When calculating the Cp index, what does the standard deviation represent in the formula?

Question

Options

• AThe tolerance interval
• BThe confidence interval for the result
• CThe range of the process
• DThe variance of the index

• B
  4% (1)
• C
  89% (25)
• D
  7% (2)

Explanation

In the Cp formula - Cp = (USL − LSL) / 6σ - the standard deviation (σ) in the denominator represents the natural spread or variability of the process output, making C correct. Specifically, 6σ captures the "voice of the process," spanning nearly all of its variation, so it functionally describes how wide the process range is.

Why the distractors are wrong:

• A (Tolerance interval): The tolerance interval is the numerator - the distance between the Upper and Lower Specification Limits (USL − LSL), not σ.
• B (Confidence interval): A confidence interval relates to estimation uncertainty around a statistic; it has no direct role in the Cp formula itself.
• D (Variance of the index): Variance is σ², not σ - and "variance of the index" isn't a meaningful term in this context.

Memory tip: Think of it as a fraction comparing the customer's voice (tolerance) to the process's voice (spread). The standard deviation is the process's voice - it tells you how widely the process naturally "speaks."

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