# capability

Process capability indices

## Syntax

```S = capability(data,specs) ```

## Description

`S = capability(data,specs)` estimates capability indices for measurements in `data` given the specifications in `specs`. `data` can be either a vector or a matrix of measurements. If `data` is a matrix, indices are computed for the columns. `specs` can be either a two-element vector of the form `[L,U]` containing lower and upper specification limits, or (if `data` is a matrix) a two-row matrix with the same number of columns as `data`. If there is no lower bound, use `-Inf` as the first element of `specs`. If there is no upper bound, use `Inf` as the second element of `specs`.

The output `S` is a structure with the following fields:

• `mu` — Sample mean

• `sigma` — Sample standard deviation

• `P` — Estimated probability of being within 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)`

Indices are computed under the assumption that data values are independent samples from a normal population with constant mean and variance.

Indices divide a “specification width” (between specification limits) by a “process width” (between control limits). Higher ratios indicate a process with fewer measurements outside of specification.

## Examples

collapse all

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 = struct with fields: 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``` ## References

 Montgomery, D. Introduction to Statistical Quality Control. Hoboken, NJ: John Wiley & Sons, 1991, pp. 369–374.

## Version History

Introduced in R2006b