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  curve— we  have  a  legend  to  help  us— 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  like— and  I'm  happy  with  the  factor  limits,  I  think  it's  a  reasonable  operating  region— 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?