SPC Control Charts & Analysis 3 — Questions and Answers
Question 1: What is the primary purpose of the R chart in an X-bar & R chart pair?
- Monitor the process mean over time
- Detect shifts in subgroup variability (Correct answer)
- Track individual measurements
- Estimate process capability
Correct answer: Detect shifts in subgroup variability
The R chart monitors within-subgroup variability (range), ensuring the spread of the process remains stable before interpreting the X-bar chart.
Question 2: Zone C on a control chart (using the Western Electric zone rules) corresponds to which sigma band?
- Beyond ±3 sigma
- Between ±2 and ±3 sigma
- Between ±1 and ±2 sigma
- Within ±1 sigma (Correct answer)
Correct answer: Within ±1 sigma
Zone C is the innermost zone, spanning within ±1 sigma of the centerline, where approximately 68% of points should fall.
Question 3: Which attribute control chart is used when subgroup sizes are constant and you are counting the number of defective units (not defects)?
- p-chart
- np-chart (Correct answer)
- c-chart
- u-chart
Correct answer: np-chart
The np-chart tracks the actual count of defective units per subgroup and requires constant subgroup size.
Question 4: A control chart shows 15 consecutive points alternating above and below the centerline. This pattern most likely indicates:
- A process shift
- Systematic over-adjustment (tampering) (Correct answer)
- A trend toward the upper limit
- Stratification of the data
Correct answer: Systematic over-adjustment (tampering)
Alternating zigzag patterns often indicate tampering, where operators over-correct the process in response to each reading.
Question 5: For an X-bar chart with subgroup size n=5, which D4 constant value is used to compute the UCL of the R chart?
- 2.114 (Correct answer)
- 2.004
- 2.282
- 1.924
Correct answer: 2.114
For n=5, the D4 constant is 2.114, so the UCL for the R chart equals D4 × R-bar = 2.114 × R-bar.
Question 6: What distinguishes a u-chart from a c-chart?
- u-chart uses continuous data; c-chart uses discrete data
- u-chart allows variable inspection area; c-chart requires constant area (Correct answer)
- u-chart tracks proportions; c-chart tracks counts of defectives
- u-chart requires normal distribution; c-chart uses binomial
Correct answer: u-chart allows variable inspection area; c-chart requires constant area
The u-chart expresses defects per unit and accommodates variable inspection areas or subgroup sizes, whereas the c-chart requires a constant area of opportunity.
Question 7: On an I-MR chart, the Moving Range is calculated as:
- The range across all historical observations
- The absolute difference between consecutive individual values (Correct answer)
- The standard deviation of a subgroup
- Half the difference between UCL and LCL
Correct answer: The absolute difference between consecutive individual values
The Moving Range is |Xi − Xi-1|, the absolute value of the difference between each pair of consecutive individual measurements.
SPC Control Charts & Analysis 3
What is the primary purpose of the R chart in an X-bar & R chart pair?