Data points on a P chart follow the binomial distribution.
Term | Description |
---|---|
xi | number of defectives for subgroup i |
ni | size of subgroup i |
Term | Description |
---|---|
![]() | number of defectives in subgroup ![]() |
![]() | size of subgroup ![]() |
Each subgroup proportion is converted to a z-score (
):
Next, a moving range of length 2 is used to evaluate the variation in the z-scores and calculate Sigma Z ():
where 1.128 is an unbiasing constant.
Term | Description |
---|---|
![]() | proportion of defectives for subgroup ![]() |
![]() | process proportion |
![]() | size of subgroup ![]() |
![]() | moving range of length 2 |
The LCL for each subgroup is equal to the greater of the following:
or
The UCL for each subgroup is equal to the lesser of the following:
or
Term | Description |
---|---|
![]() | process proportion |
![]() | parameter for Test 1. The default is 3. (For more information, go to Select tests for special causes for Laney P' Chart.) |
![]() | size of subgroup ![]() |
![]() | see "Sigma Z" |