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Cp and Cr: Process Capability Ratios

Capability indices: Cr

The Cr capability ratio is used to summarize the estimated spread of the system compared to the spread of the specification limits (upper and lower). The lower the Cr value, the smaller the output spread. Cr does not consider process centering.

When the Cr value is multiplied by 100, the result shows the percent of the specifications that are being used by the variation in the process. Cr is calculated using an estimated sigma  and is the reciprocal of Cp. In other words, Cr = 1/Cp.

See also:
>> How do I compare the Cp/Pp and Cpk/Ppk?
>> Cpk
>> Cpm
>> Cp
>> Ppk
>> Pp
>> Pr
>> Capability indices

Additional reference material

Additional sections from legacy cp:

Capability indices: Cp

The Cp index is used to summarize a system’s ability to meet two-sided specification limits (upper and lower). Like Cpk, it uses estimated sigma and, therefore, shows the system’s potential to meet the specifications. However, it ignores the process average and focuses on the spread. If the system is not centered within the specifications, Cp alone may be misleading.

The higher the Cp value, the smaller the spread of the system’s output. Cp is a measure of spread only. A process with a narrow spread (a high Cp) may not meet customer needs if it is not centered within the specifications.

If the system is centered on its target value, Cp should be used in conjunction with Cpk to account for both spread and centering. Cp and Cpk will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.

See also:
>> How do I compare the Cp/Pp and Cpk/Ppk?
>> Cpk
>> Cr
>> Cpm
>> Ppk
>> Pp
>> Pr
>> Capability indices

Additional sections from legacy capability-indices-f:

Capability indices

Capability indices use estimated sigma.

Cp

Cp for one-sided specifications

If you are using one sided specifications, use the following formulas to determine the Cp:

Upper specification

Lower specification

Cr

Cpk

Where:

Zmin is the smaller of Zupper and Zlower.

Using estimated sigma:

Cpm

Where:

T = specification target (nominal)

Xi = a given individual reading of ” i ”

n = total number of individual readings

= symbol for summation

Cp

Cp for one-sided specifications

If you are using one sided specifications, use the following formulas to determine the Cp:

Upper specification

Lower specification

Cr

Cr

Cpk

Cpk

Where:

Zmin is the smaller of Zupper and Zlower.

Using estimated sigma:

Cpm

Cpm

Where:

T = specification target (nominal)

Xi = a given individual reading of ” i ”

n = total number of individual readings

= symbol for summation

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