Methods and formulas for Laney U' Chart

Select the method or formula of your choice.

Plotted points

The plotted points represent the defect rate for each subgroup, :

Data points on a U chart follow the Poisson distribution.

Notation

TermDescription
number of defects for subgroup
size of subgroup

Center line

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

Notation

TermDescription
number of defects in subgroup
size of subgroup

Sigma Z

Each subgroup rate 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
defect rate for subgroup
process mean
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)

Notation

TermDescription
process mean
parameter for Test 1. The default is 3. (For more information go to Select tests for special causes for Laney U' Chart.)
size of subgroup
see "Sigma Z"
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