Hello.
My
name
is
Laura
Lancaster.
I
am
a
statistical
developer
in
the
JMP
group.
Today,
I'm
here
to
talk
to
you
about
dissolved
combinations
and
operating
region
optimization
for
critical
quality
attributes
with
the
JMP
17
profiler.
Everything
we're
going
to
talk
about
today
has
to
do
with
the
Prediction Profiler,
and
I
hope
that
everyone
is
familiar
with
it.
It's
a
wonderful
tool.
But
if
you're
not,
the
Prediction Profiler
is
a
tool
in
JMP
that's
great
for
interactively
exploring,
visualizing,
and
optimizing
the
models
that
you
create
in
JMP.
Specifically,
we're
going
to
talk
about
two
recent
new
features
that
were
added
to
the
Prediction Profiler.
The
first
is
the
ability
to
explore
and
optimize
the
models
that
you've
created
in
DOE
in JMP
that
have
known
disallowed
combination
strength.
The
second
is
the
ability
to
determine
an
optimal
operating
region
for
your
manufacturing
processes
that
ensure
both
quality
and
maximum
production
flexibility.
Let's
go
ahead
and
get
started
talking
about
exploring
and
optimizing
models
from
designed
experiments
with
this
all
combination
constraints.
I
t
often
happens
that
when
you're
designing
experiments,
it's
not
possible
or
it's
not
desirable
for
various
reasons
to
be
able
to
experiment
over
the
usual
entire
rectangular
design
region.
When
that
happens,
you
need
to
be
able
to
apply
constraints
to
your
design
region
before
you
create
the
design
and
certainly
before
you
run
the
design.
Thankfully,
ever
since
JMP
6,
which
has
been
a
long
time,
the
custom
design
platform
has
been
able
to
create
design
experiments
with
constrained
design
regions.
Since
then,
constraint
support
has
also
been
added
to
fast,
flexible
filling
designs
and
covering
array
designs.
Now,
what
types
of
constraints
are
available
in
JMP's
DOE platforms?
The
first
type
of
constraint
is
the
simpler
of
the
two.
It's
linear
constraints
on
continuous
and
mixture
factors.
H
ere's
a
picture
where
we
have
two
linear
inequality
constraints
that
are
shown
in
the
gray
shaded
region.
Then
the
design,
you
can
see
stays
out
of
the
disallowed
linear
constrained
region.
The
next
type
of
constraint
is
called
a
disallowed
combination
constraint.
It's
a
more
general
and
can
be
more
complicated
type
of
constraint.
It
can
consist
of
continuous,
discrete,
numeric
and
or
categorical
factors.
What
it
is
is
a
constraint
that's
a
JSL
Boolean
expression
that
evaluates
to
true
for
factor
combinations
that
are
not
in
your
design
region.
Here's
an
example.
We
have
a
two-
factor
design
where
X1 L1
and
X2 L3
cannot
be
in
the
design.
They're
disallowed
and
they're
written
as
a
JSL
Boolean
expression,
which
you
can
see
right
here.
N
otice
that
this
design
is
created
and
stays
out
of
this
disallowed
region.
Now,
originally,
all
of
these
disallowed
combination
constraints
had
to
be
entered
as
JSL
like
this.
But
then
in
JMP
12,
a
disallowed
combination
filter
was
added
that
made
it
easier
to
create
these
JSL
expressions
if
you
have
fairly
easy
disallowed
combinations
such
as
individual
factor
ranges
combined
with
and/
or
expressions.
We'll
look
at
an
example
of
this
shortly.
Now,
what
about
the
Prediction Profiler
with
constrained
regions?
Why
is
it
important
for
the
Prediction Profiler
to
be
able
to
obey
constraints
when
you
have
models
with
constraints?
Well,
if
the
profiler
ignores
constraints,
then
it's
possible
that
the
user
could
navigate
to
predictions
that
are
not
feasible
and
they
may
not
realize
it.
So
you
could
end
up
in
an
area
that's
not
possible,
not
desirable,
and
you
certainly
haven't
tested
there.
It's
an
extrapolation,
so
this
is
bad.
Then
probably
even
worse,
if
you
want
to
optimize
your
model,
you
could
end
up
with
an
infeasible
optimal
solution.
If
that
happens,
the
user
would
have
to
either
try
to
manually
find
a
feasible
optimal
solution,
which
could
be
really
hard
or
even
impossible,
or
they
would
have
to
use
another
tool.
What
were
the
challenges
with
getting
the
Prediction Profiler
to
obey
constraints?
Why
did
it
take
so
much
longer
to
get
these
constraints
in
the
profiler
versus
DOE?
Well,
the
main
reason
had
to
do
with
the
constrained
optimization.
The
desirability
function
is
a
nonlinear
function.
That
means
that
our
optimization
has
a
nonlinear
objective
function
and
possibly
both
continuous
and
categorical
factor
variables
that
could
be
involved
in
constraints.
This
is
known
as
a
mixed
integer
nonlinear
programming
problem,
and
it's
an
extremely
difficult
type
of
optimization
problem
unless
you
know
something
favorable
about
your
objective
function
or
your
constrained
region.
It's
just
very, very
hard.
But
good
news,
the
Prediction Profiler
now
works
with
all
the
same
constraints
as
the
DOE platforms.
Turns
out
that
the
Prediction Profiler
has
actually
obeyed
linear
constraints
on
continuous
variables
all
the
way
back
to
JMP
8,
j
ust
a
couple
of
releases
after
they
were
added
in
JMP
6.
We
were
able
to
do
this
sooner
because
these
constraints,
these
linear
constraints
on
continuous
variables
have
really
nice
properties.
B
ecause
of
that,
we
were
able
to
implement
a
wolf-
reduced
gradient
variant
algorithm.
That
algorithm
does
a
really,
really
good
job
of
finding
the
global
optimum,
especially
if
you
don't
have
categorical
variables.
In
that
case,
you
should
find
the
global
optimum.
Now,
since
JMP
16,
the
Prediction Profiler
now
also
obeys
disallowed
combination
constraints
on
both
continuous
and
categorical
variables.
Now,
this
was
a
lot
harder
because
these
constraints
are
very
general.
You
could
put
absolutely
anything
inside
that
JSL Boolean
expression.
So
we
cannot
assume
anything
favorable
about
our
constrained
region
in
these
cases.
Thus,
we
had
to
implement
a
genetic
heuristic
algorithm,
which
is
a
very
general
type
of
algorithm
for
the
constrained
optimization.
B
ecause
of
this,
we
can't
guarantee
a
global
optimum
solution.
But
you
should
find
a
solution
that's
very
close
to
global
optimum,
if
not
the
global
optimum.
Let's
go
ahead
and
start
looking
at
some
examples.
First,
we're
going
to
look
at
a
chemical
reaction
experiment.
This
experiment
has
one
response,
and
the
goal
is
to
maximize
yield.
We
have
three
factors.
Two
of
them
are
continuous,
time
and
temperature,
and
catalyst
is
categorical.
We
have
two
constraints.
When
catalyst
B
is
used,
temperature
must
be
above
400.
When
catalyst
C
is
used,
temperature
must
be
below
650.
W
e
used
Custom
DOE to
create
a
response
surface
design
with
dis
allowed combinations.
Because
these
are
fairly
simple
constraints,
we
were
able
to
use
the
disallowed
combinations
filter.
You
can
see
here
that
when
I
set
catalyst
to
B,
temperature
cannot
be
below
400.
This
is
my
first
disallowed
region.
Also
if
catalyst
is
C,
the
temperature
cannot
be
above
650.
Then
once
we
created
the
design,
you
can
see
that
the
design
points
stay
out
of
the
constrained
regions
that
are
gray
here.
These
are
the
dissolved
combinations
regions.
Then
we
ran
the
experiment
and
we
used
Fit Least
Squares
to
fit
a
response
surface
model
to
the
data.
Now,
I
want
to
show
you
how
you
would
use
the
Prediction Profiler
to
explore
the
model
and
find
the
maximum
yield.
I'm
going
to
go
get
out
of
PowerPoint
and
go
to
JMP
really
quickly.
Here
is
the
data
table
from
the
chemical
reaction
experiment
that
we
created
with
JMPs
custom
design
platform.
We've
already
run
it
and
entered
all
the
results.
The
important
thing
I
want
to
point
out
is
that
Custom
DOE added
this
data
table
script
called
Disallowed
Combinations.
When
you
open
it
up,
you
see
it's
got
the
JSL
Boolean
expression
of
my
disallowed
combinations.
And
this
is
what
the
Prediction Profiler
reads
in,
and
that's
how
it
knows
about
my
disallowed
combinations
constraints.
I've
already
saved
my
response
surface
model,
and
I'm
going
to
run
it
and
go
down
to
the
profiler.
Because
I
have
that
disallowed
combinations
constraint
saved
in
the
table,
it's
able
to
read
those
in
and
the
profiler
can
obey
the
constraints. I
f
I
set
catalyst
to
B,
notice
that
I
cannot
get
to
a
temperature
400
or
below.
If
I
set
catalyst
to
C,
I
cannot
get
to
a
temperature
650
or
above
because
those
are
disallowed
regions.
Also,
when
I
maximize
yield,
I
end
up
with
a
solution
that
is
feasible,
it's
not
in
a
disallowed
region.
Now,
what
would
have
happened
in
a
version
of
JMP
prior
to
JMP
16?
Well,
we
can
see
what
would
have
happened
by
looking
at
the
exact
same
data
table
without
the
disallowed
combination
script.
I'm
going
to
run
the
same
exact
model
and
go
to
the
profiler.
Now
this
time,
the
profiler
doesn't
know
about
my
constraints.
So
when
I
set
catalyst
to
B,
I
can
go
down
into
a
disallowed
region
down
to
350.
Catalyst
C,
I
can
wander
up
into
another
disallowed
region,
temperatures
above
650.
W
hen
I
do
the
optimization,
I
do
end
up
with
an
infeasible
solution.
I'm
in
the
disallowed
region
where
catalyst
is
C
and
temperature
is
750.
I
would
be
forced
to
have
to
try
to
manually
find
a
feasible
solution
that's
not
in
a
disallowed
region.
But
thankfully,
that's
been
solved
since
JMP
16.
Let's
go
clean
up
and
let's
go
to
another
example.
Okay,
the
next
example
we're
going
to
look
at
is
a
tablet
production
experiment.
The
goal
of
this
experiment
is
to
maximize
dissolution.
We
have
five
factors.
Four
are
continuous
and
one
is
categorical.
We
have
two
constraints.
The
first
constraint
is
that
when
screen
size
is
3,
mill time
has
to
be
below
16,
and
my
spray
rate
and
coating
viscosity
follow
this
nonlinear
constraint.
I
used
Custom
DOE next
to
create
a
response
surface
design
with
disallowed
combinations
using
these
two
constraints.
Because
this
is
a
complicated
constraint,
we
could
not
use
the
disallowed
combinations
filter,
so
we
had
to
enter
it
as
a
script,
which
is
not
hard
to
do.
Here's
where
I've
entered
that
nonlinear
constraint
as
a
script.
Notice
I've
flipped
the
inequality
to
show
what's
disallowed
instead
of
what
should
be
allowed. T
hen
I've
also
added
screen
size
equals
3 and
mill
time
greater
than
16
as
the
other
disallowed
region.
Now,
we
can
see
by
looking
at
two
different
slices
of
my
design.
This
first
graph
is
spray
rate
versus
coating
viscosity.
I
can
see
that
all
the
design
points
stay
out
of
the
disallowed
region
set
by
this
nonlinear
constraint.
W
hen
I
look
at
screen
size
versus
mill
time,
when
screen
size
is
3,
m
ill time
cannot
be
above
16.
Then
we
ran
the
experiment,
and
we
used
Fit Least Squares
to
fit
a
response
surface
model
to
the
data.
N
ow
we're
going
to
use
Prediction Profiler
to
explore
the
model
and
find
the
maximum
dissolution.
I'm
going
to
go
back
to
JMP.
This
is
the
tablet
production
experiment
that
was
produced
by
JMP's
Custom
DOE platform.
N
otice
that
once
again,
it
has
saved
the
disallowed
combinations
data
table
script
to
the
table.
I'm
going
to
look
at
that.
You
see
that
it's
the
JSL
Boolean
expression
of
my
dis
allowed combinations,
and
this
is
what
the
profiler
will
read
in.
I've
saved
the
response
surface
model
to
the
table.
When
we
go
to
the
profiler
to
explore
the
model,
you
can
see
that
it
obeys
my
disallowed combinations
constraint.
When
screen
size
is
3,
mill time cannot
be
above
16.
Also,
spray
rate
and
coating
viscosity
obey
that
nonlinear
inequality
constraint.
When
I
maximize
the
solution,
I
end
up
with
an
optimal
solution
that's
feasible
and
notice
that
it's
actually
on
the
constraint
boundary.
T
hat
tells
me
that
if
I
had
not
been
recognizing
the
constraints,
I
almost
certainly
would
have
ended
up
with
an
optimal
solution
that
wasn't
feasible,
and
I
would
have
had
to
try
to
manually
find
it,
which
would
have
been
very
difficult,
if
not
impossible.
All
right
.
Let's
move
on
to
the
next
topic.
Here
we
go.
Back
to
PowerPoint.
Okay
.
Our
next
topic
is
operating
region
optimization
for
critical
quality
attributes.
This
is
where
I'm
going
to
introduce
the
new
Design Space Profiler
that's
new
to
JMP
17.
What
do
we
mean
by
design
space
when
we're
talking
about
the
Design Space Profiler?
Well,
this
is
an
important
concept
that's
used
in
pharmaceutical
development
that
identifies
the
optimal
operating
region
that
gives
maximal
flexibility
of
your
production
while
still
assuring
quality.
This
concept
was
introduced
by
the
FDA
and
the
International
Conference
on
Harmonization
when
those
agencies
decided
to
adopt
Quality
by
Design
principles
for
development,
manufacturing,
and
regulation
of
drugs.
W
hen
they
did
that,
they
put
out
some
really
important
guideline
documents,
ICH Q8-Q12,
that
most
drug
companies
follow.
Specifically,
we
want
to
look
at
ICH Q8 (
R2)
,
which
covers
design
space.
It
defines
design
space
as
the
multidimensional
combination
and
interaction
of
material
attributes
and
process
parameters
that
have
been
demonstrated
to
provide
assurance
of
quality.
Now,
there
are
a
number
of
steps
that
need
to
be
taken
to
determine
design
space
for
a
product,
and
several
of
them
need
to
be
done
before
you
can
get
to
the
Design Space Profiler
and
JMP.
One
of
the
first
things
that
you
need
to
do
is
you
need
to
determine
what
your
critical
quality
attributes
are
and
what
the
appropriate
spec
limits
are
to
maintain
quality.
We'll
refer
to
these
critical
quality
attributes
as
CQAS.
The
ICH document
defines
a
critical
quality
attribute
as
a
physical,
chemical,
biological,
or
microbiological
property
or
characteristic
that
should
be
within
an
appropriate
limit,
range,
or
distribution
to
ensure
the
desired
product
quality.
This
is
the
important
first
step.
Next,
we
want
to
use
designed
experiments
to
determine
what
are
our
critical
manufacturing
process
parameters
that
affect
those
critical
quality
attributes.
We'll
refer
to
these
as
CPPs,
critical
process
parameter,
because
ICH Q8
defines
a
critical
process
parameter
as
a
process
parameter
whose
variability
has
an
impact
on
a
critical
quality
attribute
and
therefore
should
be
monitored
or
controlled
to
ensure
the
process
produces
the
desired
quality.
Then,
once
you've
determined
your
CQAs
and
your
CPPs,
then
you
want
to
find
a
really
good
prediction
model
for
your
CQAs
in
terms
of
your
critical
process
parameters.
Once
you've
done
all
of
that,
you
can
use
the
Design Space Profiler
to
determine
a
good
design
space
for
your
product.
Let's
talk
a
little
more
specifically
about
the
Design Space Profiler
and
JMP.
The
goal
of
the
Design Space Profiler
is
to
determine
a
good
design
space
by
trying
to
find
the
largest
hyper
rectangle
that
fits
into
the
acceptable
region
that's
defined
by
your
critical
quality
attribute
specifications
applied
to
that
prediction
model
that
you
found.
Once
you
found
that
hyper
rectangle,
it
will
give
the
lower
and
upper
limits
of
your
critical
process
parameters
that
determine
a
good
design
space.
The
problem
is
that
that
acceptable
region
is
usually
non
linear,
and
finding
the
largest
hyper
rectangle
in
a
non
linear
region
is
a
very, very
difficult
mathematical
problem.
Because
of
that,
we
wonder
how
does
the
Design Space Profiler
actually
determine
Design
Space
then?
Well,
instead
of
trying
to
find
the
largest
hyper
rectangle
mathematically,
we
use
a
simulated
approach.
What
it
does
is
it
generates
thousands
of
uniformly
distributed
points
throughout
the
space
defined
by
your
initial
CPP
limits.
Then
it
uses
that
prediction
model
that
you
found
to
simulate
responses
for
your
CQAs.
Note,
because
your
prediction
model
is
not
without
error,
you
should
always
add
response
error
to
your
simulations.
Once
you've
got
your
simulated
set,
it
calculates
an
in-spec
portion,
accounting
the
total
number
of
points
in
that
set
that
are
in-spec
for
all
your
CQAs
from
all
the
points
that
are
within
the
current
CPP
factor
limits.
This
is
easiest
to
see
by
actually
looking
at
an
example
and
going
to
JMP
and
looking
at
the
Design Space Profiler.
That's
what
we're
going
to
do
next.
We're
going
to
look
at
an
example
of
a
pain
cream
study.
The
goal
of
this
study
was
to
repurpose
a
habit-
forming
oral
opioid
drug
into
a
cream
that
provides
the
same
relief
as
the
oral
drug.
T
he
first
thing
that
we
needed
to
do
was
determine
our
critical
quality
attributes
for
this
drug.
We
determined
that
there
were
three
of
them
entrapment
efficiency,
vesicle
size,
and
in-
vitro
release.
We
also
needed
to
determine
what
are
the
spec
limits
that
assure
quality.
That's
what
these
numbers
are.
Next,
we
ran
experiments
to
determine
which
of
our
manufacturing
process
factors
affect
these
critical
quality
attributes.
It
turns
out
there
were
three
of
them.
They
are
emulsifier,
lipid,
and
lecithin,
and
these
are
the
initial
factor
limits
for
these
CPPs.
Next,
we
used
custom
design
and
Fit Least Squares
to
find
response
surface
models
for
our
three
critical
quality
attributes
in
terms
of
our
three
critical
process
parameters.
Once
we
did
all
of
that,
now
we're
able
to
go
to
the
Design Space Profiler
and
JMP
to
determine
a
design
space
for
this
pain
cream.
Let's
go
back
to
JMP.
I'm
going
to
open
up
my
pain
cream
study.
T
his
was
my
response
surface
model
design
created
in
JMP's
DOE platform.
I've
got
my
design
in
terms
of
my
three
critical
process
parameters
here,
and
these
are
my
three
critical
quality
attribute
responses
here.
The
important
thing
I
want
to
point
out
is
that
for
each
of
these
critical
quality
attribute
responses,
I've
saved
spec
limits
as
column
properties.
T
hat
is
because
the
Design Space Profiler
has
to
know
what
the
spec
limits
are
for
your
critical
quality
attributes.
So
if
you
don't
enter
them
as
column
properties,
you'll
be
prompted
to
enter
them
once
you
launch
the
Design Space Profiler,
unless
you've
added
them
here.
I've
already
saved
my
response
surface
models
as
a
script.
I'm
going
to
run
that
script.
It
launches
Fit Least Squares,
and
I
have
it
set
up
to
automatically
show
the
Prediction Profiler.
This
is
the
same
Prediction Profiler
that
you're
probably
used
to
seeing.
I
have
my
three
responses,
my
critical
quality
attributes
here,
my
three
critical
process
parameters,
my
factors
here,
and
I
can
explore
the
model
as
usual.
But
now
I
want
to
try
to
figure
out
a
design
space
for
my
manufacturing
process.
Now
I
can
easily
do
that
by
going
to
the
production
profiler,
little
red
triangle
menu,
and
several
down.
I
see
there's
a
new
option
for
Design Space Profiler,
and
if
I
select
that
right
below
the
Prediction Profiler,
the
Design Space Profiler
will
appear.
As
I
noted,
if
I
hadn't
already
had
spec
limits
attached
to
my
responses,
it
would
prompt
me
for
that.
But
now
I
can
see
that
it's
brought
them
in
from
my
column
properties.
You
can
see
right
down
here.
It's
also
brought
in
an
error
standard
deviation.
These
values
are
coming
from
the
root
mean
squared
error
of
my
Least Squares
models.
Y
ou
can
see
here,
RMSE
is
here,
is
the
same
value
for
in-vitro
release
as
the
error
standard
deviation
here.
Of
course,
you
can
change
these,
you
can
even
delete
them.
But
we
highly
recommend
that
you
have
some
error
for
your
predictions
since
your
predictive
models
are
not
perfect,
not
without
error.
Okay.
The
first
thing
you
might
notice
about
this
profiler
is
that
it
looks
a
little
different
in
that
each
factor
cell
has
two
curves
instead
of
the
usual
one
curve.
That's
because
we're
trying
to
find
factor
limits.
W
e're
trying
to
find
an
interval,
we're
trying
to
find
the
operating
region,
the
design
space
where
we're
optimizing
our
operating
region.
The
blue
curveâ
we
have
a
legend
to
help
usâ
this
represents
the
in-spec
portion
as
the
lower
limit
changes,
and
the
red
curve
represents
the
in-spec
portion
as
the
upper
limit
changes.
You
can
see
how
if
I
were
to
change
the
upper
limit
of
emulsifier,
it
would
increase
my
in-spec
portion.
That
would
be
a
good
thing.
That's
how
that
works.
Also
the
in-spec
portion,
you
don't
see
the
value
over
here
on
the
left
like
you
usually
do,
but
it's
right
over
here
to
the
right
of
the
cells.
It's
initially,
79.21%
of
my
points
are
in-spec
and
that's
in-spec
for
all
of
the
responses
to
all
of
the
CQAs.
If
you
want
to
see
the
individual
in-spec
portions,
you
can
find
them
down
here
next
to
the
specific
response.
Also,
you
can
notice
this
volume
portion
is
telling
me
that
I
am
currently
using
all
of
my
simulated
data
and
that's
because
the
factor
limits
are
set
at
their
full
range
initially.
To
be
able
to
change
the
factor
limits
or
try
to
change
the
operating
region,
you
can
either
move
the
markers
as
usual
or
you
can
enter
different
factor
limit
values
here
in
this
table
or
right
here
below
the
cells
or
you
can
use
these
buttons
.
I
really
like
these
buttons.
If
I
click
on
Move
Inward,
it's
going
to
find
the
biggest
increase
in
in-spec
portion.
It's
going
to
find
the
move
that
gives
me
the
biggest
increase.
It's
going
to
find
the
steepest
upward
path
.
Move
Outward
would
do
the
opposite.
It
would
find
the
steepest
path
downward.
If
I
click
Move
Inward,
notice
that
my
emulsifier
lower
limit
has
increased
from
700
to
705,
and
my
in-spec
portion
has
increased
to
81.95.
If
I
click
it
again,
now
my
lecithin
lower
limit
has
increased
from
30
to
31,
and
my
in-spec
portion
has
gone
up
to
84.5.
I
can
keep
doing
this.
But
before
I
keep
doing
this
until
I
find
the
desired
in-spec
portion
that
I
likeâ
and
I'm
happy
with
the
factor
limits,
I
think
it's
a
reasonable
operating
regionâ
there
are
several
options
in
the
Design
Space
Profiler
menu
that
I
like
to
look
at.
The
first
one
is
make
and
connect to
random
table.
W
hat
this
does
is
it
creates
a
new
random
table
of
uniformly
distributed
points.
You
always
want
to
add
random
noise.
It's
going
to
use
the
same
random
errors
we
used
before.
I'm
going
to
click
Okay.
Now,
I
get
this
table
of
10,000
new
random
points,
and
they
are
color-
coded.
The
ones
that
are
marked
as
green
are
in-
spec,
the
ones
that
are
red
are
out
of
spec,
and
the
ones
that
are
selected
are
within
my
current
factor
limits,
my
current
operating
region.
It's
useful
to
look
at
the
table,
but
I
really
like
to
look
at
these
graphs
that
are
produced
by
some
of
these
saved
scripts.
If
I
run
Scatterplot
Matrix
Y,
it
will
give
me
a
response
view
of
all
my
data
.
The
shaded
region
that's
green
here
is
the
spec
limits. T
hen
I
also
like
to
look
at
the
Scatterplot Matrix
X,
which
gives
me
the
factor
space
view.
It's
nice
if
I
can
look
at
them
both
at
the
same
time.
While
I'm
altering
my
factor
limits,
if
I
click
on
Move
Inward
again,
you
can
see
how
the
points
change
.
I
find
it
even
more
useful.
You
also
see
how
the
factor
space
changes.
I
find
it
even
more
useful
to
hide
all
the
points
that
are
not
in
my
current
operating
region,
then
I
don't
even
have
to
look
at
them.
Now,
as
I
keep
clicking
on
Move
Inward,
you
can
see
how
that
operating
region
is
shrinking.
If
you
only
want
to
be
concerned
with
the
out-
of-
spec
points,
you
can
click
on
Y
Out
of
Spec,
and
that
will
only
show
the
out
-of-
spec
points
that
are
occurring.
Notice
that
my
in-spec
portion,
as
I
keep
moving
my
factor
limits
in,
is
increasing
.
I'm
going
to
keep
going
until
I
either
hit
100%
or
my
operating
region
looks
like
something
I
can't
that
isn't
feasible,
that
I
just
won't
be
able
to
attain.
I'm
going
to
keep
clicking
Move
Inward.
Things
still
look
good.
Move
Inward,
just
going
to
keep
clicking
it.
Okay,
I
hit
100,
and
I
still
think
that
these
factor
limits
represent
an
operating
region
that
I
think
I
should
be
able
to
attain.
To
be
able
to
look
at
that
further,
I
can
send
the
midpoints
of
these
factor
limits
to
the
original
profilers,
see
what
that
looks
like.
I
think
that
looks
pretty
good.
I
can
also
send
the
limits
to
the
simulator
in
the
Prediction Profiler,
and
I
can
decide
to
use
different
distributions.
I
actually
think
that
my
critical
process
parameters
follow
normal
distributions.
I'm
going
to
select
this
Normal
with
Limits
at
3 Sigma
.
It
turns
on
the
simulator,
and
it
sets
my
distributions
to
normal,
and
it
figures
out
the
mean
and
standard
deviations
for
these
limits
with
Sigma,
3 Sigma.
Of
course,
you
can
change
all
these
values
as
you
think
seems
fit
for
your
own
situation,
for
your
own
manufacturing
process.
You
can
change
the
distribution,
you
can
change
the
mean
cedar
deviations.
I'm
just
going
to
leave
it,
and
I'm
going
to
see
what
simulating,
what
the
normal
distributions
looks
like.
It
looks
really
good.
You
can
see
my
defect
rate.
When
I
keep
hitting
Simulate,
it's
often
0.
I
also
like
to
simulate
to
the
table
to
be
able
to
just
get
a
view
of
what
my
capability
analysis
would
look
like
just
as
a
sanity
check.
I
f
you
come
down
here,
you
can
simulate
the
table,
and
it's
going
to
use
these
normal
distributions
for
the
critical
process
parameters.
It's
going
to
use
the
same
errors
for
your
predictions
as
we
used
before.
I'm
going
to
click
Make
Table,
and
when
I
do
that,
it
automatically
creates
some
scripts.
One
of
them
is
distribution.
If
I
run
that,
I
can
very
easily
look
at
my
capability
reports
because
I
saved
my
spec
limits
as
column
properties.
I
see
that
the
capability
looks,
at
least
for
the
simulated
data,
it
looks
really
quite
good.
So
I'm
pretty
happy
with
this,
even
though
this
is
just
on
the
simulated
data.
Of
course,
I
need
to
check
the
real
data,
but
I'm
really
happy
with
what
I'm
seeing
so
far.
I
think
I'm
going
to
use
these
limits
as
my
design
space.
Now,
just
to
note
before
I
go
further,
I
have
a
good
situation
here,
but
let's
say
that
you
didn't
have
a
good
situation
where
your
in-spec
portion
wasn't
where
you
wanted
it
to
be,
and
you
really
can't
adjust
your
factor
limits
anymore.
You
could
do
what-
if
scenarios
by
changing
your
spec
limits
or
your
errors
if
you
think
that
is
something
that
could
reasonably
happen.
But
I
have
a
good
situation,
and
I'm
happy.
I
am
going
to
use
this
option
Save
X Spec Limits, and that's going to save
these
factor
limits
back
to
my
original
data
table,
to
my
critical
process
parameters,
so
I
can
save
these
factor
limits.
When
I
do
that,
when
I
go
back
to
my
original
table,
you
can
see
that
those
factor
limit
settings
have
been
saved
as
Spec
Limits
to
my
critical
process
parameters.
I
find
it
really
helpful
to
be
able
to
look
at
this
design
space
in
terms
of
the
contour
responses
and
the
acceptable
region.
I've
already
saved
my
predictions
as
formulas
and
I
have
a
script
saved
to
run
the
Contour Profiler.
I'm
going
to
run
that
.
This
is
going
to
give
me
my
contour
responses
for
all
combinations
of
my
factors,
my
critical
process
parameters.
I
don't
know
if
you
can
see
the
faint
rectangles,
but
that
is
my
design
space
as
defined
by
those
factor
limits
that
got
saved
as
spec
limits
on
my
critical
process
parameters.
The
shaded
colored
areas,
these
are
my
spec
limit
response
contours.
You
can
see
that
my
design
space
is
nicely
within
an
acceptable
region
for
all
these
contours
.
It's
even
further
in.
It's
not
touching
them.
That's
because
we
added
that
error end
for
our
predictions.
I'm
really
happy
with
this.
Okay,
let's
get
back
to
PowerPoint.
I
just
want
to
give
you
a
few
takeaways
about
the
Design Space Profiler
before
we
wrap
up.
First
of
all,
that
in-spec
portion
that
we
saw
in
the
Design Space Profiler
shouldn't
be
taken
as
a
probability
statement
unless
you
believe
that
your
factors,
your
critical
process
parameter
factors,
actually
follow
a
uniform
distribution
because
that's
what
was
used
to
distribute
them.
Also,
the
Design Space Profiler
is
not
meant
for
models
that
have
a
large
number
of
factors
or
very
small
factor
ranges
because
of
the
simulated
approach
that
it
takes.
It's
also
recommended,
as
I've
mentioned
several
times,
to
always
add
random
error
to
your
responses
because
your
prediction
models
are
not
without
error.
And
finally,
I
just
wanted
to
make
a
statement
that
even
though
this
was
motivated
by
pharmaceutical
industry,
it
really
is
applicable
much
further
than
that.
In any
case
where
you
want
to
find
an
optimal
operating
region
and
you
want
to
maintain
flexibility
and
quality,
then
this
can
be
helpful.
There
were
many
things
about
the
Design
Space
Profiler
I
didn't
have
time
to
show.
I
really
hope
that
you
will
check
it
out.
Any
questions?
