Lean Six Sigma Exam
Process Capability (Cp, Cpk, Sigma Level) Practice Questions
150 practice questions with detailed explanations — aligned to the Lean Six Sigma Exam.
Master Process Capability (Cp, Cpk, Sigma Level) 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 150 questions, review any that trip you up, and use the related topics below to round out your preparation.
Q1.What is the difference between Cp and Cpk?
A.Cp measures long-term capability; Cpk measures short-term capabilityB.Cp measures potential capability (centered); Cpk accounts for process centeringC.Cp is for two-sided specs; Cpk is for one-sided specsD.Cp uses the mean; Cpk uses the medianB. Cp measures potential capability (centered); Cpk accounts for process centeringExplanation: Cp (process capability ratio) measures potential capability assuming the process is perfectly centered between the specification limits. Cpk is the actual capability index — it accounts for where the process mean sits relative to both limits. A process can have high Cp (wide spec relative to variation) but low Cpk if the mean is off-center.
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Q2.A process has Cpk = 1.00. What is the approximate DPMO (defects per million opportunities)?
A.66,807B.3,400C.233D.2,700D. 2,700Explanation: A Cpk of 1.00 corresponds to ±3 sigma performance, which yields approximately 2,700 DPMO (2,700 defects per million opportunities) — assuming a centered normal distribution. This equates to roughly 99.73% yield. A Cpk of 1.33 corresponds to ±4 sigma (~63 DPMO) and a Cpk of 1.67 to ±5 sigma (~0.57 DPMO).
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Q3.What sigma level corresponds to 3.4 DPMO, the Six Sigma standard?
A.4 sigmaB.5 sigmaC.6 sigmaD.5.5 sigmaC. 6 sigmaExplanation: Six Sigma quality = 3.4 DPMO. This is achieved at ±6 sigma with a 1.5-sigma long-term shift allowance (the standard Motorola convention). Without the shift, ±6 sigma would yield ~0.002 DPMO. The 3.4 DPMO target accounts for typical long-term process drift.
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Q4.A process has USL = 20, LSL = 10, mean = 14, and standard deviation = 1. What is the Cpk?
A.1.00B.1.33C.1.67D.0.83B. 1.33Explanation: Cpk = min[(USL − mean)/(3σ), (mean − LSL)/(3σ)] = min[(20−14)/(3×1), (14−10)/(3×1)] = min[6/3, 4/3] = min[2.00, 1.33] = 1.33. The lower tail is the binding constraint because the mean is shifted toward the LSL.
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Q5.When a process is 'capable' but 'not stable,' what is the recommended action?
A.Proceed — capability is all that mattersB.Investigate and eliminate assignable causes before assessing capabilityC.Widen the specification limitsD.Increase sample size and recalculate CpkB. Investigate and eliminate assignable causes before assessing capabilityExplanation: Process capability indices (Cp, Cpk) are only meaningful when the process is in statistical control (stable). If a control chart shows out-of-control signals (special causes), Cpk calculations are unreliable. You must first identify and eliminate assignable causes, bringing the process into control, before evaluating capability.
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