Given USL = 100, LSL = 40, μ = 70, σ = 5, compute Cp and Cpk.

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Multiple Choice

Given USL = 100, LSL = 40, μ = 70, σ = 5, compute Cp and Cpk.

Explanation:
Process capability indices tell how well a process fits within specification limits. Cp looks at the potential capability assuming the process is centered, while Cpk checks actual capability by also accounting for how far the process mean is from the limits. Calculate Cp: (USL − LSL) / (6σ) = (100 − 40) / (6 × 5) = 60 / 30 = 2.0. Calculate Cpk: first find the distances to the limits in units of σ: - Upper: (USL − μ) / (3σ) = (100 − 70) / (3 × 5) = 30 / 15 = 2.0 - Lower: (μ − LSL) / (3σ) = (70 − 40) / (3 × 5) = 30 / 15 = 2.0 Cpk = min(upper, lower) = 2.0. Since the mean is exactly centered between the limits, Cp equals Cpk, both equal to 2.0.

Process capability indices tell how well a process fits within specification limits. Cp looks at the potential capability assuming the process is centered, while Cpk checks actual capability by also accounting for how far the process mean is from the limits.

Calculate Cp: (USL − LSL) / (6σ) = (100 − 40) / (6 × 5) = 60 / 30 = 2.0.

Calculate Cpk: first find the distances to the limits in units of σ:

  • Upper: (USL − μ) / (3σ) = (100 − 70) / (3 × 5) = 30 / 15 = 2.0

  • Lower: (μ − LSL) / (3σ) = (70 − 40) / (3 × 5) = 30 / 15 = 2.0

Cpk = min(upper, lower) = 2.0.

Since the mean is exactly centered between the limits, Cp equals Cpk, both equal to 2.0.

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