SPC Process Variation & Capability 3 — Questions and Answers
Question 1: A short-term capability study is best described as measuring variation:
- Over many months including all sources of variation
- Within a brief window capturing mainly within-subgroup variation (Correct answer)
- Across multiple machines and operators simultaneously
- Using 100% inspection data from production
Correct answer: Within a brief window capturing mainly within-subgroup variation
Short-term capability (Cp/Cpk) is measured over a brief period to capture within-subgroup variation, minimizing between-subgroup sources.
Question 2: When calculating the estimated process standard deviation using the average range method, which constant is used?
- d2 (Correct answer)
- c4
- A2
- D4
Correct answer: d2
The constant d2 is used to convert the average range (R-bar) to an estimate of the process standard deviation: σ̂ = R̄/d2.
Question 3: A process with Cp = 1.5 but Cpk = 0.9 most likely has which characteristic?
- Low process variation but the mean is significantly off-center (Correct answer)
- High process variation centered within specifications
- No detectable special causes present
- A process mean exactly at the specification midpoint
Correct answer: Low process variation but the mean is significantly off-center
When Cp is high but Cpk is low, the process spread is narrow but the mean is shifted away from the target, reducing one-sided capability.
Question 4: Which of the following is a Western Electric run rule for detecting special causes?
- One point beyond 1-sigma
- Two out of three consecutive points beyond 2-sigma on the same side (Correct answer)
- Four consecutive points alternating above and below the mean
- Six points within 1-sigma of the centerline
Correct answer: Two out of three consecutive points beyond 2-sigma on the same side
Two out of three consecutive points in Zone A (beyond 2σ) on the same side is a standard Western Electric run rule signaling a special cause.
Question 5: In a unilateral tolerance scenario (only one specification limit), which capability index is most appropriate?
- Cp
- Cpk (Correct answer)
- Cpm
- Pp
Correct answer: Cpk
Cpk is appropriate for unilateral tolerances because it measures the distance to the relevant single specification limit.
Question 6: What effect does reducing subgroup size have on an X-bar chart's sensitivity to process shifts?
- Increases sensitivity to small shifts
- Decreases sensitivity to small shifts (Correct answer)
- Has no effect on sensitivity
- Eliminates common cause variation
Correct answer: Decreases sensitivity to small shifts
Smaller subgroups widen control limits (higher variation in X-bar), reducing the chart's ability to detect small process mean shifts.
Question 7: The Cpm index (Taguchi capability index) incorporates which additional factor compared to Cp?
- The measurement system's gage R&R
- The deviation of the process mean from the nominal target (Correct answer)
- The number of subgroups in the study
- The proportion of out-of-specification output
Correct answer: The deviation of the process mean from the nominal target
Cpm penalizes processes whose mean deviates from the nominal target, even if the mean is within specification limits.
SPC Process Variation & Capability 3
A short-term capability study is best described as measuring variation: