Statistics Quality Control & Assurance 3 — Questions and Answers
Question 1: Process capability index Cpk differs from Cp in that Cpk:
- Uses the range instead of standard deviation
- Accounts for process centering relative to specification limits (Correct answer)
- Is only used for attribute data
- Requires at least 200 data points
Correct answer: Accounts for process centering relative to specification limits
Cpk adjusts for how well-centered the process mean is between the specification limits, while Cp assumes the process is perfectly centered.
Question 2: In Six Sigma terminology, a process operating at 6-sigma quality level produces approximately how many defects per million opportunities (DPMO)?
- 3.4 (Correct answer)
- 66,807
- 233
- 1,350
Correct answer: 3.4
A Six Sigma process produces approximately 3.4 DPMO, accounting for the standard 1.5-sigma long-term shift in the process mean.
Question 3: Which DMAIC phase involves identifying the root cause of a quality problem?
- Define
- Measure
- Analyze (Correct answer)
- Control
Correct answer: Analyze
The Analyze phase uses tools like fishbone diagrams, hypothesis testing, and regression to identify root causes of defects or variation.
Question 4: A quality engineer uses an Operating Characteristic (OC) curve. The y-axis of this curve represents:
- The sample size required for inspection
- The probability of accepting the lot (Correct answer)
- The number of defectives in the sample
- The producer's risk alpha
Correct answer: The probability of accepting the lot
The OC curve plots the probability of lot acceptance (y-axis) against the true lot fraction defective (x-axis) for a given sampling plan.
Question 5: Total Quality Management (TQM) emphasizes which of the following as the primary driver of quality improvement?
- Increased inspection at the end of production
- Statistical control charts only
- Customer focus and continuous improvement involving all employees (Correct answer)
- Strict adherence to engineering tolerances
Correct answer: Customer focus and continuous improvement involving all employees
TQM is a management philosophy centered on customer satisfaction and continuous improvement (kaizen) through organization-wide participation.
Question 6: In a fishbone (Ishikawa) diagram used in quality analysis, the 'bones' typically represent:
- Individual defective items found in inspection
- Major categories of potential causes such as Man, Machine, Method, Material (Correct answer)
- Steps in the production process flow
- Data points plotted over time
Correct answer: Major categories of potential causes such as Man, Machine, Method, Material
The bones of a fishbone diagram represent major cause categories (the 6 M's or 4 P's) branching off the spine leading to the effect (quality problem).
Question 7: Which statistical test is most appropriate for determining whether the variance of a process has changed after an improvement initiative?
- Two-sample t-test
- Chi-square goodness-of-fit test
- F-test (Levene's test or Bartlett's test) (Correct answer)
- One-proportion z-test
Correct answer: F-test (Levene's test or Bartlett's test)
An F-test or its robust variants (Levene's, Bartlett's) compares variances from two independent samples to test for equality of variance.
Statistics Quality Control & Assurance 3
Process capability index Cpk differs from Cp in that Cpk: