Capability Ratio, Cp

The Capability Ratio, Cp, compares the space available to a process that is allotted by the Tolerance, with the space required by the process, as defined by 6 Sigma(X). The formula for the Capability Ratio is:

The relationship between the space available and the space required is further clarified in Figure 1. Here, a generic distribution of individual values is shown in the context of the specification limits (the space available) and the process limits (the space required). Note that the process limits shown in Figure 1 are calculated using Shewhart’s generic formula, Average ± 3 Sigma(X), where Sigma(X) is a generic placeholder for one of several within-subgroup measures of dispersion. This is the same Sigma(X) used in the denominator of the Capability Ratio equation.

By way of integrating the specification limits into its calculation, the Capability Ratio can be thought of as characterizing the elbow room* of a process. When the difference between the specification limits is large, i.e. the tolerance is large, elbow room increases. When the difference between the specification limits is small, i.e. the tolerance is small, elbow room decreases.

While elbow room provides us with an easy way to relate the space available to the space required, it does not account for how centered a process is within the specification limits. It is for this reason that the Capability Ratio is typically paired with the Centered Capability Ratio, Cpk.

*The term elbow room originates from the work of the statistician and quality control expert Donald J. Wheeler.

The Capability Ratio, like all process parameters, is not well-defined until the underlying causal system is operated predictably. Whenever a process is operated unpredictably, that is it is influenced by both common causes of routine variation and assignable causes of exceptional variation, the process parameters, including the process mean, the process standard deviation, and the process capability indices, will change over time. While we can always compute statistics regardless of the characterization (predictable or unpredictable), the only time this arithmetic can be used to estimate process parameters is when the process is operated predictably. When a process is operated unpredictably “the process parameters are changing and are therefore divorced from the statistics” used to calculate them. (Wheeler, More Capability Confusion, (Quality Digest, May 2017), 2).