I chart

Select the method or formula of your choice.

In This Topic

Plotted points
Center line
Control limits

Plotted points

Each data point, x_i, is an observation.

Center line

The center line represents the process mean, μ. If you do not specify a historical value for the process mean, Minitab uses the mean of the observations.

Control limits

If you do not specify a historical value for the process standard deviation, σ, then Minitab estimates σ from your data using the specified method.

Lower control limit (LCL)

Upper control limit (UCL)

Notation

Term	Description
μ	process mean
k	parameter for Test 1. The default is 3.

Extended control limits: Between/within approach

Use the between/within approach to calculate extended control limits from within-subgroup and between-subgroup standard variation.

Subgroup size = 1

Where u_I and u_O are quantiles of the standardized normal distribution.

For the expected mean square, calculate σ̂_O as follows:

Notation for between/within approach

Term	Description
μ̂	estimate of process mean
σ̂_I	estimate of within-subgroup standard deviation
σ̂_O	estimate of between-subgroup standard deviation. If there is only 1 subgroup, then σ̂_O = 0.
n	length of the moving range when the subgroup size is 1
α_I	false alarm probability for within-subgroup standard deviation
Φ^-1	the inverse cumulative distribution function of the standard normal distribution
α_O	false alarm probability for between-subgroup standard deviation
MS_S	the mean square associated with subgroup-to-subgroup variation
MSE	mean squared error. The within-subgroup mean square subtracted from the subgroup mean square before estimating the between-subgroup standard deviation component.
C	coefficient for the expected mean square for subgroups as a random factor. For the calculations of expected mean squares and for information on unbalanced or more complex models, see Montgomery¹ and Neter². D.C. Montgomery (1991). Design and Analysis of Experiments, Third Edition. John Wiley & Sons. J. Neter, W. Wasserman and M.H. Kutner (1985). Applied Linear Statistical Models, Second Edition. Irwin, Inc.

Extended control limits: Min/max mean approach

Use the min/max mean approach to calculate extended control limits from the minimum and maximum group means.

Subgroup size = 1

Where u_I is the quantile of the standardized normal distribution.

For the m largest subgroup means:

For the m smallest subgroup means:

Notation for min/max approach

Term	Description
μ̂	estimate of process mean
μ̂_max	estimate of the maximum process mean. Using the length of the moving range as the subgroup size, this estimate is the weighted average of the `m` largest subgroup means. If the analysis specifies to use more subgroups than are in the data, `m` is the number of subgroups.
μ̂_min	estimate of the minimum process mean. Using the length of the moving range as the subgroup size, this estimate is the weighted average of the `m` smallest subgroup means. If the analysis specifies to use more subgroups than are in the data, `m` is the number of subgroups.
m	number of subgroup means to average
σ̂_I	estimate of within-subgroup standard deviation
n	length of the moving range when the subgroup size is 1
Φ^-1	the inverse cumulative distribution function of the standard normal distribution
α_I	false alarm probability for within-subgroup standard deviation

Standard deviation for extended limits

When extended limits are selected, use the following standard deviation for stored variation values and additional sigma limits.