Welcome,
everybody,
to
this
presentation
about
a
use
case
of
curve
alignment.
Experienced
analysts
often
say
that
in
a
larger
analytical
project,
plus
minus
60
%
of
the
total
time
goes
into
the
preparation
of
data.
If
curves
play
a
role
and
especially
the
alignment
of
curve
is
needed,
then
that
is
certainly
close
to
the
truth.
Curves
are
very
specific
types
of
data,
and
JMP
has
some
tools
to
work
with
curves
and
to
address
all
the
related
problems.
In
the
sample
library,
there
is
the
Algae
Mitscherlich data,
which
is
one
of
my
favorite
data
sets
with
that
respect
because
it
has
the
option
to
deal
with
many
aspects
of
fitting
curves.
This
is
just
an
example
of
the
development
of
Algae
density
in
different
treatments.
The
type
of
curves
that
I'm
going
to
talk
about
are
typically
observations
or
measurements
over
time.
But
this
doesn't
mean
any
loss
in
generality.
The
presented
concepts
work
in
all
kinds
of
curve
relationships.
This
is
an
example,
A
lgae
measurement
over
time,
and
one
of
the
aspects
that
is
in
the
focus
of
the
analysis
for
this
data
set
is
to
specify
curves,
specific
types
of
curves
that
have
a
known
shape
and
are
driven
by
certain
parameters
and
then
to
estimate
those
parameters
based
on
the
data.
In
those
cases,
the
parameters
very
often
have
a
technical
meaning
like
slope,
inflection
point,
limit
that
gets
approached.
That
platform
here
also
has
the
sliders
that
let
you
analyze
how
changing
one
of
those
parameters
affects
the
shape
of
the
curve.
In
the
specific
case
that
we
are
going
to
talk
about,
we
are
not
specifically
interested
in
the
curve.
The
curve
itself
is
only
a
help
because
we
are
facing
another
problem.
This
is
the
data
set,
or
this
is
a
part
of
the
data
set
that
goes
back
to
the
real
problem.
We
had
this
series
of
measurements,
one
and
another
series
of
measurements,
and
they
belong
to
two
different
devices.
U
nfortunately,
the
clocks
of
these
devices
were
not
in
sync.
But
luckily,
each
of
the
devices
had
one
sensor
that
measured
the
same
substance.
W
e
could
look
for
times
where
the
measurements
were
very
close
to
each
other.
Then
try
to
find
out
how
to
correct
one
of
the
clocks,
so
to
say,
so
that
we
get
aligned
measurements,
and
then
use
those
to
evaluate
the
data
from
all
the
centers
that
have
been
available
in
that
data
set.
What
was
the
problem
of
the
task?
You
see
the
curves
here.
The
red
curve
is
the
one
that
we
took
as
the
reference
curve,
and
the
blue
one
is
the
one
that
we
wanted
to
shift.
You
see
not
only
that
the
curves
are
quite
some
distance
away,
although
they
should
theoretically
have
measured
the
same
substance
at
the
same
time,
but
also
the
time
points
of
each
series
is
completely,
or
the
time
point
of
both
series
are
completely
unrelated.
With
the
bare
eye,
we
don't
see
any
lag
that
we
could
use
to
correct
one
of
the
data
sets.
Therefore,
I
looked
intoâ¦
I
compared
the
time
points,
not
the
Y
measurements,
the
time
points
of
the
two
series.
If
there
was
just
a
shift,
then
we
would
expect
to
see
all
the
data,
all
the
points
exactly
on
one
line.
But
here
you
see
there
are
ups
and
downs,
so
this
is
obviously
not
the
case.
Perhaps
we
can
see
more,
we
can
understand
more
if
we
calculate
row
by
row
in
the
data
table,
we
calculate
the
difference
of
the
two
times
and
look
at
those.
Here
with
some
fantasy,
we
see
a
little
bit
of
curvature,
so
till
the
end,
it
seems
to
be
closer
related
than
to
the
beginning.
But
in
the
beginning,
this
looks
like
real
random
data.
This
as
well
does
not
help
us
a
lot
to
figure
out
how
to
relate
the
data.
I
thought
I
had
the
link
to
the
data
table,
but
we
can
look
in
this
screenshot
as
well.
This
is
the
data
set
that
you
have
seen
before,
a
little
bit
annotated.
We
see
that
two
lines
have
specific
markers,
the
star
and
the
circle.
This
is
due
to
the
fact
that
the
whole
measurement
project
had
a
ramp-
up
phase,
and
at
the
star
point,
the
measurement
series,
the
measurement
time,
the
real
process
time
started.
The
circle
is
there
where
we,
after
visual
or
manual
inspection,
saw
the
starting
point
in
the
second
time
series,
and
we
want
to
align
both.
W
e
need
to
change
the
relationship
of
the
rows,
of
the
data
and
the
rows.
We
want
to
shift
one
of
the
data
sets,
and
that
reminded
me
of
the
paternoster
that
I
like
to
use
when
many
years
ago
I
was
working
for
a
company
that
had
a
very
old
administrative
building
and
we
had
the
paternoster
in
there.
It
came
to
me
that
the
strategy
that
we
are
following
is
part
of
paternoster shift,
which
gives
the
word
elevator
pitch
a
completely
new
meaning,
by
the
way.
How
do
we
find
the
right
steps,
the
right
place
to
fit?
We
do
not
have
similar
or
identical
time
points
in
both
series
of
times.
We
need
to
construct
those
time
points
somehow.
Of
course,
this
is
done
through
interpolation.
T
he
first
thing
that
comes
into
mind
is
linear
interpolation,
and
if
I
zoom
in
into
only
a
part
of
the
data
set,
then
it
is
evident
that
linear
interpolation,
so
just
checking,
so
to
say,
the
regression
between
neighboring
time
points
has
some
problems,
especially
if
we
look
into
areas
where
we
have
horizontal
lines,
which
may
easily
happen.
Then
the
time
point
in
that
range
is
quite
arbitrary.
It
always
leads
to
the
same
results.
The
opposite
is
true.
If
we
are
in
an
area
with
a
very
steep
ascent,
then
a
little
change
on
the
X-
axis
or
the
time
may
lead
to
significant
changes
in
the
Y
value.
T
his
is
not
a
very
good
technique.
We
can
use
splines
to
interpolate between
the
values.
You
know
splines,
certainly
from
the
graph
builder.
If
you
make
a
scatter
plot,
then
by
default,
the
smoother
is
switched
on
and
the
smoother
provides
splines.
You
can
even
change
the
stiffness
or
the
degree
of
fit
or
the
closeness
to
the
data
with
a
slider
in
the
graph
builder.
The
advantage
of
using
a
spline
as
an
interpolation
tool,
also
takes
into
consideration
points
further
away.
T
hey
build
a
smooth
curve.
That
is
why
in
the
graph
builder,
it's
called
the
smoother.
This
makes
it
easier
to
use
those
for
interpolation and
to
use
these
as
well
as
a
base
in
our
alignment
process.
We
need
to
fit
splines.
How
can
we
do
this
or
which
platforms
do
help?
First
of
all,
simple
tool
is
Fit
Y
by
X
comes
into
mind
very
fast
when
you
work
with
JMP
and
do
that
data
analysis.
This
is
the
data,
one
of
the
curves.
There
is
the
spline
fit,
and
here
is
the
slider
that
let
me
choose
how
close
or
how
close
I
want
to
fit
my
data.
Very
good,
very
easy
to
use,
and
you
can
save
the
spline
but
only
the
values,
not
the
formulas.
We
are
keen
on
getting
the
formula
for
the
spline.
Next
stop,
Fit
Model.
If
you
have
a
continuous
variable,
you
select
it,
you
can
give
this
the
attribute
of
being
a
knotted
spline
effect.
When
you
do
so, you
are
prompted
to
say
how
many
knots
that
spline
should
have,
the
more, the more
flexible.
I
accept
the
default,
say
run.
We
get
the
typical
report
from
Fit
Model.
A
lso,
we
have
fit
models,
functions
of
saving
formulas.
We
can
use
Fit
Model,
save
the
formula.
Little
disadvantage
here
is
I
need
to
specify
the
number
of
knots
before
I
start
the
analysis.
Once
the
analysis
is
done
within
the
platform,
I
don't
have
the
option
to
play
with
it
or
change
it
like
it
is,
for
example,
in
Fit Y
by
X.
Another
tool
is
the
Functional
Data Explorer
. T
he
Functional
Data
Explorer
has
splines
as
a
core
function,
and
it
is
also
functionality
to
find
optimal
definitions,
optimal
fits
for
the
splines.
You
can
export
everything.
It's
a
bit
because
simple
tasks
like
this
is
not
where
the
Functional
Data
Explorer
is
made
for.
You
need
some
more
clicks
to
come
to
a
result.
A
lso,
it's
only
available
for
people
who
have
JMP role.
Remains,
the
Graph
Builder.
You
have
seen
it
before,
and
this
time
I
want
to
show
the
spline
control
as
well.
As
I
said,
we
can
use
the
slider
to
determine
the
fit.
A
very
nice
feature,
by
the
way,
is
that
you
can
check
this
box,
then
through
a
bootstrap
sampling
method,
the
confidence
interval
for
the
smoother
is
calculated
or
estimated.
You
see
how
that
changes when
I'mâ¦
Now
you
can
see
better,
I
have
a
lot
of
data
and
there
is
not
too
much
variability.
H
ere
the
confidence
band
is
quite
small.
But
if
we
zoom
into
one
of
these
areas
here,
for
example,
that
place
and
look
at
what
happens
when
I
change
this,
then
we
see
that
the
smoother
can
evenâ¦
That
the
line
of
the
smoother
can
even
walk
out
of
its
own
confidence
band.
This
is
another
visual
help
to
find
out
a
good
fit
for
the
smoother,
for
the
spline.
It
should
stay
within
its
own
confidence
limit.
Then
comes
the
very
important
option
here.
We
can
save
the
formula.
Then
we
have
a
formula
for
this
spline.
The
graph
builder
surprises
as
a
modeling
tool.
Who
had
expected
this?
How
does
that
help?
This
is
again
part
of
my
data
table,
small
part.
You
see
that
now
I
have
two
columns
here
where
I
saved
the
formulas
for
the
smoother
too.
Down
here
in
the
colored
rows,
I
put
some
arbitrary
time
points
in.
That
leads
to
an
interpolated response
relative
to
the
time
point
that
I
have
given.
It
only
works
for
interpolation.
We
cannot
extrapolate
this
way,
it's
only
with
interpolation.
But
this
way
I
can,
for
example,
manually
add
different
time
points.
I
have
this
one
here
plus
X
seconds
in
that
case
,
and
then
I
can
see
what
is
the
difference
of
the
interpolated
value.
Now
I
can
put
reference
times
in
and
I
see
exactly
what
is
the
expected
value,
plus
minus
a
little
bit
for
both
measurements.
I
did
this
for
two
different
phases.
I
can
go
here
and
experiment
anymore.
In
my
journal,
you
see
in
the
yellow
rows,
I
added
eight
seconds.
In
the
orange
ones,
10
seconds.
Depending
on
what
you
want
to
do,
this
is
the
principle
of
how
you
can
work
with
this.
If
your
task
is
a
one-
off
task,
this
is
good
enough.
You
can
go
in
here,
play
with
the
data,
see
the
difference.
Our
task
was
more
regular.
The
good
thing
is
everything
can
be
controlled
with
JSL.
As
usual,
for
many
commands
that
you
do
manually
on
line,
you
have
corresponding
JSL
statement,
and
I
just
listed
some.
This
is
not
a
working
program.
First
of
all,
you
need
to
set
up
the
graph,
clear.
Then
you
have
commands
that
you
can
send
to
the
graph
and
specifically
to
the
smoother
element
in
your
graph.
We
can
change
the
smoother
so
we
could
even
interactively
try
to
determine
good
fits.
We
can
also
give
the
command
to
save
the
formula
in
the
data
table.
That
is
the
command
that
plays
an
important
role
for
our
solution
here.
You
can
read
out
the
current
settings
of
the
Lambda
slider
and
something
small.
How
did
we
want
to
use
this?
The
concept
here
was,
of
course,
first
you
need
to
determine
what
is
the
reference
curve
and
what
is
the
objective
curve,
the
one
that
needs
to
be
shifted.
Then
you
calculate
the
spline
function
for
the
reference
curve
and
determine
the
direction
of
shift.
Where
are
we?
Do
we
need
to
shift
our
time
up
or
down?
Then
we
move
the
Y
values
of
the
objective
curve,
one
row
in
the
desired
direction
and
calculate
the
spline
function
for
this
new
curve.
Save
that,
use
a
reference
value,
and
then
calculate
the
differences
in
Y
for
each
row.
Then
we
take
the
total
sum
of
those
differences
as
a
criterion
when
to
break
the
process.
Because
after
every
step,
we
calculate
that
difference,
we
save
the
difference,
we
do
the
next
step,
and
we
check,
was
there
an
improvement?
If
yes,
we
move
up
or
down
one
row
more,
and
then
we
repeat
that
whole
activity
until
there
is
no
improvement
anymore.
The
whole
program
in
the
real
project,
of
course,
runs
behind
the
scenes.
You
wouldn't
see
anything.
But
I
added
did
some
graphs
to
make
it
visual
to
demonstrate
how
that
works
step
by
step.
The
starting
situation
is
this
one.
On
the
left-
hand
graph,
you
see
the
dashed
line
and
the
solid
line.
The
dashed
line
is
the
reference
line.
The
solid
line
needs
to
be
moved.
On
the
right
side,
you
see
the
differences
per
row.
In
the
beginning,
the
differences
areâ¦
You
see
that
here
in
the
starting
area,
the
differences
here
are
pretty
small.
Then
they
get
larger
and
larger,
and
they
are
negative.
That
is
why
it
goes
down
here
on
a
negative
scale,
very
small
differences
in
the
beginning,
and
then
they
get
up
larger.
This
is
the
starting
situation.
You
will
see
this
picture
again.
Then
the
program
will
start
shifting
the
reference
curve
one
cell
up
in
our
situation,
our
case.
Then
you
see
how
these
graphs
update
for
every
step.
Yes,
first
we
need
to
tell
JMP
what
are
the
time
and
measurement
values
for
the
reference
and
the
objective
curve.
Here
we
go.
It
will
take
a
little
bit
in
the
beginning,
then
afterwards
the
steps
come
faster.
You
see
how
for
every
step,
the
blue
curve
approaches
the
dotted
curve,
and
how
the
differences
decrease.
The
last
step
did
not
improve
the
situation
anymore,
therefore,
the
program
stepped
one
step
back.
Now,
we
have
the
data
table
in
a
situation
where
we
shifted
up
the
objective
curve.
Now
we
can
use
this
shift
for
all
the
other
measurements,
for
all
the
other
sensor
results
that
we
had
for
this
device
and
start
the
analysis.
That
was
it.
I
hope
I
could
inspire
you
a
little
bit.
It
was
an
interesting
presentation.
If
you
have
any
questions,
please
don't
hesitate
to
contact
me.
My
email
was
on
top
of
the
presentation,
bernd.heinen@stabero.c
om.
Thank
you
very
much.
