Shewhart control charts
controlchart(X)
controlchart(x,group)
controlchart(X,group)
[stats,plotdata] = controlchart(x,[group])
controlchart(x,group,'name
',value
)
controlchart(X)
produces an xbar chart
of the measurements in matrix X
. Each row of X
is
considered to be a subgroup of measurements containing replicate observations
taken at the same time. The rows should be in time order. If X
is
a time series object, the time samples should contain replicate observations.
The chart plots the means of the subgroups in time order, a
center line (CL
) at the average of the means, and
upper and lower control limits (UCL
, LCL
)
at three standard errors from the center line. The standard error
is the estimated process standard deviation divided by the square
root of the subgroup size. Process standard deviation is estimated
from the average of the subgroup standard deviations. Out of control
measurements are marked as violations and drawn with a red circle.
Data cursor mode is enabled, so clicking any data point displays information
about that point.
controlchart(x,group)
accepts a grouping variable
group
for a vector of measurements x
.
group
is a categorical variable, numeric vector, character vector, string
array, or cell array of character vectors the same length as x
. Consecutive
measurements x(n)
sharing the same value of group(n)
for 1
≤ n
≤ length(x)
are defined to be a subgroup. Subgroups can
have different numbers of observations.
controlchart(X,group)
accepts
a grouping variable group
for
a matrix of measurements in X
. In this case, group
is
only used to label the time axis; it does not change the default grouping
by rows.
[stats,plotdata] = controlchart(x,[group])
returns
a structure stats
of subgroup statistics and parameter
estimates, and a structure plotdata
of plotted
values. plotdata
contains one record for each chart.
The fields in stats
and plotdata
depend
on the chart type.
The fields in stats
are selected from the
following:
mean
— Subgroup means
std
— Subgroup standard
deviations
range
— Subgroup ranges
n
— Subgroup size, or total
inspection size or area
i
— Individual data values
ma
— Moving averages
mr
— Moving ranges
count
— Count of defects
or defective items
mu
— Estimated process mean
sigma
— Estimated process
standard deviation
p
— Estimated proportion
defective
m
— Estimated mean defects
per unit
The fields in plotdata
are the following:
pts
— Plotted point values
cl
— Center line
lcl
— Lower control limit
ucl
— Upper control limit
se
— Standard error of plotted
point
n
— Subgroup size
ooc
— Logical that is true
for points that are out of control
controlchart(x,group,'
specifies
one or more of the following optional parameter name/value pairs,
with name
',value
)name
in single quotes:
charttype
— The name of
a chart type chosen from among the following:
'xbar'
— X
bar
or mean
's'
— Standard deviation
'r'
— Range
'ewma'
— Exponentially weighted
moving average
'i'
— Individual observation
'mr'
— Moving range of individual
observations
'ma'
— Moving average of
individual observations
'p'
— Proportion defective
'np'
— Number of defectives
'u'
— Defects per unit
'c'
— Count of defects
Alternatively, a parameter can be a string array or cell array listing multiple compatible chart types. There are four sets of compatible types:
'xbar'
, 's'
, 'r'
,
and 'ewma'
'i'
, 'mr'
, and 'ma'
'p'
and 'np'
'u'
and 'c'
display
— Either 'on'
(default)
to display the control chart, or 'off'
to omit
the display
label
— A character vector, string array, or cell array of
character vectors, one per subgroup. This label is displayed as part of the data cursor for a
point on the plot.
lambda
— A parameter between
0 and 1 controlling how much the current prediction is influenced
by past observations in an EWMA plot. Higher values of 'lambda'
give
less weight to past observations and more weight to the current observation.
The default is 0.4.
limits
— A three-element vector specifying the values of the
lower control limit, center line, and upper control limits. Default is to estimate the center
line and to compute control limits based on the estimated value of sigma. Not permitted if
there are multiple chart types.
mean
— Value for the process
mean, or an empty value (default) to estimate the mean from X
.
This is the p
parameter for p
and np
charts,
the mean defects per unit for u
and c
charts,
and the normal mu
parameter for other charts.
nsigma
— The number of sigma
multiples from the center line to a control limit. Default is 3.
parent
— The handle of the
axes to receive the control chart plot. Default is to create axes
in a new figure. Not permitted if there are multiple chart types.
rules
— The name of a control rule, or a string array or cell
array containing multiple control rule names. These rules, together with the control limits,
determine if a point is marked as out of control. The default is to apply no control rules, and
to use only the control limits to decide if a point is out of control. See controlrules
for more information. Control rules are applied to charts that
measure the process level (xbar
, i
, c
,
u
, p
, and np
) rather than the
variability (r
, s
), and they are not applied to charts
based on moving statistics (ma
, mr
,
ewma
).
sigma
— Either a value for
sigma, or a method of estimating sigma chosen from among 'std'
(the
default) to use the average within-subgroup standard deviation, 'range'
to
use the average subgroup range, and 'variance'
to
use the square root of the pooled variance. When creating i
, mr
,
or ma
charts for data not in subgroups, the estimate
is always based on a moving range.
specs
— A vector specifying
specification limits. Typically this is a two-element vector of lower
and upper specification limits. Since specification limits typically
apply to individual measurements, this parameter is primarily suitable
for i
charts. These limits are not plotted on r
, s
,
or mr
charts.
unit
— The total number
of inspected items for p
and np
charts,
and the size of the inspected unit for u
and c
charts.
In both cases X
must be the count of the number
of defects or defectives found. Default is 1 for u
and c
charts.
This argument is required (no default) for p
and np
charts.
width
— The width of the
window used for computing the moving ranges and averages in mr
and ma
charts,
and for computing the sigma estimate in i
, mr
,
and ma
charts. Default is 5.