NPCHART Statement: SHEWHART Procedure
Constructing Charts for Number Nonconforming (np Charts)
The following notation is used in this section:
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expected proportion of nonconforming items produced by the process |
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proportion of nonconforming items in the |
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number of nonconforming items in the |
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number of items in the |
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average proportion of nonconforming items taken across subgroups:
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number of subgroups |
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incomplete beta function:
for |
th subgroup 
, 
, and 
, where 
is the gamma function Plotted Points
Each point on an 
chart represents the observed number (
) of nonconforming items in a subgroup. For example, suppose the first subgroup (see Figure 15.60) contains 12 items, of which three are nonconforming. The point plotted for the first subgroup is 
.
Note that a 
chart displays the proportion of nonconforming items 
. You can use the PCHART statement to create charts; see PCHART Statement: SHEWHART Procedure.
Central Line
By default, the central line on an chart indicates an estimate for 
, which is computed as 
. If you specify a known value (
) for , the central line indicates the value of 
. Note that the central line varies with 
.
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, LCL and UCL respectively, are computed as
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A lower probability limit for can be determined using the fact that
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Refer to Johnson, Kotz, and Kemp (1992). This assumes that the process is in statistical control and that is binomially distributed. The lower probability limit LCL is then calculated by setting
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and solving for LCL. Similarly, the upper probability limit for can be determined using the fact that
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The upper probability limit UCL is then calculated by setting
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and solving for UCL. The probability limits are asymmetric about the central line. Note that both the control limits and probability limits vary with 
.
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 P0= option or with the variable _P_ in the LIMITS= data set.