# Cp

Definition of Cp:

Process capability index: a measure of the ability of a process to produce consistent results – the ratio between the permissible spread and the actual spread of a process.

Permissible spread is the difference between the upper and lower specific limits of acceptibility (a.k.a. total tolerance); actual spread is defined, arbitrarily, as the difference between upper and lower 3 x sigma deviations from the mean value (representing 99.7% of the normal distribution).

As a formula, Cp = (USL-LSL)/(6 x sigma).

Note this takes no account of how well the output is centered on the target (nominal) value. For that see Cpk.

You can think of the process capability index Cp in 3 ways:

1. Cp measures the capability of a process to meet its specification limits. It is the ratio between the required and actual variability.
2. More mathematically, the Cp is the ratio of the Spec difference (upper – lower) divided by 6-sigma, which is the spread of a normal curve. Minitab gives the following explanation: ‘Capability statistics are basically a ratio between the allowable process spread (the width of the specification limits) and the actual process spread (6s)’
3. Graphically, think of positioning a normal curve centered between the specs. Now look at the tail areas that exceeds the specs. The smaller the area, the larger the Cp. In this sense it is equivalent to looking at the popular PPM measure (parts-per-million) which gives the area of the normal curve that exceeds the specs.
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