Chapter Contents |
Previous |
Next |

UCHART Statement |

The following notation is used in this section:

u | expected number of nonconformities per unit produced by process |

u_{i} | number of nonconformities
per unit in the i^{ th} subgroup.
In general, u_{i} = c_{i}/n_{i}. |

c_{i} | total number of nonconformities in the
i^{ th} subgroup |

n_{i} | number of inspection units in the i^{ th}
subgroup |

average number of nonconformities per unit taken
across subgroups. The quantity is computed
as a weighted average:
| |

N | number of subgroups |

has a central distribution with degrees of freedom |

The *number of nonconformities* in the *i*^{ th}
subgroup is denoted by *c*_{i}. The *number of nonconformities
per unit* in the *i*^{ th} subgroup is
denoted by *u*_{i}=*c*_{i}/*n*_{i}. In Figure 41.10, the number
of defective welds per unit in the third subgroup is *u _{3}*=2/2.5=0.8.

A *u* chart plots the quantity
*u*_{i} for the *i*^{ th} subgroup.
A *c* chart plots the quantity
*c*_{i} for the *i*^{ th} subgroup
(see Chapter 33, "CCHART Statement").
An advantage of a *u* chart is that the value of the central
line at the *i*^{ th} subgroup does not depend
on *n*_{i}. This is not the case for a *c* chart, and consequently,
a *u* chart is often preferred when the number of units *n*_{i}
is not constant across subgroups.

- as a specified multiple (
*k*) of the standard error of*u*_{i}above and below the central line. The default limits are computed with*k*=3 (these are referred to as*limits*). - as probability limits defined in terms of , a specified probability that
*u*_{i}exceeds the limits

The lower and upper control limits, LCLU and UCLU, respectively, are given by

The limits vary with *n*_{i}.

The upper probability limit UCLU for *u*_{i} can be
determined using the fact that

The limit UCLU is then calculated by setting

Likewise, the lower probability limit LCLC for *u*_{i} can be
determined using the fact that

The limit LCLC is then calculated by setting

You can specify parameters for the limits as follows:

- Specify
*k*with the SIGMAS= option or with the variable _SIGMAS_ in a LIMITS= data set.

- Specify with the ALPHA= option
or with the variable _ALPHA_ in a LIMITS= data set.

- Specify a constant nominal sample size for the control limits with the LIMITN= option or with the variable _LIMITN_ in a LIMITS= data set.
- Specify
*u*with the U0= option or with the variable _U_ in a LIMITS= data set._{0}

Chapter Contents |
Previous |
Next |
Top |

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.