Calculates capability statistics (R.W. Payne).

### Option

`PRINT` = string tokens |
Controls output (`cpk` , `ppk` , `histogram` ); default `cpk` , `ppk` |
---|

### Parameters

`DATA` = variates or pointers |
Data measurements |
---|---|

`SAMPLES` = factors or scalars |
Factor identifying samples or scalar indicating the size of each sample |

`LOWERLIMIT` = scalars |
Specifies the lower specification limit for each set of data |

`UPPERLIMIT` = scalars |
Specifies the upper specification limit for each set of data |

`CPK` = scalars |
Saves the index C_{pk} |

`PPK` = scalars |
Saves the index P_{pk} |

### Description

`SPCAPABILITY`

calculates capability statistics. These are used to assess the extent to which the output of a process lies within its specification limits. The data values consist of samples of measurements made on successive occasions, which are specified by the `DATA`

and `SAMPLES`

parameters. `DATA`

can be set to a variate containing the measurement and `SAMPLES`

to a factor identifying the samples. Alternatively, if the samples are all of the same size and occur in the `DATA`

variate one sample at a time, you can set `SAMPLES`

to a scalar indicating the size of each sample. Finally, if the samples are in separate variates, you can set `DATA`

to a pointer containing the variates (`SAMPLES`

is then unset). The `LOWERLIMIT`

parameter supplies the lower specification limit of the process, and the `UPPERLIMIT`

parameter supplies the upper limit.

There are two indexes that can be calculated. The index *C _{pk}* is the minimum of the two quantities

*C*and

_{pl}*C*. These are defined as

_{pu}*C _{pl}* = (

`LOWERLIMIT`

– *mean*) / (3 ×

*sigma*)

*C _{pu}* = (

`UPPERLIMIT`

– *mean*) / (3 ×

*sigma*)

where *sigma* is the within-sample standard deviation (see for example Ryan 1989, Chapter 7). The alternative index, *P _{pk}*, is the minimum of the two quantities

*P*and

_{pl}*P*. These have similar definitions to

_{pu}*C*and

_{pl}*C*, except that

_{pu}*sigma*now also includes the between-sample variation.

The `PRINT`

option controls which of these are printed, with settings `cpk`

and `ppk`

. There is also a setting `histogram`

, which plots a histogram of the data together with vertical lines indicating the lower and upper limits. By default `PRINT=cpk,ppk`

. Alternatively, the indexes can be saved, in scalars, using the parameters `CPK`

and `PPK`

.

Option: `PRINT`

.

Parameters: `DATA`

, `SAMPLES`

, `LOWERLIMIT`

, `UPPERLIMIT`

, `CPK`

, `PPK`

.

### Method

`SPCAPABILITY`

estimates the within-sample standard deviation (for *C _{pk}*) by the average of the standard deviations of the samples, each divided by a bias correction constant

*c*

_{4}:

*c*_{4} = √(2/*n*) × `GAMMA`

(*n*/2) / `GAMMA`

((*n*-1)/2)

where *n* is the sample size. Similarly the standard deviation for *P _{pk}* is the bias-corrected standard deviation of the samples, all pooled together.

### Action with `RESTRICT`

Neither the `DATA`

variates nor the `SAMPLE`

factors may be restricted.

### Reference

Ryan, T.P. (1989). *Statistical Methods for Quality Improvement*. Wiley, New York.

### See also

Procedures: `SPCCHART`

, `SPCUSUM`

, `SPEWMA`

, `SPPCHART`

, `SPSHEWHART`

.

Commands for: Six sigma.

### Example

CAPTION 'SPCAPABILITY example',\ !t('Data from Montgomery (1985), Introduction',\ 'to Statistical Process Control, page 207.'); STYLE=meta,plain VARIATE Diameter READ Diameter 74.030 74.002 74.019 73.992 74.008 73.995 73.992 74.001 74.011 74.004 73.988 74.024 74.021 74.005 74.002 74.002 73.996 73.993 74.015 74.009 73.992 74.007 74.015 73.989 74.014 74.009 73.994 73.997 73.985 73.993 73.995 74.006 73.994 74.000 74.005 73.985 74.003 73.993 74.015 73.988 74.008 73.995 74.009 74.005 74.004 73.998 74.000 73.990 74.007 73.995 73.994 73.998 73.994 73.995 73.990 74.004 74.000 74.007 74.000 73.996 73.983 74.002 73.998 73.997 74.012 74.006 73.967 73.994 74.000 73.984 74.012 74.014 73.998 73.999 74.007 74.000 73.984 74.005 73.998 73.996 73.994 74.012 73.986 74.005 74.007 74.006 74.010 74.018 74.003 74.000 73.984 74.002 74.003 74.005 73.997 74.000 74.010 74.013 74.020 74.003 73.988 74.001 74.009 74.005 73.996 74.004 73.999 73.990 74.006 74.009 74.010 73.989 73.990 74.009 74.014 74.015 74.008 73.993 74.000 74.010 73.982 73.984 73.995 74.017 74.013 : SPCAPABILITY Diameter; SAMPLES=5; LOWERLIMIT=73.95; UPPERLIMIT=74.05