Question 1

Which control chart is used to monitor the proportion of defective items in a sample of variable size?

Accepted Answer

The p chart monitors the proportion (fraction) of defective units. It is used when sample sizes vary. The np chart monitors the number of defective units but requires constant sample size. The c chart monitors defects per unit with constant sample size, and the u chart monitors defects per unit with variable sample size.

Question 2

On an X-bar chart, control limits are set at:

Accepted Answer

Control limits on an X-bar chart are ±3 standard deviations of the subgroup means, calculated as X̄ ± A₂R̄ (using control chart constants). Control limits are based on process variation — NOT specification limits. They represent what the process naturally produces, not what the customer requires.

Question 3

A control chart shows 9 consecutive points on one side of the centerline. What does this indicate?

Accepted Answer

Nine or more consecutive points on one side of the centerline is a 'run' — a classic Western Electric rule violation indicating a process shift (special cause). Even if all points are within control limits, this non-random pattern signals that the process mean has changed and investigation is required.

Question 4

When should you use an X-bar & S chart instead of an X-bar & R chart?

Accepted Answer

The R chart (range) is efficient for small subgroups (n ≤ 8–10). For larger subgroups (n > 10–15), the sample standard deviation (s) is a more efficient and accurate estimate of process dispersion than the range, so the X-bar & S chart is preferred.

Question 5

A c chart monitors defects in a product with a constant sample size of 1 unit. The average defect count is 4. What are the UCL and LCL (approximately)?

Accepted Answer

For a c chart: UCL = c̄ + 3√c̄ = 4 + 3√4 = 4 + 6 = 10. LCL = c̄ − 3√c̄ = 4 − 6 = −2, floored at 0 (defect counts cannot be negative). So UCL = 10, LCL = 0.

Question 6

An X-bar and R chart is being used to monitor a filling process. The R chart shows all points within control limits, but the X-bar chart has 9 consecutive points above the centerline. What does this indicate?

Accepted Answer

Nine or more consecutive points on the same side of the centerline is a Western Electric Rule violation indicating a non-random pattern — a special cause, typically a sustained shift in the process mean. The R chart being in control confirms variation is stable, but the mean has shifted.

Question 7

Which type of control chart is most appropriate for monitoring the number of defects per unit when the sample size varies?

Accepted Answer

A u-chart tracks the average number of defects (nonconformities) per unit when sample sizes vary. A c-chart also counts defects but requires constant sample size. The p-chart and np-chart track proportion and count of defective items, not defects per unit.

Question 8

A p-chart is used to track the fraction of defective invoice line items per batch. This is an example of what type of data?

Accepted Answer

Attribute data is discrete — items are classified as conforming or non-conforming (pass/fail, defective/non-defective). The p-chart is the appropriate control chart for attribute data expressed as a proportion of defectives.

Question 9

Control chart UCL and LCL are set at ±3 standard deviations from the centerline. What percentage of points should fall within these limits if only common cause variation is present?

Accepted Answer

For a normally distributed process, ±3σ control limits capture 99.73% of the data when only common cause variation exists. Points outside these limits signal special causes. The 99.99966% figure refers to Six Sigma quality level (±6σ from the mean).

Question 10

An individuals and moving range (I-MR) chart is most appropriate when:

Accepted Answer

The I-MR chart is designed for processes where only one observation is available per sampling period (n=1) — common in chemical, pharmaceutical, and service processes. It tracks individual measurements (I chart) and the moving range between consecutive points (MR chart).

Control Charts (X-bar, R, P, C, U charts) Practice Questions

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