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Finding Optimal Operating Regions for Critical Quality Attributes with the Design Space Profiler - (2023-US-30MP-1447)

Laura Lancaster, Principal Research Statistician Developer, JMP


Quality by Design (QbD) is a systematic approach for building quality into a product. The Design Space Profiler, new within the Prediction Profiler in JMP 17, helps solve the fundamental QbD problem of determining an optimal operating region that assures quality as defined by specifications associated with critical quality attributes (CQAs) while still maintaining flexibility in production. 


We explain JMP’s approach to solving this difficult problem and demonstrate how to use the Design Space Profiler to find these optimal subregions of the design space. The Prediction Profiler in JMP has long been a powerful tool for visualizing and optimizing models; having the Design Space Profiler within the Prediction Profiler makes it an indispensable tool for high-quality product and process innovation.



Hello. My  name  is  Laura  Lancaster.

I'm  a  statistical  developer   in  the  JMP  group,

and  today  I'm  here  to  talk  about finding  optimal  operating  regions

for  critical  quality  attributes with  the   design space profiler.

The  first  thing  I  wanted  to  talk  about  is

the  general  quality  paradigm   called  quality by design,

also  commonly  referred   to  as  QbD  for  short.

Quality by design  is  a  systematic  approach for  incorporating  quality

into  the  entire  product  lifecycle   beginning  at  the  design  phase.

It  was  first  introduced  by  Joseph  Juran, and  it  was  made  popular  in  his  book,

Juran  on  Q uality by Design   way  back  in  1992.

It  was  a  very  popular  book, and  a  few  years  after  it  was  published,

the  FDA  and  the  International  Conference on  Harmonization,  also  referred  to  as  ICH,

adopted  these   quality by design  principles for  the  development,

manufacturing,  and  regulation  of  drugs.

They  published  several  guidelines

for  implementing   quality by design in  the  pharmaceutical  industry

called  ICH  Q8- Q12,  and  we're  going   to  focus  on  ICH  Q8  guidelines.

What  exactly  do  we  mean  by  design  space?

Well,  this  is  a  very  important  concept

in  the  pharmaceutical  industry for  quality  by  design,

and  it's  defined  in  the  ICH  Q8( R2)  guidelines  as

the  multidimensional  combination and  interaction of  material  attributes

and  process  parameters   that  have  been  demonstrated

to  provide  assurance  of  quality.

Essentially,  the  design  space  is  what identifies  your  optimal  operating  region

that's  going  to  give  you  maximal  flexibility  in  your  production

while  still  assuring   that  you  get  a  quality  product.

JMP's  new   design space profiler,   new  in  JMP  17,

helps  us  find  this  design  space, this  optimal  operating  region.

Now  there's  actually  several  steps that  need  to  be  taken  before  you  can  use

the   design space profiler to  determine  your  design  space.

These  are  outlined  in  the  Q8  guidelines,

and  so  we're  going to  run  through  those  steps.

The  first  step  that  you  want  to  take

is  you  want  to  define   your  quality  target  product  profile,

and  this  is  defined   as  a  prospective  summary

of  the  quality  characteristics of  a  drug  product

that  ideally  will  be  achieved   to  ensure  the  desired  quality,

taking  into  account  safety and  efficacy  of  your  drug.

Next,  you  want  to  determine  what  are the  critical  quality  attributes

and  what  are  their  appropriate specification  limits.

A  critical  quality  attribute, also  referred  to  as  a  CQA,

is  defined  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.

Once  you've  determined  those,

then  you're  going   to  design  experiments  to  determine

what  are  the  critical  manufacturing   process  parameters

that  affect  these  critical   quality  attributes.

A  critical  process  parameter, also  referred  to  as  a  CPP  for  short,

is  a  process  parameter  whose  variability has  impact  on  a  critical  quality  attribute

and  therefore  should   be  monitored  or  controlled

to  ensure  the  process  produces   the  desired  quality  product.

Once  you've  determined  all  of  that,

then  you're  going  to  find   a  good  prediction  model

for  your  critical  quality  attributes

in  terms  of  your  critical   process  parameters.

Once  you've  done  that,

then  you  can  use   the   design space profiler  in  JMP

to  determine  your  design  space for  your  optimal  operating  region.

Let's  talk  a  little  more  specifically about  the   design space profiler  in  JMP.

First  of  all,  as  I  mentioned, it's  new  in  JMP  17,

and  it  resides within  the  Prediction  Profiler.

Hopefully  everyone  is  familiar with  the  Prediction  Profiler  in  JMP.

It's  a  wonderful  tool  for  exploring,

visualizing  and  optimizing  any  model   that  you  produce  within  JMP.

The  goal  of  the   design space profiler

is  to  determine  a  good  design  space by  finding  the  largest  hyper-rectangle

that  fits  into  that  acceptable  region that's  defined

by  your  critical  quality  attribute  spec   limits  applied  to  your  prediction  model.

Now,  once  you  have  that  hyper-rectangle,

that  gives  you  your  lower  and  upper  limits of  your  critical  process  parameters

to  determine  a  good  design  space for  maintaining  a  quality  product.

Now,  I  just  wanted  to  mention  very  quickly

that  a  design  space   does  not  have  to  be  a  rectangular,

but  having  a  rectangular  design  space   makes  it  really  convenient

for  checking  each  factor  one  at  a  time.

Now,  the  problem  with  this  approach

is  that  the  acceptable  region   is  usually  nonlinear,

and  finding  the  largest  hyper-rectangle

in  a  nonlinear  region  is a  very  difficult  mathematical  problem.

How  does   design space profiler  work  then?

Well,  instead  of  using   the  mathematical  approach

to  finding  the  largest  hyper-rectangle,   it  uses  a  simulated  approach.

It  generates  thousands  of  uniformly distributed  points  throughout  the  space

defined  by  your  initial  critical  process perimeter  factor  limits.

Then  it  uses  a  prediction  model

to  simulate  your  responses   for  your  critical  quality  attributes.

Note  that  it's  always  best  to  include   some  error  for  your  prediction  model

because  your  prediction  model   is  not  perfect,  it's  not  without  error.

Then  once  you  have   that  simulated  set  of  data,

you're  going  to  take  that  set and  calculate  the  in-spec  portion

by  counting  the  total  number  of  points that  are  in- spec  for  all  the  responses,

all  your  critical  quality  attributes from  the  points  that  are  within  the  space

defined  by  the  current  CPP  factor  limit settings of  your  current  design  space.

Now  the  easiest  way  to  see  how  this  works is  to  go  to  an  example  and  go  to  JMP.

That's  what  we're  going  to  do.

We're  going  to  look  at  an  example for  a  pain  cream  study.

The  goal  of  this  study  is  to  repurpose a  habit-forming  oral  opioid  drug

into  a  topical  pain  cream  that  provides the  same  relief  as  the  oral  drug.

The  first  thing  they  did  was  figure  out their  quality  target  product  profile,

and  then  they  were  able  to  determine  what their  critical  quality  attributes  were.

It  turns  out  there  were  three  of  them:

entrapment  efficiency,  vesicle  size, and  in vitro  release,

and  these  are  the  spec  limits

that  give  a  quality  product   for  these  critical  quality  attributes.

Next,  they  ran  experiments  to  determine what  are  the  process  parameters

that  affect   these  critical  quality  attributes.

It  turns  out  there  were  three   critical  process  parameters:

emulsifier,  lipid,  and  lecithin.

These  are  the  initial factor  limit  settings.

Once  they  did  that,

they  used  the  Custom  Designer  in  JMP   to  design  response  surface  model  designs.

They  ran  the  experiment, and  then  they  used  Fit  Least  Squares

to  fit  response  surface  models   for  the  three  critical  quality  attributes

in  terms  of  the  three   critical  process  parameters.

Once  they  did  all  of  that,

now  we  can  go  to  the   design space profiler in  JMP  to  determine  the  design  space.

Let's  go  to  JMP.

This  is  my  data  table  that  was  created from  Custom  Designer  when  I  created

a  design  for  the  response  surface  models of  my  three  critical  quality  attributes

as  responses  in  my  three   critical  process  parameters  as  factors.

It's  what  I  have  right  here.

I  wanted  to  note   that  I  went  ahead  and  I  added

the  critical  quality  attribute  spec  limits as  column  properties

because  the   design space profiler

has  to  know  what the  spec  limits  are  to  work.

If  you  don't  add  them   as  column  properties,

you'll  be  prompted  to  add  them when  you  launch  the   design space profiler.

But  I've  already  done  that.

I've  also  already  saved  the  script

for  my  models  that  I  created using  Fit  Least  Square.

I'm  going  to  go  ahead  and  run  that.

It  automatically  launches Fit  Least  Squares.

I  have  the  models  closed  and  just the  Prediction  Profiler  open.

Notice  that  it  looks  like  the  Prediction Profiler  that  you're  used  to  seeing.

I've  also  added  the  spec  limits

as  reference  lines  just  so  I  can  see  them   in  relation  to  my  models.

To  get  to  the   design space profiler, all  you  do  is  go

to  the  Prediction  Profiler  menu, turn  it  on,  and  a few  down,

you'll  see  there's  a  new  option called   design space profiler.

If  I  click  on  that,

the   design space profiler  will  appear right  below  the  Prediction  Profiler.

Now  notice  that  because  I  had  added the  spec  limits  as  column  properties,

it  automatically  brought  those  in.

If  you  go  to  the  bottom  right-hand  side,

you'll  see  where  it's  brought   in  my  spec  limits

for  my  three  responses   or  three  critical  quality  attributes.

You'll  also  notice   that  it's  brought  in  some  error,

which  it's  going  to  use  as  my  error   for  my  prediction  model.

This  has  come  in  from  the  Least  Square model's  root  mean  squared  error.

For  example,  up  here, if  I  go  to  my  in-vitro  release  model,

you  can  see  the  root  mean   square  error  is  1.2972,

and  that's  the  same  value

that's  listed  down  here  as the  error  standard  deviation.

Now  you  can  change  these   if  you  think  these  are  not  accurate,

these are too  big  or  whatever.

You  can  even  completely  remove them  and  have  no  error,

but  we  highly  recommend   that  you  do  add  some  error  to  your  models.

Okay,   there  are  several  things   that  you  might  notice  are  different

about  this  design space profiler  than  other  profilers.

One  of  the  first  things  you'll  notice  is that  over  here  on  the  Y-axis,

instead  of  having  a  value   like  you  normally  do,

like  up  here  in  the  Prediction  Profiler, it  just  says   in-spec portion.

But  the  actual  value  for  the  Y- axis is  actually  over  here  to  the  right.

My  in-spec  portion  for  all  three critical  quality  attributes  when  I  have

the  initial  factor  limits  set   at  the  full  range  is  71.2%.

Then  you  can  also  see  over  here that  it  says  the  volume  portion  is  100%.

That's  because  I'm  using  100%

of  the  entire  simulated   data  set  starting  up

because  everything's at  the  full  factor  range.

Another  thing  that's  different  is   for  each  factor  cell,

you'll  see  that  there's  two  curves   instead  of  the  usual  one  curve.

That's  because  we're  looking for  factor  limits,

so  a  lower  and  upper  limit   for  each  factor.

The  blue  curve  represents  the  in-spec portion  as  the  lower  limit  changes.

There's  a  handy  legend over  here  to  help  me.

The  red  curve  represents  the  in-spec portion  as  the  upper  limit  changes.

I  can  interact  with  this  profiler

to  change  my  factor  limit  settings or  my  design  space.

I  can  move  these  markers.

I  want  to  obviously  move  this to  get  a  higher   in-spec portion,

and  so  you  would  want  to  find a curve  that  has  an  upward  slope.

I  can  move  this  one  inward by  dragging  this  marker.

I  could  also  just  enter  values   down  here  below  the  cells.

I  could  enter  values  here   in  these  fields  next  to  the  factors.

Or  there's  also  another  way,

which  is  to  use  these  buttons, move  inward  and  move  outward.

This  move  inward  button,  if  I  click  on  it, it's  going  to  give  the  largest...

It's going to make the move,

it's going to give the largest increase  in  inspect  portion.

It's  going  to  look  for  the  curve with  the  steepest  path.

If  I  click  on  move  outward, if  I  were  trying  to  increase

the  sizes  of  my  design  space, it  would  give  me  the  least  decrease.

I  would  look  for the  least  steep path  downward.

Let  me  go  ahead  and  click  move  inward.

I  noticed  when  I  click  that, the  lower  limit  for  a  emulsifier  went

from  700- 705,   and  the  in-spec  portion  went  up.

Now,  if  I  want  to  look  at...

This  is  the  in-spec  portion   for  all  three  critical  quality  attributes,

but  if  I  want  to  look   for  them  individually,

they're  to  the  far  right-hand  side

of  each  response   or  each  critical  quality  attribute.

I  can  see  the  in-spec  portion for  each  one  individually.

But  up  here  it's  finding   it  corporately  for  all  of  them.

Let's  click  move  inward  again and  notice  that  a  emulsifier  went  in  again

and  now  it's  up  to  710 and  my  in-spec  portion  is  up  to  78.

The  volume  portion  now  is   down  to  89.79%.

Click  it  again. Now  my  lecithin  lower  limit  went  up.

My  goal,  I'm  going  to  see  if  I  can  get my  in-spec  portion  all  the  way  up  to  100%,

if  I  still  can  maintain  factor  limits that  seem  reasonable  and  realistic.

But  before  I  do  that, there  are  several  options

from  the  menu  of  the  design  space  profiler

that  I  really  like  to  use  while  I'm  doing  this.

The  first  one  is  I  like  to  turn  on  make and  connect  random  table.

This  is  going  to  create   a  new  table  of  random  data.

It's  going  to  do  10,000  by  default, I'm  going  to  leave  that.

I'm  going  to  add  random  noise.

It's  the  same  random  noise  added

to  the   design space profiler  based on  these  bare  standard  deviations.

Click  okay  and  I  get  a  new  set   of  10,000  data  points,

uniformly  distributed throughout  the  factor  space.

These  data  points  are  color  coded.

The  green  points  are   in-spec  for  all  of  my  critical  quality  attributes

and  the  red  are  out.

Anything  that's  selected  is  still   within  my  design  space

or  my  current  factor  limit  settings.

What  I  really  like  about  this  table  is

the  graphs  that  are  created  by  the  scripts that  are  automatically  saved  to  the  table.

I  really  like  to  look at  the  scatterplot  matrix  Y.

Let  me  turn  that  on.

This  gives  me  a  view  of  my  data with  all  combinations

of  my  response variables and  my  critical  quality  attributes.

It  has  the  spec  limits  drawn  on  and  it  has the   in-spec portion  shaded  green

and  all  the  red  points  are  out  of  spec and  the  green  points  are  in- spec.

I  also  like  to  look  at  the  factor  space,

and  so  I  could  do  that  by  looking at  the  scatter  plot  matrix  X.

This  is  going  to  give  me  my  factor  space or  my  critical  process  parameter  space.

Once  again,  same  color  coding

and  what's  shaded  is within  the  current  factor  settings.

See  if  I  can  situate  this   so  we  can  look  at  both  of  these

while  I'm  adjusting   my  factor  limits  over  here.

Okay,   you  can  see  as  I  move  inward,

you  can  see  how   the  shaded  area  is  shrinking

for  my  factor  space,  my  design  space,

and  the  number  of  out-of-spec points  are  also  shrinking.

Now,  I  really  like  to  also  turn on  the  connect/hide  mode,

and  what  that  does  is  it  just  hides   any  points  that  are  no  longer

within  my  current  factor  limit  settings or  my  current  design  space.

Now  if  I  keep  clicking  move  inward,

you  can  see  how the  red  points  are  starting  to  disappear.

One  other  option  you  can  use, if  you  prefer,

is  you  can  choose  to  only  look   at  the  points  that  are   in-spec

or  only  look  at  the  points that  are  out  of  spec.

I'm  going  to  turn  Y  out  of  spec  on

to  only  look  at  the  points   that  are  still  out  of  spec.

I'm  going  to  see  if  I  can  hit  100.

Move  inward. I'm  going  to  keep  going.

Still  looks  good.

Keep  going.

Okay,   now  I've  hit  100 %,   and  I  think  this  design  space,

these  factor  limits  do  look   like  they're  probably  reasonable.

You  might  notice  that  I  still  have a  red  point  over  here  because  this  is

a  separate  set  of  simulated  data,

but  I'm  not  worried  about   that  one  random  point.

Okay,   let's  examine  this design  space  that  I  have  set  here.

What  I  want  to  do  is  I  want  to  send the  midpoint  of  this  design  space

back  to  the  Prediction  Profiler to  see  what  that  looks  like.

I  can  easily  do  that  with  this  option that  says,  "Send  midpoints  to  profiler."

When  I  do  that,  it  automatically  sends

the  midpoint  of  this  current  design  space back  to  the  profiler so  I  can  look  at  it.

I'm  going  to  turn  on  the  desirability, and  I  think  that  looks  quite  good.

I'm  going  to  go  ahead and  save  this  setting.

I  want  to  do  that  just   so  I  can  compare  this  against

the  optimal  setting  if  I  were  to  optimize

by  maximizing  all   of  my  critical  quality  attributes,

which  is  something  you  may or   not  want  to  compare  against.

But  it's  very  easy  to  do   and  I  can  look  at  the  difference.

You  can  see  there's  not  a  huge  difference

in  the  desirability  between  the  center of  my  design  space  and  the  optimal  value

if  I  maximized  all   my  critical  quality  attributes.

I'm  pretty  good  with  this  center   of  this  design  space.

I'm  going  to  turn  it  back  to  that  point.

Another  thing  that  you  can  do  is... Well,  I  don't  really  believe...

The   design space profiler uses  uniformly  distributed  points,

but  I  think  that  my  critical  process

parameters  actually  follow a  normal  distribution.

It's  very  easy  to  send  these  limits   back  to  the  profiler

and  back  to  the  simulator

so  I  can  simulate  using   the  normal  distributions.

If  I  click  Send  Limits  to  Simulator and  choose  normal

with  limits  at  three  sigma, what  it's  going  to  do  is  it's  going

to  send  the  limits  back   to  the  simulator  and  figure  out

what  my  standard  deviation  would  be  if that  design  space  was  set  at  three  sigma.

Of  course,  you  can  change  these  values, you  can  change  the  distribution.

I'm  going  to  use  these  settings   and  see  when  I  simulate

what  my  defect  rate  looks  like.

Looks  like  it's  at  zero  every  time I'm  clicking  this,  which  is  great.

I  also  want  to  see   what  happens  way  out  at  the  tails.

I  can  easily  do  that  by  using the  normal  weighted  distribution.

Let  me  turn  that  on  for  each  of  these.

This  is  a  way  to  check what  happens  to  the  tails.

Now  when  I  click  simulate,

it's  not  quite  zero  because  I'm  testing way  at  the  tails,  but  it's  still  very  low.

I'm  very  happy  with  this.

I  also  like  to  run  a  sanity  check for  capability,

and  I  can  easily  do  that  by  using the  Simulate  to  Table  option,

which  is  going  to  simulate  using the  normal  distribution

for  my  critical  process  parameters and  the  prediction  models  with  the  error,

the  same  error  I  used  before.

I  click  Make  Table, I  get  a  simulated  table

and  it  has  a  save  distribution  script  that  if  I  run,

will  automatically  open  up  capability

because  I  saved  my  spec  limits   as  column  properties.

When  I  check  these  capability  reports for  the  three  critical  quality  attributes,

it  looks  very  good.

Of  course,  this  is  simulated  data, so  you  want  to  check  it  on  real  data,

but  I'm  pretty  happy  with  what  I'm  seeing about  my  design  space  right  now.

I  want  to  save  this  design  space,

and  you  can  easily  do  that  by  going to  the   design space profiler  menu

and  checking  Save  X  Spec  Limits, and  this  will  save

these  factor  limit  settings  back to  the  original  data  table

as  spec  limits  in  your  critical   process  parameter  columns.

I  want  to  click  that  and  I  go

back  to  my  original   data  table  just  back  here.

Close  these.

Okay,  there  it  is.

When  I  get  back  to  my  original  data  table, you  can  see  that  these  spec  limits

have  been  saved  to  my  critical process  parameter  columns.

This  is  a  great  way  to  save  this information  if  I  save  the  data  table.

It's  also  nice  because  if  I  do  that and  I  save  my  predictions  as  formulas,

I  can  look  at  the  design  space in  terms  of  the  contour  profiles.

I  can  do  that  by  using the  graph  contour  profiler.

I've  already  gone  ahead and  saved  a  script  for  this.

I'm  going  to  run  it  and  I  have  it  set  up to  show  the  contour  profilers

in  terms  of  all of  my  critical  process  parameters.

You  can  see  this  faint  rectangle  is my  design  space

and  the  shaded  contours or  the  contours  are  my  spec  limits.

You  can  see  how   my  design  space  is  well  within...

It's  well  within  my  spec  limit  contours.

I  have  that  nice  buffer   because  I  added  the  error,

so  I  can  look  at  that  in  terms of  all  of  my  critical  process  parameters.

I'm  very  happy  with  this  design  space.

Let's  go  ahead  and  look at  a  different  example.

Okay,   this  is  an  example

that's  outside  of  the  realm of  the  pharmaceutical  industry.

It's  a  polymer  manufacturing  study,

and  the  goal  of  this  study  is  to  improve the  quality  of  their  white  polymer.

I  wanted  to  use  an  example  to  show

that  these  methods  can  be generalized  in  any  industry.

It  doesn't  have  to  be  pharmaceutical.

This  example  was  inspired

by  an  example  that's  in  the   Visual  Six Sigma  Second  Edition  book  that  uses  JMP.

It's  a  great  book. It's  in  my  references.

I  highly  recommend  you  check  it  out if  you  haven't  ever  looked  at  it.

They  want  to  improve  their  white  polymer

and  they  figured  out  that   they  had  two  critical  quality  attributes:

melt  flow  index  and  color  index.

These  are  the  spec  limits  which  will ensure  quality  for  the  white  polymer.

They  ran  experiments  to  figure  out which  process  parameters

affected  these  critical   quality  attributes.

There  were  three  of  them,

Amps  for  slurry  tank  stirrer,

viscosity  modifier percent ,   and  percent  of  filler.

These  were  the  initial factor  limit  settings.

Another  thing   that  was  different  about  the  study

is  that  they  used  historical  data

to  find  prediction  models for  their  critical  quality  attributes

in  terms  of  their  critical process  parameters.

They  used  two  different  platforms and  two  different  types  of  models

for  these  critical  quality  attributes.

They  used  generalized  regression  platform

and  the  Lasso  method  to  find   a  model  for  the  melt flow  index,

and  they  used  the  fit  neural  platform

to  find  a  neural  model   for  the  color  index.

Because  they've  used   two  different  platforms

and  two  different  types  of  models, they  need  to  use  the  profiler  platform

that's  underneath the  graph  menu  in  JMP.

To  use  that,  you  need  to  save your  models  as  formula  columns.

I  want  to  show  you  how  you  can  still  use

the  Prediction  Profiler  platform to  use  the   design space profiler.

Let's  go  back  to  JMP.

I'm  going  to  open  up  the   polymer  data.

This  is  historical  data.

I've  got  my  two   critical  quality  attribute  columns,

my  three  critical process  parameter  columns.

I've  gone  ahead  and  saved the  spec  limits  as  column  properties,

and  these  are  my  two  models.

This  is  the  model  I  created with  generalized  regression.

This  is  the  model  I  created  with  neural.

I've  gone  ahead  and  saved

both  of  these  models   to  the  table  as  formulas.

I've  also  saved the  Prediction  Profiler  platform  script,

which  I'm  going  to  run,

and  you  can  see  this  is  my  Prediction Profiler  in  terms  of  these  two  models.

The   design space profiler,  once  again,

I  go  to  the  Prediction  Profiler  menu, turn  on  the   design space profiler.

It's  slightly  slower  here  just  because  I'm using  formulas  and  I  have  a  neural  model.

But  once  again,   it  opens  up  and  it  shows  me  that

with  the  initial  factor  limit  settings, my  in-spec  portion  is  about  65 %.

It  looks  like  what  I'm  going  to  want to  do  is  I'm  going  to  want  to  decrease

the  upper  limit  of  my  XF  factor critical  process  parameter.

Indeed,  if  I  click  move  inward,

see  how  my  in-spec  portion  is  going  up by  decreasing  the  XF  upper  factor  limit.

I  want  to  see  if  I  can  get  to  100 %.

If  I  can  get  there   and  have  reasonable  factor  limits,

see  what  things  look  like  if  I  keep  heading  for  that.

Okay,   I've  gone  to  100 %.

My  factor  limits  on  XF  are  a  little  tight,

so  let's  see  what  this  looks  like in  the  prediction  profiler.

I'm  going  to  send  a  midpoint  up  there.

I  think  it  still  looks relatively  reasonable.

But  one  thing  I  wanted  to  point  out  is

if  you  do  end  up you're  not  happy  with  things,

you  can  actually  also  use  this  design space  profiler  to  do  what  if  scenarios,

if  it  were  realistic  to  be  able   to  change  your  spec  limits,

let's  say  you  were  able to  make  them  wider,

or  what  if  your  consumer  demands   that  they're  tighter?

You  can  check  out   what  if  scenarios  as  well

by  changing  these down  here  in  these  fields.

But  in  this  case,  I  think  I'm  pretty happy  with  this  design  space.

I  think  it  will  work.

I'm  going  to  go  ahead  and  save  the  spec limits  to  the  original  data  table.

See,  they  got  saved  here.

Once  again,  I've  saved  a  script for  the  contour  profiler.

I'm  going  to  run  that  really  quickly.

Once  again,  I  can  see  my  design  space   in  terms  of  my  contours.

That's  the  faint  rectangles  here, and  the  shaded  regions  are  my  spec  limits.

I  could  see  how  the  design  space   is  well  within  my  specs,

so  I'm  pretty  happy  with  this.

Let's  go  back  to  PowerPoint  just to  give  you  some  takeaways.

Okay,   some  quick  takeaways about  the   design space profiler.

First  of  all,  the  in-spec  portion  that's reported  in  the   design space profiler,

those  values  should  not  be  considered probability  statement  unless  you  think

that  your  critical  process  parameter factors  follow  a  uniform  distribution

within  the  limits  because  that's  what's being  used  to  create  that  statement  there.

Also,  the   design space profiler   is  not  meant  for  models

that  have  large  number  of  factors   or  very  small  factor  ranges,

and  that  is  because  of  the  simulated nature  of  the  approach  it  takes.

It's  also  recommended,  as  I  mentioned a  couple  of  times  in  my  talk,

to  always  use  random  error for  your  prediction  models,

for  your  responses  because   your  models  are  not  without  error.

Finally,  finding  a  good  design  space   is  applicable  to  more  than  just

the  pharmaceutical  industry, even  that's  where  the  idea  came  from.

That  second  example   was  just  to  demonstrate

how  it  can  be  used  in  any  industry

where  you  care  about  having   a  robust  process  in  maintaining  quality.

These  are  my  references, and  here's  contact  information.

I  wasn't  able  to  show  you  everything  about the  design  space  profiler,

so  I  hope  that  you  will  check  it  out.

If  you  have  any  questions   or  if  you  have  any  feedback,

please  contact  me.

Thank  you  so  much.