Question 1

What is the difference between Cp and Cpk?

Accepted Answer

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.

Question 2

A process has Cpk = 1.00. What is the approximate DPMO (defects per million opportunities)?

Accepted Answer

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).

Question 3

What sigma level corresponds to 3.4 DPMO, the Six Sigma standard?

Accepted Answer

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.

Question 4

A process has USL = 20, LSL = 10, mean = 14, and standard deviation = 1. What is the Cpk?

Accepted Answer

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.

Question 5

When a process is 'capable' but 'not stable,' what is the recommended action?

Accepted Answer

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.

Question 6

A process has a Cpk of 0.8. What does this indicate?

Accepted Answer

Cpk measures how centered and capable a process is relative to specification limits. A Cpk below 1.0 means the process is producing output outside one or both spec limits — it is not capable. A Cpk ≥ 1.33 is typically considered capable.

Question 7

What is the difference between Cp and Cpk?

Accepted Answer

Cp = (USL – LSL) / (6σ) and measures the spread of the process relative to specification width — assuming the mean is perfectly centered. Cpk adjusts for process mean shift by taking the minimum of (USL – mean)/3σ and (mean – LSL)/3σ.

Question 8

A process must achieve a Cpk ≥ 1.67 to meet customer requirements. What sigma level does this approximately correspond to?

Accepted Answer

Cpk of 1.67 corresponds to a 5-sigma process. The relationship is: sigma level ≈ 3 × Cpk. So Cpk 1.00 ≈ 3σ, Cpk 1.33 ≈ 4σ, Cpk 1.67 ≈ 5σ, and Cpk 2.00 ≈ 6σ.

Question 9

Which of the following is a prerequisite for a meaningful process capability study?

Accepted Answer

Capability indices (Cp, Cpk) are only meaningful when the process is stable — i.e., in statistical control with no special causes. Calculating Cpk on an unstable process produces misleading results because the variation is not predictable.

Question 10

Long-term process capability is measured by Ppk, while short-term is measured by Cpk. What is the typical relationship between these two indices?

Accepted Answer

Ppk uses the overall (long-term) standard deviation from all data collected, while Cpk uses the within-subgroup (short-term) standard deviation. Long-term variation is always ≥ short-term variation, so Ppk ≤ Cpk. The ratio Cpk/Ppk is sometimes called the 'capability ratio.'

Process Capability (Cp, Cpk, Sigma Level) Practice Questions

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