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 |
|
Control charts are used to monitor the
output of a process. They are used to give
timely warning of 'special causes' entering
the process. They generally monitor either
the process mean, the process variation
or a combination of both.
Control charts can be divided into two
types; control charts for attributes and
control charts for variables. Control charts
for variables monitor characteristics that
are measured on a continuous
scale, size, weight etc. The
main use of control charts for attributes
is to monitor characteristics that are classified
as either 'pass' or 'fail'.
The best known type of control chart is
the X-bar & R
chart. This is widely used
in high volume production, particularly
in the automotive industry. However other
types of charts, for example the cusum
chart, are often more effective
on process improvement and six
sigma. X-bar & R charts
are usually used with Process
Capability Studies.
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 well-established and the mean and standard
deviation are known.
| X-Bar 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:
| X-Bar
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 X-Bar and R Charts,
particularly for larger sample sizes:
| X-Bar 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 |
|
D4 and d2 are taken
from tables of standard factors, based on
a subgroup size of 2:
|
