Which statement best describes the relationship between Cp and Cpk when the process is perfectly centered?

Which statement best describes the relationship between Cp and Cpk when the process is perfectly centered?

• A. They are unrelated.
• B. Cp and Cpk are equal when the process is perfectly centered.
• C. Cp is greater than Cpk in all cases.
• D. Cpk is greater than Cp in all cases.

Answer: (B)

When the process is perfectly centered, Cp and Cpk become equal because they both reflect how spread the process is relative to the tolerance, but Cpk also accounts for how far the mean is from the center. Cp uses the full tolerance range (USL minus LSL) and the process spread (6 sigma) to measure potential capability, assuming the mean is centered. Cpk, on the other hand, uses the smaller distance from the mean to either tolerance limit, scaled by 3 sigma, which captures the actual capability given where the mean sits. If the mean is exactly in the middle, those two distances to the limits are equal, so Cp evaluates to the same value as Cpk. When the mean shifts away from center, Cpk becomes smaller than Cp, reflecting reduced actual capability due to miscentering. Hence the statement that they are equal when the process is perfectly centered is the correct description.

When the process is perfectly centered, Cp and Cpk become equal because they both reflect how spread the process is relative to the tolerance, but Cpk also accounts for how far the mean is from the center. Cp uses the full tolerance range (USL minus LSL) and the process spread (6 sigma) to measure potential capability, assuming the mean is centered. Cpk, on the other hand, uses the smaller distance from the mean to either tolerance limit, scaled by 3 sigma, which captures the actual capability given where the mean sits. If the mean is exactly in the middle, those two distances to the limits are equal, so Cp evaluates to the same value as Cpk. When the mean shifts away from center, Cpk becomes smaller than Cp, reflecting reduced actual capability due to miscentering. Hence the statement that they are equal when the process is perfectly centered is the correct description.