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, p_i:

Data points on a P chart follow the binomial distribution.

Term	Description
x_i	number of defectives for subgroup i
n_i	size of subgroup i

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

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:

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

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"