UCHART Statement: SHEWHART Procedure

Plotted Points

Each point on a chart indicates the number of nonconformities per unit () in a subgroup. For example, Figure 15.96 displays three sections of pipeline that are inspected for defective welds (indicated by an X). Each section represents a subgroup composed of a number of inspection units, which are 1000-foot-long sections. The number of units in the th subgroup is denoted by , which is the subgroup sample size.

Figure 15.96 Terminology for Charts and Charts

The number of nonconformities in the th subgroup is denoted by . The number of nonconformities per unit in the th subgroup is denoted by . In Figure 15.96, the number of defective welds per unit in the third subgroup is .

A chart plots the quantity for the th subgroup. A chart plots the quantity for the th subgroup (see CCHART Statement: SHEWHART Procedure). An advantage of a chart is that the value of the central line at the th subgroup does not depend on . This is not the case for a chart, and consequently, a chart is often preferred when the number of units is not constant across subgroups.

Central Line

On a chart, the central line indicates an estimate of , which is computed as by default. If you specify a known value () for , the central line indicates the value of .

Control Limits

You can compute the limits in the following ways:

• as a specified multiple () of the standard error of above and below the central line. The default limits are computed with (these are referred to as limits).

• as probability limits defined in terms of , a specified probability that exceeds the limits

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

The limits vary with .

The upper probability limit UCLU for can be determined using the fact that

The limit UCLU is then calculated by setting

and solving for UCLU.

Likewise, the lower probability limit LCLC for can be determined using the fact that

The limit LCLC is then calculated by setting

and solving for LCLC. For more information, refer to Johnson, Kotz, and Kemp (1992). This assumes that the process is in statistical control and that has a Poisson distribution. Note that the probability limits vary with and are asymmetric around the central line. If a standard value is available for , replace with in the formulas for the control limits.

You can specify parameters for the limits as follows:

• Specify 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 with the U0= option or with the variable _U_ in a LIMITS= data set.