementing the X-bar chart which monitors the process mean.
Question 6: A CPHQ candidate reviews a control chart showing six consecutive points steadily increasing. Which Western Electric rule is violated?
- One point beyond 3σ
- Six points in a row steadily increasing or decreasing (Correct answer)
- Two of three points beyond 2σ
- Fifteen points within 1σ
Correct answer: Six points in a row steadily increasing or decreasing
Six consecutive points trending in one direction (all increasing or all decreasing) violates Western Electric Rule 3, indicating a process trend.
Question 7: Common cause variation in a healthcare process is best described as:
- Variation from a one-time equipment failure
- Inherent, random variation present in every stable process (Correct answer)
- Variation caused by a new staff member's error
- Variation detectable only by control charts
Correct answer: Inherent, random variation present in every stable process
Common cause variation is the natural, random variation inherent to a stable process, requiring systemic improvement to reduce.
CPHQ Statistical Process Control 2
A quality manager notices that 8 consecutive data points on a control chart all fall on the same side of the centerline.
What does this pattern indicate?