Statistical control charts – concepts and uses MCQs With Answer

Statistical control charts – concepts and uses MCQs With Answer

Introduction: Statistical control charts are essential tools in pharmaceutical quality management for monitoring process stability and detecting variability due to assignable causes. This set of MCQs is designed for M.Pharm students to deepen understanding of chart selection (variables vs attributes), interpretation of control limits, calculation principles, and decision rules such as Western Electric guidelines. Questions cover X-bar, R, s, p, c, and u charts, subgrouping strategies, capability vs stability, Average Run Length (ARL), and actions for out-of-control signals. Use these questions to strengthen both theoretical knowledge and practical judgement when applying control charts to pharmaceutical processes.

Q1. What is the primary purpose of a control chart in pharmaceutical manufacturing?

• To estimate the shelf life of a drug product
• To monitor process stability and detect assignable causes of variation
• To validate cleaning procedures in production equipment
• To perform chemical purity analysis of raw materials

Correct Answer: To monitor process stability and detect assignable causes of variation

Q2. Which control chart is most appropriate for monitoring the mean of a continuous quality characteristic when subgroup sizes are constant and >1?

• p-chart
• X-bar chart
• c-chart
• np-chart

Correct Answer: X-bar chart

Q3. For monitoring variability within subgroups, which chart is commonly paired with the X-bar chart?

• p-chart
• R-chart (range chart)
• c-chart
• u-chart

Correct Answer: R-chart (range chart)

Q4. Which chart should be used for counting defects per unit where the area of opportunity varies?

• c-chart
• p-chart
• u-chart
• X-bar chart

Correct Answer: u-chart

Q5. What is the conventional location of control limits on a control chart relative to the center line?

• At ±2 standard deviations from the center line
• At ±1 standard deviation from the center line
• At ±3 standard deviations from the center line
• Exactly at the process specification limits

Correct Answer: At ±3 standard deviations from the center line

Q6. Which statement best distinguishes common cause variation from assignable cause variation?

• Common causes are single events; assignable causes are many small sources
• Common causes affect only one unit; assignable causes affect the entire process
• Common causes are inherent to the system; assignable causes are identifiable and correctable
• Common causes can be eliminated by operator training; assignable causes cannot

Correct Answer: Common causes are inherent to the system; assignable causes are identifiable and correctable

Q7. If points on an X‑bar chart fall within control limits but show a sustained upward trend, what does this indicate?

• The process is perfectly capable and needs no action
• There may be a non-random pattern suggesting an assignable cause despite being within limits
• Control limits must be recomputed immediately using a larger sigma
• A single outlier should be removed to stabilize the chart

Correct Answer: There may be a non-random pattern suggesting an assignable cause despite being within limits

Q8. Which rule is part of the Western Electric rules for detecting non-random patterns?

• One point beyond ±1σ
• Two out of three consecutive points beyond ±2σ on the same side
• Three consecutive points exactly on the center line
• Five sequential points alternating above and below the center line

Correct Answer: Two out of three consecutive points beyond ±2σ on the same side

Q9. What does Average Run Length (ARL) represent in control chart performance?

• The average number of defects per unit
• The average number of samples taken until a signal occurs
• The average subgroup size used for an X-bar chart
• The average process capability index Cp

Correct Answer: The average number of samples taken until a signal occurs

Q10. When should a p-chart be preferred over a u-chart?

• When monitoring defects per unit with varying opportunities
• When subgroup sizes are constant and the measure is proportion defective
• When measuring the mean of a continuous variable
• When the defect counts per sample are high and highly variable

Correct Answer: When subgroup sizes are constant and the measure is proportion defective

Q11. How are control limits typically calculated for an X-bar chart using process standard deviation σ and subgroup size n?

• Center line ± 3σ
• Center line ± 3(σ/√n)
• Center line ± 3(σ·√n)
• Center line ± σ/3

Correct Answer: Center line ± 3(σ/√n)

Q12. In a control chart context, what is “rational subgrouping”?

• Randomly selecting samples from unrelated processes
• Grouping samples so within-subgroup variation is minimized and between-subgroup variation reflects process change
• Using subgroups large enough to include all possible variation sources
• Grouping based on convenience rather than process logic

Correct Answer: Grouping samples so within-subgroup variation is minimized and between-subgroup variation reflects process change

Q13. Which control chart is appropriate when monitoring the number of defects in a fixed area or time where the opportunity is constant?

• p-chart
• c-chart
• X-bar chart
• np-chart

Correct Answer: c-chart

Q14. What action is recommended when a control chart signals an out‑of‑control condition?

• Ignore it if process specifications are still met
• Stop production immediately and discard all previous lots
• Investigate possible assignable causes and take corrective action before changing control limits
• Adjust control limits to re-include the outlying point

Correct Answer: Investigate possible assignable causes and take corrective action before changing control limits

Q15. What effect does increasing subgroup size have on the width of X‑bar chart control limits, assuming σ constant?

• Control limits widen (become further from center)
• Control limits narrow (become closer to center)
• Control limits remain unchanged
• Control limits become irrelevant

Correct Answer: Control limits narrow (become closer to center)

Q16. Which chart is best for monitoring individual measurements when subgrouping is not possible?

• X-bar and R chart
• Individuals (I) and Moving Range (MR) chart
• c-chart
• p-chart

Correct Answer: Individuals (I) and Moving Range (MR) chart

Q17. How should non-normal measurement data be handled when using control charts based on normal-theory limits?

• Assume normality and proceed without change
• Apply data transformation or use nonparametric or attribute-based charts
• Discard data until it appears normal
• Use smaller subgroup sizes to force normality

Correct Answer: Apply data transformation or use nonparametric or attribute-based charts

Q18. What does a point beyond the upper control limit on an R-chart indicate?

• An unusually small within-subgroup variability
• An unusually large within-subgroup variability, suggesting special cause
• The process mean has shifted downward
• The sample size is too large to be reliable

Correct Answer: An unusually large within-subgroup variability, suggesting special cause

Q19. Which of the following control chart enhancements is specifically designed to detect small, persistent shifts more quickly?

• 3-sigma Shewhart chart without modification
• Exponentially Weighted Moving Average (EWMA) or CUSUM chart
• Simple moving average of subgroup ranges
• p-chart with doubled subgroup size

Correct Answer: Exponentially Weighted Moving Average (EWMA) or CUSUM chart

Q20. In process capability assessment, what does Cp measure?

• The centering of the process around the target
• The capability of the process relative to specification width ignoring centering
• The proportion of nonconforming units
• The probability of a false alarm on a control chart

Correct Answer: The capability of the process relative to specification width ignoring centering

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