Hello
everyone.
Today
my
topic
is,
Heros
or
Zeros:
A
Product
Distribution
Analysis
Using
JMP.
First,
a
little
bit
background.
An
organization
with
an
established
process
may
decide
to
implement
process
control
and
process
discipline
in
their
organization.
For
example,
if
you
have
a
product
moving
from
the
development
stage
to
the
mass
production
stage,
at
this
conjunction,
one
of
the
problems
that
can
happen
in
that
we
may
have
process
variation
issue.
The
variation
can
be
too
large
or
the
variation
doesn't
meet
the
expectation.
The
variation
here
can
be
the
variation
of
mean,
the
variation
of
standard
deviation,
etc.
We
will
want
to
find
out
what
the
root
cause
is
for
such
variation
problem
and
try
to
fix
that.
But
before
that,
we
will
need
to
figure
out
what
type
of
variation
we
are
facing
because
the
type
of
variation
will
dictate
what
kind of action
and
investigation
strategy
we
should
take.
The
demonstration
here
today
will
investigate
these
through
an
explanatory
analysis.
We
use
standard
deviation
as
statistics
of
interest
here.
The
issue
is
we
have
a
process
that
has
a
high
overall
standard deviation,
but
we
can
also
observe
some
of
the
batches
that
has
lower
standard
deviation.
We
call
these
batches,
hero
batches.
We
will
want
to
find
out
what
caused
such
high
overall
standard
deviation,
but
before
that,
we
need
to
figure
out
what
process
variation
we
are
facing,
what
kind of process
variation
can
give
us
what
we
observed.
In
general,
there
will
be
two
types
of
situation
here.
One
is
that
we
have
a
completely
random
process
and
the
variation
is
systemic,
as
we
can
see
here.
Although
the
process
is
random,
but
depends
how
we
batch
it
and
how
we
sample
it.
Some
of
the
batches
may
have
lower
sample
standard
deviation
than
the
others.
Another
situation
is
that
our
process
is
not
random.
As
we
can
see
here,
this
process
goes
up
and
down.
It
has
some
mean
shift.
It's
not
a
random
process,
but
depends
on
how
we
batch
it.
Some
of
the
batches
that
reside
in
the
stable
period
will
have
relatively
lower
sample
standard
deviation
compared
to
some
of
the
batches
that
reside
in
the
unstable
period
that
might
have
larger
standard
deviation.
We
can
also
define
a
threshold
such
as
here,
point
A,
standard
deviation.
We
compare
this
threshold
to
the
batch
standard
deviation.
It
will
tell
us
how
many
of
the
batches
satisfy
the
criteria.
With
these
two
scenarios
in
mind,
we
can
formulate
a
statistical
hypothesis
test
to
test
what
process
variation
we
are
dealing
with.
We
can
assume
our
process
is
random,
then
how
likely
we
will
observe
what
we
observed?
A
more
detailed
statement
is
like
this,
assuming
batches
with
low
standard
deviation
are
just
due
to
sampling
lack
and
the
historical
data
is
representative
of
the
population,
then
the
simulated
batches
generated
from
the
same
distribution
should
have
a
passing
rate
that
is
statistically
indistinguishable
than
the
actual
passing
rate
of
the
historical
data.
On
the
right-hand
side,
you
can
see
this
wheel.
This
is
the
procedure
we
went
through
to
make
this
testing
happen.
First,
we
will
need
to
define
a
threshold.
Through
this
threshold,
we
can
calculate
the
passing
rate.
We
compare
the
batches
in
the
historical
data
through
this
threshold
to
get
the
percentage
of
the
historical
batches
that
are
good
batches.
Because
we
also
assume
that
our
process
is
random,
we
can
fit
the
historical
data
to
several
distribution
and
then pick
the
best
fitted
one.
Using
this
fitted
distribution,
we
can
generate
a
set
of
K
samples.
K
here
is
the
same
as
the
number
of
samples
in
each
batches
in
the
historical
data.
We
repeat
this
procedure
N
times.
N here
is
the
same
as
the
number
of
batches
in
the
historical
data.
For
each
simulated
batches,
we
can
then
calculate
their
sample
standard
deviation.
Compare
this
sample
standard
deviation
to
the
threshold
we
defined
before,
it
will
give
us
a
set
of
binomial
data.
With
this
binomial
data
and
the
passing
rate
we
already
have,
we
can
perform
a
one-sample
proportion
test
to
test
our
hypothesis.
Using
JMP,
we
are
able
to
integrate
this
entire
procedure
into
an
application.
Here,
I
will
do
a
quick
demonstration
to
show
you
how
this
application
works.
This
application
can
import
any
of
the
data
file
with
a
value
column
and
also
index
column
that
indicates
the
batch
index.
With
a
click
of
button,
it
will
automatically
fit
our
data
to
several
distribution
and
pick
the
best
one.
Right
now,
the
best
fitted
one
is
a
normal
distribution.
We
can
then
set
up
the
number
of
simulated
data
sets
we
want
and
also
the
size
of
the
set
and
also
the
threshold.
When
we
click,
it
will
perform
the
hypothesis
testing
I
mentioned
before.
It
also
shows
the
percentage
of
historical
batches
that
are
good
and
also
the
percentage
of
the
simulated
batches
that
are
good.
At
the
last,
it
will
show
you
a
visualization
of
a
histogram
which
indicates
the
proportion
of the
simulated
batches
that
are
good.
Now,
we
go
back
to
the
testing,
the
hypothesis
testing.
The
data
we
have
here
shows
we
reject
the
null
hypothesis.
We
check
the
P
value,
we
reject
the
null
hypothesis
with
95%
confidence.
The
95%
confidence
is
the
default
setting
here.
This
conclusion
suggests
the
process
is
not
random
and
the
good
batches
do
exist
in
the
stable
period
of
the
process.
This
conclusion
can
lead
to
several
action
items.
For
example,
we
can
investigate
the
process
variable,
the
process
parameter
between
the
stable
period
and
the
unstable
period
and
see
what
changed.
Of
course,
we
can
also
get
a
different
testing
result
where
we
cannot
reject
the
null hypothesis.
These
suggest
our
process
might
be
random.
We
might
have
systemic
variation
and
these
will
lead
to
completely
different
investigation
and
action
method.
For
example,
the
worst-case
scenario,
in
order
to
reduce
the
systemic
variation,
we
might
need
to
completely
change
the
manufacturing
environment.
With
this,
I
conclude
my
today's
presentation.
I
also
want
to
thank
John
Daffin,
who
is
a
colleague
of
mine.
He
brought
up
this
interesting
question
to
my
attention
during
a
project
meeting.
I
also
want
to
thank
you
today
for
hearing
my
presentation.
I'm
very
appreciative
of
it.
