# Process Capability and Process Capability Index

Process Capability and Process Capability Index

Process Capability: A process works in a predefined sequence to give an output expected to meet defined specifications, engineering tolerances and thus customer requirements. Process capability is the measure of process effectiveness and denoted as Cp. This can be mathematically interpreted as allowable variation (USL-LSL) divided by 6 times the standard deviation (denoted by sigma **σ**).

Cp= (USL-LSL)/6**σ**

Here USL is Upper Specification Limit, LSL is Lower Specification Limit and sigma (**σ**) indicates the Standard Deviation.

The process capability is value thus arrived at will indicate effectiveness of the process.

1. Cp = 1 Acceptable

2. Cp < 1 Poor process

3. Cp = 1.3 - 1.5 Good

4. Cp = 2 Excellent, 6 Sigma

Thus, as a general rule, any value lesser than 1 indicates a poor process and thus not acceptable. With this understanding we proceed to the actual or practical process capability.

Process Capability Index: Generally a process that varies within the specifications is acceptable. However, it is critical and important to know where the process actually lies within the given band of specification. A process may be delivering with minimum variation, but may not be running close the target. It might be running towards or close to one side of specification limit. Conversely, the process may be running, on average, exactly at the target, within the specification band, but with high variation.

Process Capability Index, denoted as Cpk, indicates how close a process is running to its specification limits considering the natural variability present in the process. Larger the Cpk value, more likely the process to be within specification.

Calculation of Cpk requires mean of the data collected, standard deviation and the upper and lower limits. The mathematical interpretation of Process Capability Index is:

Cpk = minimum of [(Mean - LSL/3**σ**), (USL-Mean /3**σ**)]

To understand how Cpk gives more insight over the Cp, let us see the following example.

Let us consider production of metal sheet of 4 mm thickness with a standard deviation of 0.04 mm. The lower thickness specification is 3.80 mm and upper thickness specification is 4.10 mm. The mean of the entire thickness data is 4 mm.

A. Process Capability (Cp):

Cp = (USL-LSL)/6

Cp = (4.10 - 3.80)/ (0.04x6)

Cp = 1.25

It means the process runs within the specification limits, and thus acceptable.

B. Process Capability Index (Cpk):

Cpk = minimum of [(Mean - LSL/3), (USL-Mean /3)]

Cpk = minimum of [((4 - 3.80)/(3 x 0.04)), ((4.10 - 4)/ (3 x 0.04))]

Cpk = minimum of [((4 - 3.80)/(3 x 0.04)), ((4.10 - 4)/ (3 x 0.04))]

Cpk = minimum of [(1.67), (0.83)]

Thus , Cpk = 0.83

It means that the variation is more on the USL side.

The general indications one gets from the Cpk values.

- Cpk=1/2: Process is running away from centre, very-very close to any of the specification limit
- Cpk=1: Process is running in the between the of centre and any of the specification limit
- Cpk=2: Process is running near the centre, away from any of the specification limit
- Cpk=3: Process is running almost close to or at the centre, away from any of the specification limit

Concluding the above, the Cp value of the process indicates it running within the specification band, Cpk indicates high variation within process.

Speaking in nutshell, Cp indicates the smartness of the histogram curve and Cpk indicates the location of the histogram curve within the specification band. A high Cpk index indicates a good process with a small spread in relation to the specification band, running close to the centre, within that band. Same values of Cp and Cpk of a process indicate that it is running exactly in the middle of the specification range.

## Leave a Comment