Statistics Quality Control & Assurance 2 — Questions and Answers
Question 1: In a p-chart used for attribute data, what does 'p' represent?
- The process capability index
- The proportion of defective items in a sample (Correct answer)
- The number of defects per unit
- The process standard deviation
Correct answer: The proportion of defective items in a sample
In a p-chart, p represents the proportion (fraction) of nonconforming or defective items found in each sample.
Question 2: Which type of variation in a process is also called 'common cause' variation?
- Assignable cause variation
- Special cause variation
- Random variation (Correct answer)
- Systematic variation
Correct answer: Random variation
Random (common cause) variation is inherent to the process and results from many small, unavoidable sources, unlike assignable (special) cause variation.
Question 3: A manufacturer wants to estimate the minimum sample size to detect a 1.5-sigma shift in the process mean with 80% power using an X-bar chart. Which factor does NOT directly affect this calculation?
- The desired significance level (alpha)
- The subgroup size
- The supplier's lead time (Correct answer)
- The magnitude of the shift to detect
Correct answer: The supplier's lead time
Supplier lead time is a logistics factor and has no role in the statistical power calculation for control chart sample size.
Question 4: What is the purpose of a gage R&R (Repeatability and Reproducibility) study?
- To determine the process capability index
- To quantify how much of total variation is due to the measurement system (Correct answer)
- To set control limits on an X-bar chart
- To identify outliers in production data
Correct answer: To quantify how much of total variation is due to the measurement system
A gage R&R study partitions total observed variation into product variation versus measurement system variation (repeatability + reproducibility).
Question 5: On a control chart, a run of 8 consecutive points on the same side of the center line indicates:
- The process is in statistical control
- A possible process shift requiring investigation (Correct answer)
- Normal random variation
- The control limits need to be recalculated
Correct answer: A possible process shift requiring investigation
Eight consecutive points on one side of the center line is a non-random pattern (Western Electric Rule) signaling a probable process shift.
Question 6: In acceptance sampling, the Acceptable Quality Level (AQL) is best described as:
- The worst quality level a consumer is willing to accept
- The maximum fraction defective that is still considered satisfactory for the producer (Correct answer)
- The average outgoing quality limit
- The rejection number for a given sample size
Correct answer: The maximum fraction defective that is still considered satisfactory for the producer
AQL is the maximum fraction defective (or defects per unit) that is considered acceptable as a process average, representing the producer's quality standard.
Question 7: A c-chart is the appropriate control chart when:
- Tracking the proportion of defective units in variable-size samples
- Counting the total number of defects on each inspection unit of constant size (Correct answer)
- Measuring continuous data like weight or temperature
- Monitoring the sample range across subgroups
Correct answer: Counting the total number of defects on each inspection unit of constant size
A c-chart tracks the count of defects per inspection unit when the sample (inspection unit) size remains constant.
Statistics Quality Control & Assurance 2
In a p-chart used for attribute data, what does 'p' represent?