The following notation is used in this section:
p |
expected proportion of nonconforming items produced by the process |
|
proportion of nonconforming items in the ith subgroup |
|
number of nonconforming items in the ith subgroup |
|
number of items in the ith subgroup |
|
average proportion of nonconforming items taken across subgroups: |
N |
number of subgroups |
|
incomplete beta function: for , , and , where is the gamma function |
Each point on an chart represents the observed number () of nonconforming items in a subgroup. For example, suppose the first subgroup (see Figure 17.58) contains 12 items, of which three are nonconforming. The point plotted for the first subgroup is .
Note that a p chart displays the proportion of nonconforming items . You can use the PCHART statement to create p charts; see PCHART Statement: SHEWHART Procedure.
By default, the central line on an chart indicates an estimate for , which is computed as . If you specify a known value () for p, the central line indicates the value of . Note that the central line varies with .
You can compute the limits in the following ways:
as a specified multiple (k) of the standard error of 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 exceeds the limits
The lower and upper control limits, LCL and UCL respectively, are computed as
A lower probability limit for can be determined using the fact that
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
and solving for LCL. Similarly, the upper probability limit for can be determined using the fact that
The upper probability limit UCL is then calculated by setting
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 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 with the P0= option or with the variable _P_
in the LIMITS= data set.