Methods and formulas for Laney P' Chart

Select the method or formula of your choice.

Plotted points

Each plotted point represents the proportion of defectives for one subgroup, pi:

Data points on a P chart follow the binomial distribution.

Notation

TermDescription
xinumber of defectives for subgroup i
nisize of subgroup i

Center line

The center line represents the proportion of defectives for your process, . If you do not specify a historical value, then Minitab uses the average proportion of defectives from your data, , to estimate .

Notation

TermDescription
number of defectives in subgroup
size of subgroup

Sigma Z

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.

Notation

TermDescription
proportion of defectives for subgroup
process proportion
size of subgroup
moving range of length 2

Control limits

Lower control limit (LCL)

The LCL for each subgroup is equal to the greater of the following:

or

Upper control limit (UCL)

The UCL for each subgroup is equal to the lesser of the following:

or

Notation

TermDescription
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"
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