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# Process Capability

### Process Capability Index, Cp:

• Process Capability is commonly measured in units of process standard deviations.  It is for continuous or variable data.
• Cp is the relationship between the process standard deviation and the range between the upper and lower specification limits.

Cp = (USL - LSL) / 6 σx

The minimum acceptable value for Cp is 1 but generally you would want something greater than 1.

### Process Capability Index, Cpk:

• Many times people use the capability index, Cpk which relates the process mean to the nominal value of the specification.

ZUSL= (USL - μx) / σ​x , ZLSL = (LSL - μx) / σ​x

We select the minimum of these two values:

Zmin = min [ ZUSL , - ZLSL]

We find the Cpk index by dividing this minimum value by 3.

Cpk = Zmin / 3

Commonly, for an acceptable process capability, Cpk should be  1.00 but normally greater than 1.

# Process Capability Assessment

The following example shows how to do a process capability assessment.

### Example

You need to make some decisions regarding the procurement of bolts from three different suppliers for your CubeSat. You have requested that the shank diameter (above the thread) have specifications of $1.5 \pm 0.009$ in. The SPC studies done by the suppliers have indicated that their processes are behaving consistently in statistical control with the following process parameters:

Supplier 1: X (double bar) = 1.500 inches

σ x = 0.0030 inch

Supplier 2: X (double bar) = 1.500 inches

σ x = 0.0015 inch

Supplier 3: X (double bar) = 1.4950 inches

σ x= 0.0015 inch

Which supplier would you purchase from? Why?

First of all, look at the graph below to understand the current situation.

### Process Capability Assessment: Supplier 2

All three suppliers appear to be capable of meeting minimal requirements with respect to the conformance of their products to the customer specifications.

Supplier 3 has the least amount of variation. It is generally easier to center the process than to reduce variation. It may be wise to go with Supplier 3 if the supplier agrees to center the process.