Methods and formulas for P Chart Diagnostic

Adjusted counts

Minitab calculates the adjusted defective counts (a_i) as follows:

Transformed counts

The adjusted counts are then transformed using the following formula:

Then Minitab creates a standard normal probability plot of the transformed counts using the method specified in File > Options > Individual Graphs > Probability Plots.

Notation

Term	Description
di	count of defectives for subgroup i
ni	size of subgroup i
	average subgroup size

Expected variation

The expected variation is equal to the standard deviation of the transformed counts (X_i), which is equal to .

Observed variation

To calculate the observed variation, Minitab calculates normal scores (Y,) for the transformed counts as follows:

where NSCOR is the Normal scores function (available by choosing Calc > Calculator).

For the next step, only the middle 50% of the X_i values are used, along with their corresponding Y_i values. X_i values are excluded if they are less than the 25^th percentile or greater than the 75^th percentile.

Minitab fits a least squares regression model with Y_i as the response and X_i as the predictor:

The observed variation is then 1 / β₁.

Ratio

The ratio of observed variation to expected variation is calculated as follows:

Notation

Term	Description
Xi	transformed counts (For more information, see the section "Plotted points".)
	average subgroup size
β0	intercept from the least squares regression equation
β1	slope coefficient from the least squares regression equation

upper confidence limit

The upper confidence limit for the ratio is calculated as follows:

where is the mean proportion of defectives, calculated as follows:

lower confidence limit

For the lower confidence limit for the ratio, Minitab uses a conservative, fixed value of 60%.

Notation

Term	Description
m	number of subgroups
	average subgroup size
di	count of defectives for subgroup i
ni	size of subgroup i