<s>
Control	B-General_Concept
charts	I-General_Concept
is	O
a	O
graph	O
used	O
in	O
production	O
control	O
to	O
determine	O
whether	O
quality	O
and	O
manufacturing	O
processes	O
are	O
being	O
controlled	O
under	O
stable	O
conditions	O
.	O
</s>
<s>
Control	B-General_Concept
charts	I-General_Concept
are	O
classified	O
into	O
Shewhart	B-Application
individuals	I-Application
control	I-Application
chart	I-Application
(	O
ISO	O
7870-2	O
)	O
and	O
CUSUM(CUsUM )	O
(	O
or	O
cumulative	O
sum	O
control	B-General_Concept
chart	I-General_Concept
)	O
(	O
ISO	O
7870-4	O
)	O
.	O
</s>
<s>
Control	B-General_Concept
charts	I-General_Concept
,	O
also	O
known	O
as	O
Shewhart	B-General_Concept
charts	I-General_Concept
(	O
after	O
Walter	O
A	O
.	O
Shewhart	O
)	O
or	O
process-behavior	O
charts	O
,	O
are	O
a	O
statistical	O
process	O
control	O
tool	O
used	O
to	O
determine	O
if	O
a	O
manufacturing	O
or	O
business	O
process	O
is	O
in	O
a	O
state	O
of	O
control	O
.	O
</s>
<s>
It	O
is	O
more	O
appropriate	O
to	O
say	O
that	O
the	O
control	B-General_Concept
charts	I-General_Concept
are	O
the	O
graphical	O
device	O
for	O
Statistical	O
Process	O
Monitoring	O
(	O
SPM	O
)	O
.	O
</s>
<s>
Traditional	O
control	B-General_Concept
charts	I-General_Concept
are	O
mostly	O
designed	O
to	O
monitor	O
process	O
parameters	O
when	O
the	O
underlying	O
form	O
of	O
the	O
process	O
distributions	O
are	O
known	O
.	O
</s>
<s>
Distribution-free	B-Application
control	I-Application
charts	I-Application
are	O
becoming	O
increasingly	O
popular	O
.	O
</s>
<s>
If	O
analysis	O
of	O
the	O
control	B-General_Concept
chart	I-General_Concept
indicates	O
that	O
the	O
process	O
is	O
currently	O
under	O
control	O
(	O
i.e.	O
,	O
is	O
stable	O
,	O
with	O
variation	O
only	O
coming	O
from	O
sources	O
common	O
to	O
the	O
process	O
)	O
,	O
then	O
no	O
corrections	O
or	O
changes	O
to	O
process	O
control	O
parameters	O
are	O
needed	O
or	O
desired	O
.	O
</s>
<s>
A	O
process	O
that	O
is	O
stable	O
but	O
operating	O
outside	O
desired	O
(	O
specification	B-Application
)	O
limits	O
(	O
e.g.	O
,	O
scrap	O
rates	O
may	O
be	O
in	O
statistical	O
control	O
but	O
above	O
desired	O
limits	O
)	O
needs	O
to	O
be	O
improved	O
through	O
a	O
deliberate	O
effort	O
to	O
understand	O
the	O
causes	O
of	O
current	O
performance	O
and	O
fundamentally	O
improve	O
the	O
process	O
.	O
</s>
<s>
The	O
control	B-General_Concept
chart	I-General_Concept
is	O
one	O
of	O
the	O
seven	O
basic	O
tools	O
of	O
quality	O
control	O
.	O
</s>
<s>
Typically	O
control	B-General_Concept
charts	I-General_Concept
are	O
used	O
for	O
time-series	O
data	O
,	O
also	O
known	O
as	O
continuous	O
data	O
or	O
variable	O
data	O
.	O
</s>
<s>
The	O
control	B-General_Concept
chart	I-General_Concept
was	O
invented	O
by	O
Walter	O
A	O
.	O
Shewhart	O
working	O
for	O
Bell	O
Labs	O
in	O
the	O
1920s	O
.	O
</s>
<s>
Shewhart	O
framed	O
the	O
problem	O
in	O
terms	O
of	O
Common	O
-	O
and	O
special-causes	O
of	O
variation	O
and	O
,	O
on	O
May	O
16	O
,	O
1924	O
,	O
wrote	O
an	O
internal	O
memo	O
introducing	O
the	O
control	B-General_Concept
chart	I-General_Concept
as	O
a	O
tool	O
for	O
distinguishing	O
between	O
the	O
two	O
.	O
</s>
<s>
About	O
a	O
third	O
of	O
that	O
page	O
was	O
given	O
over	O
to	O
a	O
simple	O
diagram	O
which	O
we	O
would	O
all	O
recognize	O
today	O
as	O
a	O
schematic	O
control	B-General_Concept
chart	I-General_Concept
.	O
</s>
<s>
Shewhart	O
created	O
the	O
basis	O
for	O
the	O
control	B-General_Concept
chart	I-General_Concept
and	O
the	O
concept	O
of	O
a	O
state	O
of	O
statistical	O
control	O
by	O
carefully	O
designed	O
experiments	O
.	O
</s>
<s>
His	O
ensuing	O
involvement	O
in	O
Japanese	O
life	O
,	O
and	O
long	O
career	O
as	O
an	O
industrial	O
consultant	O
there	O
,	O
spread	O
Shewhart	O
's	O
thinking	O
,	O
and	O
the	O
use	O
of	O
the	O
control	B-General_Concept
chart	I-General_Concept
,	O
widely	O
in	O
Japanese	O
manufacturing	O
industry	O
throughout	O
the	O
1950s	O
and	O
1960s	O
.	O
</s>
<s>
Bonnie	O
Small	O
,	O
worked	O
in	O
an	O
Allentown	O
plant	O
in	O
the	O
1950s	O
after	O
the	O
transistor	B-Application
was	O
made	O
.	O
</s>
<s>
Used	O
Shewhart	O
's	O
methods	O
to	O
improve	O
plant	O
performance	O
in	O
quality	O
control	O
and	O
made	O
up	O
to	O
5000	O
control	B-General_Concept
charts	I-General_Concept
.	O
</s>
<s>
A	O
control	B-General_Concept
chart	I-General_Concept
consists	O
of	O
:	O
</s>
<s>
The	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
e.g.	O
,	O
sqrt(variance )	O
of	O
the	O
mean	O
)	O
of	O
the	O
statistic	O
is	O
calculated	O
using	O
all	O
the	O
samples	O
-	O
or	O
again	O
for	O
a	O
reference	O
period	O
against	O
which	O
change	O
can	O
be	O
assessed	O
.	O
</s>
<s>
in	O
the	O
case	O
of	O
XmR	O
charts	O
,	O
strictly	O
it	O
is	O
an	O
approximation	O
of	O
standard	B-General_Concept
deviation	I-General_Concept
,	O
the	O
does	O
not	O
make	O
the	O
assumption	O
of	O
homogeneity	O
of	O
process	O
over	O
time	O
that	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
makes	O
.	O
</s>
<s>
More	O
restrictive	O
upper	O
and	O
lower	O
warning	O
or	O
control	O
limits	O
,	O
drawn	O
as	O
separate	O
lines	O
,	O
typically	O
two	O
standard	B-General_Concept
deviations	I-General_Concept
above	O
and	O
below	O
the	O
center	O
line	O
.	O
</s>
<s>
Since	O
increased	O
variation	O
means	O
increased	O
quality	O
costs	O
,	O
a	O
control	B-General_Concept
chart	I-General_Concept
"	O
signaling	O
"	O
the	O
presence	O
of	O
a	O
special-cause	O
requires	O
immediate	O
investigation	O
.	O
</s>
<s>
The	O
control	O
limits	O
provide	O
information	O
about	O
the	O
process	O
behavior	O
and	O
have	O
no	O
intrinsic	O
relationship	O
to	O
any	O
specification	B-Application
targets	O
or	O
engineering	O
tolerance	O
.	O
</s>
<s>
Control	B-General_Concept
charts	I-General_Concept
limit	O
specification	B-Application
limits	O
or	O
targets	O
because	O
of	O
the	O
tendency	O
of	O
those	O
involved	O
with	O
the	O
process	O
(	O
e.g.	O
,	O
machine	O
operators	O
)	O
to	O
focus	O
on	O
performing	O
to	O
specification	B-Application
when	O
in	O
fact	O
the	O
least-cost	O
course	O
of	O
action	O
is	O
to	O
keep	O
process	O
variation	O
as	O
low	O
as	O
possible	O
.	O
</s>
<s>
Attempting	O
to	O
make	O
a	O
process	O
whose	O
natural	O
centre	O
is	O
not	O
the	O
same	O
as	O
the	O
target	O
perform	O
to	O
target	O
specification	B-Application
increases	O
process	O
variability	O
and	O
increases	O
costs	O
significantly	O
and	O
is	O
the	O
cause	O
of	O
much	O
inefficiency	O
in	O
operations	O
.	O
</s>
<s>
Process	O
capability	O
studies	O
do	O
examine	O
the	O
relationship	O
between	O
the	O
natural	O
process	O
limits	O
(	O
the	O
control	O
limits	O
)	O
and	O
specifications	B-Application
,	O
however	O
.	O
</s>
<s>
The	O
purpose	O
of	O
control	B-General_Concept
charts	I-General_Concept
is	O
to	O
allow	O
simple	O
detection	O
of	O
events	O
that	O
are	O
indicative	O
of	O
an	O
increase	O
in	O
process	O
variability	O
.	O
</s>
<s>
This	O
simple	O
decision	O
can	O
be	O
difficult	O
where	O
the	O
process	O
characteristic	O
is	O
continuously	O
varying	O
;	O
the	O
control	B-General_Concept
chart	I-General_Concept
provides	O
statistically	O
objective	O
criteria	O
of	O
change	O
.	O
</s>
<s>
The	O
purpose	O
in	O
adding	O
warning	O
limits	O
or	O
subdividing	O
the	O
control	B-General_Concept
chart	I-General_Concept
into	O
zones	O
is	O
to	O
provide	O
early	O
notification	O
if	O
something	O
is	O
amiss	O
.	O
</s>
<s>
The	O
coarse	O
result	O
of	O
Chebyshev	O
's	O
inequality	O
that	O
,	O
for	O
any	O
probability	O
distribution	O
,	O
the	O
probability	O
of	O
an	O
outcome	O
greater	O
than	O
k	O
standard	B-General_Concept
deviations	I-General_Concept
from	O
the	O
mean	O
is	O
at	O
most	O
1/k2	O
.	O
</s>
<s>
The	O
finer	O
result	O
of	O
the	O
Vysochanskii	O
–	O
Petunin	O
inequality	O
,	O
that	O
for	O
any	O
unimodal	O
probability	O
distribution	O
,	O
the	O
probability	O
of	O
an	O
outcome	O
greater	O
than	O
k	O
standard	B-General_Concept
deviations	I-General_Concept
from	O
the	O
mean	O
is	O
at	O
most	O
4/	O
( 9k2	O
)	O
.	O
</s>
<s>
In	O
the	O
Normal	O
distribution	O
,	O
a	O
very	O
common	O
probability	O
distribution	O
,	O
99.7	O
%	O
of	O
the	O
observations	O
occur	O
within	O
three	O
standard	B-General_Concept
deviations	I-General_Concept
of	O
the	O
mean	O
(	O
see	O
Normal	O
distribution	O
)	O
.	O
</s>
<s>
The	O
control	B-General_Concept
chart	I-General_Concept
is	O
intended	O
as	O
a	O
heuristic	B-Algorithm
.	O
</s>
<s>
Deming	O
's	O
intention	O
was	O
to	O
seek	O
insights	O
into	O
the	O
cause	O
system	O
of	O
a	O
process	O
under	O
...	O
a	O
wide	O
range	B-General_Concept
of	O
unknowable	O
circumstances	O
,	O
future	O
and	O
past	O
....	O
</s>
<s>
As	O
for	O
the	O
calculation	O
of	O
control	O
limits	O
,	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
error	O
)	O
required	O
is	O
that	O
of	O
the	O
common-cause	O
variation	O
in	O
the	O
process	O
.	O
</s>
<s>
An	O
alternative	O
method	O
is	O
to	O
use	O
the	O
relationship	O
between	O
the	O
range	B-General_Concept
of	O
a	O
sample	O
and	O
its	O
standard	B-General_Concept
deviation	I-General_Concept
derived	O
by	O
Leonard	O
H	O
.	O
C	O
.	O
Tippett	O
,	O
as	O
an	O
estimator	O
which	O
tends	O
to	O
be	O
less	O
influenced	O
by	O
the	O
extreme	O
observations	O
which	O
typify	O
special-causes	O
.	O
</s>
<s>
In	O
1935	O
,	O
the	O
British	O
Standards	O
Institution	O
,	O
under	O
the	O
influence	O
of	O
Egon	O
Pearson	O
and	O
against	O
Shewhart	O
's	O
spirit	O
,	O
adopted	O
control	B-General_Concept
charts	I-General_Concept
,	O
replacing	O
3-sigma	O
limits	O
with	O
limits	O
based	O
on	O
percentiles	O
of	O
the	O
normal	O
distribution	O
.	O
</s>
<s>
When	O
a	O
point	O
falls	O
outside	O
the	O
limits	O
established	O
for	O
a	O
given	O
control	B-General_Concept
chart	I-General_Concept
,	O
those	O
responsible	O
for	O
the	O
underlying	O
process	O
are	O
expected	O
to	O
determine	O
whether	O
a	O
special	O
cause	O
has	O
occurred	O
.	O
</s>
<s>
So	O
,	O
even	O
an	O
in	O
control	O
process	O
plotted	O
on	O
a	O
properly	O
constructed	O
control	B-General_Concept
chart	I-General_Concept
will	O
eventually	O
signal	O
the	O
possible	O
presence	O
of	O
a	O
special	O
cause	O
,	O
even	O
though	O
one	O
may	O
not	O
have	O
actually	O
occurred	O
.	O
</s>
<s>
For	O
a	O
Shewhart	O
control	B-General_Concept
chart	I-General_Concept
using	O
3-sigma	O
limits	O
,	O
this	O
false	O
alarm	O
occurs	O
on	O
average	O
once	O
every	O
1/0.0027	O
or	O
370.4	O
observations	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
in-control	O
average	O
run	O
length	O
(	O
or	O
in-control	O
ARL	O
)	O
of	O
a	O
Shewhart	B-General_Concept
chart	I-General_Concept
is	O
370.4	O
.	O
</s>
<s>
It	O
turns	O
out	O
that	O
Shewhart	B-General_Concept
charts	I-General_Concept
are	O
quite	O
good	O
at	O
detecting	O
large	O
changes	O
in	O
the	O
process	O
mean	O
or	O
variance	O
,	O
as	O
their	O
out-of-control	O
ARLs	O
are	O
fairly	O
short	O
in	O
these	O
cases	O
.	O
</s>
<s>
However	O
,	O
for	O
smaller	O
changes	O
(	O
such	O
as	O
a	O
1	O
-	O
or	O
2-sigma	O
change	O
in	O
the	O
mean	O
)	O
,	O
the	O
Shewhart	B-General_Concept
chart	I-General_Concept
does	O
not	O
detect	O
these	O
changes	O
efficiently	O
.	O
</s>
<s>
Other	O
types	O
of	O
control	B-General_Concept
charts	I-General_Concept
have	O
been	O
developed	O
,	O
such	O
as	O
the	O
EWMA	B-Application
chart	I-Application
,	O
the	O
CUSUM	O
chart	O
and	O
the	O
real-time	O
contrasts	O
chart	O
,	O
which	O
detect	O
smaller	O
changes	O
more	O
efficiently	O
by	O
making	O
use	O
of	O
information	O
from	O
observations	O
collected	O
prior	O
to	O
the	O
most	O
recent	O
data	O
point	O
.	O
</s>
<s>
Many	O
control	B-General_Concept
charts	I-General_Concept
work	O
best	O
for	O
numeric	O
data	O
with	O
Gaussian	O
assumptions	O
.	O
</s>
<s>
Several	O
authors	O
have	O
criticised	O
the	O
control	B-General_Concept
chart	I-General_Concept
on	O
the	O
grounds	O
that	O
it	O
violates	O
the	O
likelihood	O
principle	O
.	O
</s>
<s>
However	O
,	O
the	O
principle	O
is	O
itself	O
controversial	O
and	O
supporters	O
of	O
control	B-General_Concept
charts	I-General_Concept
further	O
argue	O
that	O
,	O
in	O
general	O
,	O
it	O
is	O
impossible	O
to	O
specify	O
a	O
likelihood	O
function	O
for	O
a	O
process	O
not	O
in	O
statistical	O
control	O
,	O
especially	O
where	O
knowledge	O
about	O
the	O
cause	O
system	O
of	O
the	O
process	O
is	O
weak	O
.	O
</s>
<s>
Some	O
authors	O
have	O
criticised	O
the	O
use	O
of	O
average	O
run	O
lengths	O
(	O
ARLs	O
)	O
for	O
comparing	O
control	B-General_Concept
chart	I-General_Concept
performance	O
,	O
because	O
that	O
average	O
usually	O
follows	O
a	O
geometric	O
distribution	O
,	O
which	O
has	O
high	O
variability	O
and	O
difficulties	O
.	O
</s>
<s>
Some	O
authors	O
have	O
criticized	O
that	O
most	O
control	B-General_Concept
charts	I-General_Concept
focus	O
on	O
numeric	O
data	O
.	O
</s>
<s>
†Some	O
practitioners	O
also	O
recommend	O
the	O
use	O
of	O
Individuals	B-Application
charts	I-Application
for	O
attribute	O
data	O
,	O
particularly	O
when	O
the	O
assumptions	O
of	O
either	O
binomially	O
distributed	O
data	O
(	O
p	O
-	O
and	O
np-charts	B-Application
)	O
or	O
Poisson-distributed	O
data	O
(	O
u	O
-	O
and	O
c-charts	B-Application
)	O
are	O
violated	O
.	O
</s>
<s>
First	O
,	O
normality	O
is	O
not	O
necessary	O
for	O
statistical	O
control	O
,	O
so	O
the	O
Individuals	B-Application
chart	I-Application
may	O
be	O
used	O
with	O
non-normal	O
data	O
.	O
</s>
<s>
Second	O
,	O
attribute	O
charts	O
derive	O
the	O
measure	O
of	O
dispersion	O
directly	O
from	O
the	O
mean	O
proportion	O
(	O
by	O
assuming	O
a	O
probability	O
distribution	O
)	O
,	O
while	O
Individuals	B-Application
charts	I-Application
derive	O
the	O
measure	O
of	O
dispersion	O
from	O
the	O
data	O
,	O
independent	O
of	O
the	O
mean	O
,	O
making	O
Individuals	B-Application
charts	I-Application
more	O
robust	O
than	O
attributes	O
charts	O
to	O
violations	O
of	O
the	O
assumptions	O
about	O
the	O
distribution	O
of	O
the	O
underlying	O
population	O
.	O
</s>
<s>
It	O
is	O
sometimes	O
noted	O
that	O
the	O
substitution	O
of	O
the	O
Individuals	B-Application
chart	I-Application
works	O
best	O
for	O
large	O
counts	O
,	O
when	O
the	O
binomial	O
and	O
Poisson	O
distributions	O
approximate	O
a	O
normal	O
distribution	O
.	O
</s>
<s>
when	O
the	O
number	O
of	O
trials	O
for	O
p	O
-	O
and	O
np-charts	B-Application
or	O
for	O
u	O
-	O
and	O
c-charts	B-Application
.	O
</s>
<s>
Critics	O
of	O
this	O
approach	O
argue	O
that	O
control	B-General_Concept
charts	I-General_Concept
should	O
not	O
be	O
used	O
when	O
their	O
underlying	O
assumptions	O
are	O
violated	O
,	O
such	O
as	O
when	O
process	O
data	O
is	O
neither	O
normally	O
distributed	O
nor	O
binomially	O
(	O
or	O
Poisson	O
)	O
distributed	O
.	O
</s>
<s>
Such	O
processes	O
are	O
not	O
in	O
control	O
and	O
should	O
be	O
improved	O
before	O
the	O
application	O
of	O
control	B-General_Concept
charts	I-General_Concept
.	O
</s>
<s>
Additionally	O
,	O
application	O
of	O
the	O
charts	O
in	O
the	O
presence	O
of	O
such	O
deviations	O
increases	O
the	O
type	O
I	O
and	O
type	O
II	O
error	O
rates	O
of	O
the	O
control	B-General_Concept
charts	I-General_Concept
,	O
and	O
may	O
make	O
the	O
chart	O
of	O
little	O
practical	O
use	O
.	O
</s>
