To determine how a process is operating, we can calculate:

- Process Capability Index (Cpk).
- Process Capability (Cp).

Cpk are classified into two; the upper and the lower denoted Cpu and CpL respectively.

We are dividing by 3 because specification limit has an upper bound and a lower bound and since 6 sigmas (i.e. 6 standard deviations) account for nearly all eventualities on a process (assuming normal distribution), hence dividing by 3 enables us to look at only one side of the distribution.

Cpk can be determined by dividing the Z score by 3.Z = x – mean of the population / standard deviation.

- If a process is perfectly centered, it has a
**Cp of 1**indicating that the mean was 3 standard deviations (sigma) away from the upper limit and the lower limit. - And, a perfectly centered process a process who has a mean exactly in between the 2 specification limits will have a
**Cpk of 1.**

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- Cpk measures how close a process is performing compared to its specification limits and accounting for the inherent process variability.
- The larger the Cpk value, the less likely the item will be outside the specification limits.
- When Cpk is negative, the process under study will produce output that is outside the customer specification limits.
- Cpk is negative when the mean of the process is outside the customer specification limits.
- At least
*C*pk = 1.33 [4 sigma] or higher is required to satisfy most customers. - Cpk do have upper and lower value reported. If the upper value is 2 and the lower is 1, we say it has been shifted to the left.

**Cpk = Negative number,** process is out of customer’s specification.

**Cpk = 0.5, **good chance of process meeting customer’s specification.

**Cpk = 1, **process about meeting customer’s specification.

**Cpk = 2, **Great! Process meets customer’s specification but can be improved upon.

**Cpk =3, **Excellent result.

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**Cp does not account for centering.**

**Cp = (USL – LSL) / ( 6 x σr )**

**Cp = (USL – LSL) / (6 x R Bar / d2) **

If Process Mean (I.e. central tendency) is closer to the USL, use:

**[USL – X (bar) ] / [3 x R Bar / d2],** where X (bar) is the Process Mean.

If Process mean (i.e. central tendency) is closer to the LSL, use:

**[x(bar) – LSL ] / [3 x R Bar / d2],** where x(bar) is the Process Mean.

**The inverse of Cp equals the Capability Ratio (Cr)**

**Cr = 1/ Cp = ( 6 x σr ) / (USL – LSL)**

**If Cr < 0.75, **the process is capable

**If Cr = 0.75 – 1.00, **the process is capable with tight control.

**If Cr >1, **the process is not capable.

- If Cp == Cpk, then the process is perfectly centered and, if process is perfectly centered, Cp == Cpk.
- Cpk can never be larger than Cp, because Cpk accounts for centering (while Cp does not),
- Both processes are assumed stable.

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*Adebayo is a thought leader in continuous process improvement and manufacturing excellence. He is a Certified Six Sigma Master Black Belt (CSSMBB) Professional and Management Systems Lead Auditor (ISO 9001, 45001, ISO 22000/FSSC 22000 etc.) with strong experience leading various continuous improvement initiative in top manufacturing organizations. *

*You can reach him here.*

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