Lean Six Sigma Exam
Control Charts (X-bar, R, P, C, U charts) Practice Questions
140 practice questions with detailed explanations — aligned to the Lean Six Sigma Exam.
Master Control Charts (X-bar, R, P, C, U charts) to boost your score on the Lean Six Sigma Exam. Each question below mirrors the style and difficulty of real exam questions, complete with detailed explanations so you understand the why behind every answer. Work through all 140 questions, review any that trip you up, and use the related topics below to round out your preparation.
Q1.Which control chart is used to monitor the proportion of defective items in a sample of variable size?
A.c chartB.u chartC.p chartD.np chartC. p chartExplanation: 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.
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Q2.On an X-bar chart, control limits are set at:
A.±1 standard deviation from the grand meanB.±3 standard deviations of the subgroup means (±3σ/√n)C.The specification limits (USL and LSL)D.±2 standard deviations of individual data pointsB. ±3 standard deviations of the subgroup means (±3σ/√n)Explanation: 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.
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Q3.A control chart shows 9 consecutive points on one side of the centerline. What does this indicate?
A.Normal random variation — no action neededB.A special cause — the process mean has likely shiftedC.The control limits are too wideD.The sample size needs to be increasedB. A special cause — the process mean has likely shiftedExplanation: 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.
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Q4.When should you use an X-bar & S chart instead of an X-bar & R chart?
A.When sample size is less than 8B.When sample size is greater than 10–15C.When data is attribute (pass/fail) rather than variableD.When the process is not in controlB. When sample size is greater than 10–15Explanation: 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.
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Q5.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)?
A.UCL = 7, LCL = 1B.UCL = 10, LCL = 0 (or negative, floor at 0)C.UCL = 8, LCL = 0D.UCL = 6, LCL = 2B. UCL = 10, LCL = 0 (or negative, floor at 0)Explanation: 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.
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