These attribute charts are used to plot the number of nonconformities per unit (rather than units nonconforming) when the sample size is constant. The control limits are:
Upper Control Limit


Lower Control Limit


Cusum Charts plot the cumulative sum of the deviations from a target value. They are useful for identifying process changes in process improvement activities:
V Masks can be used with Cusum Charts to measure the slope. The mask is placed on the last point. If points are outside the arms of the V, then a special cause is assumed.
Used when the defects can be of varying severity. A weighting system is used to classify defects, more serious defects being given a higher weight.
The value plotted on the chart is calculated from the subgroup using:
Control limits are calculated from:
Upper Control Limit


Lower Control Limit


Based on an exponentially weighted moving average. The control limits are:
Steady State 

Upper Control Limit


Lower Control Limit


Initial Readings 

Upper Control Limit 

Lower Control Limit 

L is the number of standard deviations
i is the number of periods
The 'Steady State' control limits are normally sufficient, however ten or so points are required before the smoothed average stabilizes on these values. The 'Initial Readings' limits should be used for the first few points plotted after a process change.
Exponentially Weighted Moving Average Chart 

See EWMA Charts
These are sometimes used when the process is wellestablished and the mean and standard deviation are known.
XBar Chart 

Upper Control Limit


Lower Control Limit


R Chart 

Upper Control Limit 

Lower Control Limit 

Note that this should not be used to impose desired mean and standard deviation values.
ImR (Individual & Moving Range) Charts 

Individual & Moving Range Charts, also called XmR Charts. See XmR Charts
Not generally recommended, but save calculation as long as the subgroup size is an odd number:
Upper Control Limit


Lower Control Limit

:

Where the factors are:
n

2

3

4

5

6


1.88

1.19

0.80

0.69

0.55

It is not usual to use range charts with median charts, because it defeats the purpose of simple calculation. All the data values from the subgroup may be plotted on the chart to indicate the spread:
Moving Average Control Charts 

Moving Average charts plot a running average of the last 'w' periods. The control limits are:
Upper Control Limit


Lower Control Limit


These are attribute type charts used to plot units nonconforming when samples of equal size are taken from the process. The control limits are:
Upper Control Limit


Lower Control Limit


These are attribute type charts used to plot units nonconforming when the samples are not of equal size. This is often when samples form a natural grouping  for example the number of treatments in a hospital in a week.
Upper Control Limit


Lower Control Limit


Note that the control limits are dynamic, they depend on the size of the sample.
The problem with using Cusum charts for continuous monitoring is that slight deviations between the target and actual process average will cause a drift. Tabular cusum charts provide a 'slack' or tolerance band around the target. Excursions within this band will not be recorded. The band is often 1 standard deviation wide:
These attribute charts are used to plot the number of nonconformities per unit (rather than units nonconforming) when the sample size varies. The control limits are:
Upper Control Limit


Lower Control Limit


Note that the control limits are dynamic, they depend on the size of the sample.
See Demerits per Unit Charts
These variable charts, used as a pair, plot the mean and range of subgroups taken from the process. See 'Rational Subgroups' for guidance on how to select subgroups.
The control limits are calculated from:
XBar Charts


Upper Control Limit


Lower Control Limit


R Charts


Upper Control Limit 

Lower Control Limit 

The factors are taken from standard tables.
These variable charts, used as a pair are more efficient than XBar and R Charts, particularly for larger sample sizes:
XBar Chart


Upper Control Limit


Lower Control Limit


S Chart 

Upper Control Limit 

Lower Control Limit 

Individual and Moving Range Charts. Used when the subgroup size is one. This may be when logistic reasons prevent larger subgroups, but is more commonly when there is no basis for rational subgroups.
The chart is based on the moving range between consecutive samples:
X (Individual) Chart 

Upper Control Limit


Lower Control Limit


Moving Range Chart


Upper Control Limit


Lower Control Limit


D_{4} and d_{2} are taken from tables of standard factors, based on a subgroup size of 2:
