CQT Sample Questions & Answers
Inspection and sampling carry the top share, ahead of core concepts and quality tools, statistics with control charts, risk management, calibrating measurement equipment, and the types and components of a quality audit.
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- Question 1AdvancedSelect 2
Quality Concepts and Tools · The Seven Basic Quality Tools
A quality technician is analyzing a sudden, unexplained spike in dimensional nonconformities on a high-volume injection molding line. The technician needs to first determine if the process variation is due to common causes or special causes. Once that is established, the technician needs to brainstorm and categorize the potential root causes of the dimensional issues with the cross-functional team.
Which TWO of the seven basic quality tools are most appropriate for executing these specific tasks? (Select TWO)
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Correct answers: A, B
A Control Chart is the only basic quality tool specifically designed to distinguish between common cause (inherent) variation and special cause (assignable) variation over time by plotting data against calculated statistical control limits.
The Cause and Effect Diagram (Ishikawa or Fishbone diagram) is the ideal tool for brainstorming and categorizing potential root causes (such as Man, Machine, Material, Method, Measurement, and Mother Nature) of a specific problem or effect.
- Question 2Beginner
Statistical Techniques · Normal Distribution
A precision machining process produces steel shafts for electric motors. The process is in statistical control and the output is normally distributed. The process has a mean diameter of 15.00 mm and a standard deviation of 0.05 mm.
Based on the properties of a normal distribution, approximately what percentage of the steel shafts will have a diameter between 14.90 mm and 15.10 mm?
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Correct answer: B
The target range is 14.90 mm to 15.10 mm. The mean is 15.00 mm. The distance from the mean to either boundary is 0.10 mm. Since the standard deviation is 0.05 mm, this range represents exactly ±2 standard deviations from the mean (0.10 / 0.05 = 2). According to the empirical rule (68-95-99.7 rule) for a normal distribution, approximately 95.44% of the data falls within ±2 standard deviations of the mean.
- Question 3Intermediate
Statistical Techniques · Process Capability Measures
A manufacturing process for cutting PVC pipes has a customer specification requirement of 50 ± 5 cm. A recent capability study of the process, which is in statistical control, determined that the process mean is currently 52 cm and the standard deviation is 1 cm.
The calculated Cpk (Process Capability Index) for this process is: _____
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Correct answer: A
Cpk is calculated as the minimum of the upper capability index (Cpu) and the lower capability index (Cpl).
Upper Specification Limit (USL) = 55. Lower Specification Limit (LSL) = 45.
Cpu = (USL - Mean) / (3 * SD) = (55 - 52) / (3 * 1) = 3 / 3 = 1.00.
Cpl = (Mean - LSL) / (3 * SD) = (52 - 45) / (3 * 1) = 7 / 3 = 2.33.
The minimum of 1.00 and 2.33 is 1.00. Therefore, the Cpk is 1.00, indicating the process is just capable but shifted toward the upper specification limit. - Question 4Advanced
Statistical Techniques · Common and Special Cause Variation
A quality technician is actively monitoring an X-bar and R control chart for a critical turning operation. The R chart shows random variation within the control limits. However, on the X-bar chart, the technician observes that the last 8 consecutive subgroup averages are plotted above the centerline, though none of these points have exceeded the Upper Control Limit (UCL).
According to Western Electric rules for determining statistical control, what does this specific pattern indicate, and what is the most appropriate action for the technician to take?
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Correct answer: C
According to Western Electric rules (and general SPC methodology), finding 8 consecutive points on one side of the centerline is a statistically improbable event under normal variation. It indicates a shift in the process mean, which is a form of special cause (assignable) variation. Even if the points have not breached the UCL, the process is considered out of statistical control. The appropriate action is to investigate to find and eliminate the root cause of the shift.
flowchart LR A[Observe 8 points above centerline] --> B{Is process in control?} B -->|No| C[Rule Violation: Shift in Mean] C --> D[Identify Special Cause] D --> E[Implement Corrective Action]
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