Statistics Quality Control & Assurance 5 — Questions and Answers
Question 1: In statistical process control, the term 'rational subgroup' refers to subgroups that:
- Are selected randomly from the entire production run without time structure
- Are formed so that variation within a subgroup reflects only common causes, maximizing the chance of detecting special causes between subgroups (Correct answer)
- Contain at least 30 observations to ensure normality
- Are used exclusively with attribute control charts
Correct answer: Are formed so that variation within a subgroup reflects only common causes, maximizing the chance of detecting special causes between subgroups
Rational subgroups are collected to capture short-term, within-subgroup common-cause variation so that between-subgroup differences reveal special causes.
Question 2: A CUSUM (Cumulative Sum) control chart is preferred over a Shewhart X-bar chart when the goal is to:
- Detect large, sudden process shifts quickly
- Detect small, sustained shifts in the process mean more efficiently (Correct answer)
- Monitor the process range across subgroups
- Handle non-normal process distributions
Correct answer: Detect small, sustained shifts in the process mean more efficiently
CUSUM charts accumulate deviations from the target and are especially sensitive to small, persistent shifts (1-2 sigma) that Shewhart charts may miss for many samples.
Question 3: The Lower Control Limit (LCL) for an R-chart is sometimes set to zero. This occurs because:
- Negative ranges are physically impossible, and the calculated LCL formula can yield a negative value for small subgroup sizes (Correct answer)
- The process standard deviation is unknown
- The R-chart only uses upper control limits by convention
- The subgroup size exceeds 25
Correct answer: Negative ranges are physically impossible, and the calculated LCL formula can yield a negative value for small subgroup sizes
For small subgroup sizes (typically n ≤ 6), the D3 constant used in the LCL formula equals zero, so the calculated LCL is set to 0 since a range cannot be negative.
Question 4: In Design of Experiments (DOE) applied to quality improvement, a '2^k factorial design' refers to an experiment with:
- Two response variables and k factors
- k factors each tested at exactly two levels (Correct answer)
- k replications of a two-factor experiment
- Two blocks and k treatment combinations
Correct answer: k factors each tested at exactly two levels
A 2^k factorial design tests k factors, each at two levels (high and low), resulting in 2^k total treatment combinations when fully replicated.
Question 5: Poka-yoke (mistake-proofing) devices in quality assurance are intended to:
- Statistically sample output to estimate defect rates
- Prevent defects from occurring or detect them immediately at the source (Correct answer)
- Train operators on quality standards through feedback
- Reduce inspection time by automating data collection
Correct answer: Prevent defects from occurring or detect them immediately at the source
Poka-yoke devices physically prevent errors from occurring or provide immediate detection/feedback so defects cannot be passed to the next stage.
Question 6: When a manufacturing process produces parts whose measurements follow a bimodal distribution, this most likely indicates:
- Normal common-cause variation around a single process mean
- Two distinct process streams or machine settings are being mixed in the data (Correct answer)
- The measurement system has poor resolution
- The specification limits are too narrow
Correct answer: Two distinct process streams or machine settings are being mixed in the data
A bimodal distribution typically signals that data from two different process conditions (e.g., two machines, two shifts, two raw material lots) have been combined.
Question 7: In reliability engineering within quality assurance, the 'bathtub curve' describes the failure rate of a product over time. The three regions of this curve are:
- Burn-in, random failure, and wear-out (Correct answer)
- Inspection, production, and warranty
- Design, testing, and deployment
- Infant mortality, useful life, and obsolescence
Correct answer: Burn-in, random failure, and wear-out
The bathtub curve shows high early failures (burn-in/infant mortality), a low constant rate during useful life (random failure), and increasing failures at end of life (wear-out).
Statistics Quality Control & Assurance 5
In statistical process control, the term 'rational subgroup' refers to subgroups that: