Before going into production, many manufacturers run a *capability
study* to determine if their process will run within specifications
enough of the time. *Capability indices* produced
by such a study are used to estimate expected percentages of defective
parts.

Capability studies are conducted with the `capability`

function.
The following capability indices are produced:

`mu`

— Sample mean`sigma`

— Sample standard deviation`P`

— Estimated probability of being within the lower (`L`

) and upper (`U`

) specification limits`Pl`

— Estimated probability of being below`L`

`Pu`

— Estimated probability of being above`U`

`Cp`

—`(U-L)/(6*sigma)`

`Cpl`

—`(mu-L)./(3.*sigma)`

`Cpu`

—`(U-mu)./(3.*sigma)`

`Cpk`

—`min(Cpl,Cpu)`

As an example, simulate a sample from a process with a mean of 3 and a standard deviation of 0.005:

rng default; % For reproducibility data = normrnd(3,0.005,100,1);

Compute capability indices if the process has an upper specification limit of 3.01 and a lower specification limit of 2.99:

S = capability(data,[2.99 3.01])

S = mu: 3.0006 sigma: 0.0058 P: 0.9129 Pl: 0.0339 Pu: 0.0532 Cp: 0.5735 Cpl: 0.6088 Cpu: 0.5382 Cpk: 0.5382

Visualize the specification and process widths:

```
capaplot(data,[2.99 3.01]);
grid on
```

Was this topic helpful?