SPC Control Charts & Analysis 2 — Questions and Answers
Question 1: Which Western Electric rule is violated when two out of three consecutive points fall beyond 2 sigma on the same side of the centerline?
- Rule 1
- Rule 2 (Correct answer)
- Rule 3
- Rule 4
Correct answer: Rule 2
Western Electric Rule 2 flags two out of three consecutive points beyond 2 sigma on the same side as a signal of special cause variation.
Question 2: On an X-bar chart, the Lower Control Limit (LCL) formula using the A2 constant is:
- X-double-bar − A2 × R-bar (Correct answer)
- X-double-bar + A2 × R-bar
- X-double-bar − A2 × S-bar
- X-double-bar × A2 / R-bar
Correct answer: X-double-bar − A2 × R-bar
The LCL for an X-bar chart is calculated as X-double-bar minus A2 times R-bar, where R-bar is the average range.
Question 3: A p-chart is most appropriate when monitoring which type of data?
- Continuous measurements like diameter
- Proportion of defective items in variable-size subgroups (Correct answer)
- Number of defects per unit
- Individual measurements with moving range
Correct answer: Proportion of defective items in variable-size subgroups
A p-chart monitors the proportion (fraction) of defective items and accommodates variable subgroup sizes.
Question 4: What does a steadily increasing trend of 7 or more consecutive points on a control chart indicate?
- Random common cause variation
- A special cause trend worth investigating (Correct answer)
- The process is normally distributed
- Control limits need recalculation
Correct answer: A special cause trend worth investigating
Seven or more consecutive points trending in one direction is a classic special cause signal indicating a systematic shift or drift in the process.
Question 5: Which control chart pair is used for variables data when subgroup size is 1?
- X-bar and R chart
- X-bar and S chart
- Individuals and Moving Range (I-MR) chart (Correct answer)
- np and p chart
Correct answer: Individuals and Moving Range (I-MR) chart
The Individuals and Moving Range (I-MR) chart is designed for subgroup size of n=1, where no within-subgroup range can be computed.
Question 6: In a c-chart, what assumption is made about the distribution of defect counts?
- Normal distribution
- Binomial distribution
- Poisson distribution (Correct answer)
- Exponential distribution
Correct answer: Poisson distribution
The c-chart assumes defect counts follow a Poisson distribution, which is appropriate for rare events in a constant area of opportunity.
Question 7: When the process average shifts by 1.5 sigma, the long-term defect rate for a 6-sigma process is approximately:
- 3.4 PPM (Correct answer)
- 2,700 PPM
- 66,800 PPM
- 233 PPM
Correct answer: 3.4 PPM
A 6-sigma process with the standard 1.5-sigma long-term shift yields approximately 3.4 defects per million opportunities.
SPC Control Charts & Analysis 2
Which Western Electric rule is violated when two out of three consecutive points fall beyond 2 sigma on the same side of the centerline?