Choose Language Hide Translation Bar

Generating and Evaluating Lot Acceptance Sampling Plans using JMP® (2023-EU-30MP-1315)

In a regulated environment, systems are put in place to ensure product safety, efficacy, and quality. Even though ‘You cannot inspect quality into a product.’, as Harold F. Dodge said, the CFR - Code of Federal Regulations, 21CFR820.250(b) states, “Sampling plans, when used, shall be written and based on a valid statistical rationale.” Lot acceptance sampling plans (LASP) provide the statistical rationale and have been used in many industries. Practitioners, however, usually rely on the tables in ANSI/ASQ Z1.4 (attributes) and Z1.9 (variables). Since the operating characteristic (OC) curve is the best way to evaluate and compare lot acceptance sampling plans, an add-in was needed to facilitate this process. The evolution of appropriate sampling plans within the biotech or medical device industries that balance the customer design requirements and technology opportunities lead us to develop an interactive JMP Add-in for designing and evaluating valid lot acceptance sampling plans for attributes and variables. During this highly interactive session using JMP, we will demonstrate how to use the add-in to efficiently design and evaluate lot acceptance sampling plans by showcasing its flexibility and ease of use.

 

 

Live  from  100  SAS  Campus  Drive, your   one  and  only  SAS  world  headquarters  in  Cary,  North  Carolina.  It's   The   Sampling  Plan  Show   starring  Stan  Koprowski.   Now  here,  he  is  the  host  of   The  Sampling  Plan  Show ,  Stan  Koprowski.

Thank  you.  Thank  you  very  much.  You're  too  kind.   Thank  you.  We  love  you.  No, that's enough.  Please.  All  right,  we  have  a  great  show  for  you  today.  Before  we  get  started,  just  a  little  background  here.  I  wasn't  very  good  at  statistics.  In  fact,  I  got  a  paper  cut  from  my  statistics  homework.  What  are  the  odds?  Enough  of  that.

Today  we're  going  to  talk  about  acceptance  sampling  and  sampling  plans.  We're  going  to  learn  about  the  OC  curve  and  what  it  is.   I'll  be  honest,  this  is  one  of  my  all  time  favorite  ANSI  standards.   We're  going  to  hear  about  the  ANSI  standards.  We'll  make  some  predictions  for  the  big  sampling  plan,  and  then  finally,  we'll  show  you  some  fantastic  highlights  using  the  JMP  sampling  plan  added  with  one  of  my  all  time  favorite  industrial  statisticians,  Dr.   José Ramirez.

I'm  glad  to  be  here.  Proud  of this  show.  I   think  it's  going  to  be  fun.  S orry  to  hear  about  statistics  being  hazardous  to  your  health  with  a  paper  cut.  Man.

It  was  a  rough  journey  there,  but  we'll  get  through  it.  As  you  see,  here's  the  title  of  our  talk,  and  then  I  will  play  some  other  slides  here  for  you.  Your  book,  I  like  this  book.  We  use  this  a  lot  in  the  division.   The  Statistical  Quality  Control  book:   The  JMP  Companion .  This  is  the  companion  book  to  Doug  Montgomery's  book.  I  think  you're  going  to  mention  Doug's  book  later  in  the  talk  as  well.

That's  true.

Then  I  have  your  other  book  up  here  too,   Analyzing  and  Interpreting  Continuous  Data  Using  JMP .  I  know  you've  been  a  long  time  user  of  JMP,  probably  back  since   JMP  two.   I  think  you  were  probably  one  of  the  first  support  cases  that  came  into  tech  support  with  their  own  director  of  customer  enablement,  Jeff  Perkinson.  Jeff,  as  we  all  know,  started  out  in  tech  support  and  I'll  have  to  look  back  through  the  cases.  But  what  I  understand,  you  were  a  long  time  user  of  JMP.

Welcome  to  our  show.  I'm  glad  you  could  be  with  us  today.  Super  excited  to  have  you.   We're  going  to  talk  about  some  options  here  for  the  folks  to  call  in.  If  you  want  to  call  into  the  show  or  message, you can  message us  at  JMP L ot  Plan.  The  phone  number,  if  you  have  a  rotary  dial  phone,  you  can  call  us  up  there,  or  if  you  want  to  reach  us  on  Instagram  at  JMP  Lot  Acceptance  Sampling  Plan.  Let's  go  ahead  and  see.  I  think  I  do  hear  a  call  again.  Wait  a  minute. Let me  see  who  that  is.

Yes,  this  is  Dr.  Julian  Parris  calling  in.  I'm  the  Director  of  JMP User  Acquisition  and  I  have  a  question  for  Dr.  Ramirez.

Go  ahead,  Julian.

Dr.  Ramirez,  can  you  explain  the  difference  between  lot  acceptance  sampling  plans  and  variables  acceptance  sampling  plans?

I  don't  really  believe  that  was  Julian.  That  was  probably  Julio  from  down  by  the  school yard. Julio,  do  you  have  a  question?

Yes,  he  did.  He  was  asking  if  you  could  give  us  a  little  introduction  to  sampling  plans.

Sampling,  okay .  He's  doing  some  sampling  by  the   schoolyard.  I  wonder  what  he's  doing  there.  Julio,  since  you're  in  a  school,  you're  by  the   schoolyard,  let's  go  back  to  the  dictionary  and  look  at  sampling,  what  the  dictionary  says.  There  are  a  few  definitions  here  in  the  dictionary,  and  one  thing  I  like  about  the  first  one  it  talks  about  a  suitable  sample.   For  statisticians  that  has  the  meaning,  part  of  that  is  there,  the  sample  has  to  be  representative.   For  those  of  you  familiar  with  stats,  the  other  piece  that  we  also  include  in  a  definition  of  suitable  sample  is  random.

But  what  you're  talking  about,  about  these  sampling  plans  is  the  second  definition,  and  they  got  it  right  because  a  sampling  plan  is  essentially  deciding  on a  small  portion  of  a  lot  or  a  population.  The  population  can  be  either  infinite  or  it  can  be  a  finite  number  like  10,000  items.   We  want  to  take  a  small  sample  from  that  so  we  can  do  some  inspection.   By  inspection,  we  mean  that  we  are  going  to  decide  the  fate  of  that  population  or  the  fate  of  that  lot.

Okay,   I  understand  a  little  bit  of  what  you're  saying  there.   You're  going  to  take  a  sample  from  a  population  and  then  what's  the  difference  between  the  sample  types?  It  looks  like  you  were  talking  here  about  an  inspection.  Is  it  always  an  inspection  or  are  there  other  types  of  sampling  that  you  can  do?

Well,  in  general,  when  people  think  about  lot  acceptance  sampling  plans,  there's  some  type  of  inspection,  some  type  of  checking  that  goes  on.  T he  way  we're  going  to  do  this  sampling  is  we're  going  to  apply  some  statistical  principles  [crosstalk 00:06:22].

Oh, gosh, that's scary.

But  actually  that's  what  the  agencies  want.  For  example,  if  you  look  at  some  of  the  documents  from  the  FDA,  if  you're  required  to  do  some  type  of  sampling,  they  want  you  to  do  it  in  a  statistical  way.   How  are  we  going  to  do  that?  That's  part  of  this  show  that  we're  having.  But  in  the  old  days,  and  we're  going  to  talk  about  those  old  days,  people  used  standards,  and  those  are  the  standards  that  are  used  right  now.  The   ASQ/ANSI  Z1.4  and  Z 1.9.

That  sounds  even  scarier,  but  I'm  a  bit  confused.  I  thought  when  I  was  doing  my  research  before  I  brought  you  on  as  a  guest,  that  there  were  some  military  standards.  I  thought  the  sampling  plans  were  based  on  military  standards  and  now  you  just  told  me  there's  some  other  standards  in  play  here.  W hat's  the  story  with  this?

Well,  yeah,  that's  true.   These  sampling  plans  have  a  long  history.  They  go  back  to  probably  the  1930s,  1940s,  and  there  were  two  military  standards,  the  105 E,  which  is  the  one  that  corresponds  to  the  Z 1.4,  and  that's  what  you're  doing  using  a  technical  term,  sampling  by  attribute,  and  then  there  is  the  military  standard,   414,  which  is  the  Z 1.9  that  corresponds  to  sampling  by  variables.  You  can  think  of  discrete  versus  continuous.

What  happens  is  that  those  standards  were  taken  over  now  by  the  American  Society  for  Quality,  that's ASQ,  and  the  American  National  Standard  Institute,  the  ANSI,  and  they  rebranded  those,  and  now  they're  called  Z 1.4  and  Z 1.9.  But  they're  still  the  same  standard,  the  same  table  that  people  use  to  generate  sampling  plan.

L et's  talk  about  how  we  do  that.   The  way  to  understand  this  is  that  every  type  of  lot  acceptance  sampling  plan,  and  that  is  the  L-A-S-P  or  LASP,  has  components  and  risks.  T he  components  of  the  plan  essentially  is  how  many  samples  do  I  need  to  take  from  a  population  of  10,000  or  infinity  that  I'm  going  to  test?  I'm  going  to  do  some  inspection,  and  I  want  to  know  if  in  that  sample,  there  is  a  pre- specified  percent  defective.

We're  going  to  define  quality  as  a  percent  defective  in  the  population.   What  we're  doing  is  taking  a  sample  to  see  if  that  sample  contains  that  or  less.   In  order  to  determine  if  we're  going  to  pass  or  fail  that  lot,  we  also  relied  on  the  acceptance  number,  which  tells  us  how  many  defective  parts  out  of  the  sample  we  can  accept  in  the  plan.  Anything  that  is  greater  than  that,  it's  going  to  say  we're  going  to  reject  or  fail  the  lot.  That's  why,  as  I  said  before,  we're  determining  the  fate  of  the  lot  with  this  [inaudible 00:10:03] .

Here  we  go.  I  had  my  fate  a  long  time  ago  with  that  paper  cut.  I'm  a  little  anxious  here.  What  kind  of  fate  are  we  talking  about?

Yeah,   we're  going  to  decide  if  we  are  going  to  pass  the  lot  and  make  it  available  for  whatever  purpose  that  lot  is  being  manufactured,  or  we're  going  to  put  it  in  quarantine  [inaudible 00:10:31]   and  maybe  do  some  more  inspections  or  trying  to  understand  why  the  fraction  defective  is  larger  than  the  prespecified  one.

You  mentioned  that  there's  some  risk  involved.  What  kind  of  risk?  Is  it  out  of  my  control  or  is  it  within  my  control?  Whose  risk  is  this?

Yeah,  there's  risk,  and  that's  the  beauty  about  my  profession.  In   statistics,  you  don't  have  to  be  certain  about  anything.  I  can   95%  confident.  I  can  even  go  up  to  99%  confident,  I  don't  have  to  be  certain.   Again,  for  those  of  you  familiar  with  statistics,  you  know  what  we're  talking  about.   There's  the  chance  that  there's  a  perfectly  good  lot  that  we're  going  to  reject  because,  again,  we're  taking  a  small  sample,  so  we're  not  sampling  the  whole  population.   There's  a  risk  associated  that  this  sample  may  determine  that  a  good  lot  is  not  good  or  there's  a  chance  that  a  bad  lot  may  be  released.  Y ou  can  think  in  terms  of  false  positive.  Y ou  think  in  terms  of  a  medical  test.

That's  similar  to  like  if  you  were  to  take  the  COVID-19  test.  If  you  actually  had  it  and  it  came  back  negative ,  is  that  a  false  positive?

Yeah,  it's   like  that,  a  false  positive.   We  may  have  a  false  positive  that  means  this  lot  is  bad,  but  the  sampling  plan  that  it  was  good.  Or  vice  versa,  we  have  a  good  lot  and  we're  going  to  reject  it  because  the  sampling  [crosstalk 00:12:19] .  That's  why  it's  important  to  use  a  statistical  principle  in  designing  these  sampling  plans.  That's  part  of  why  people  use  standards.  Those  were  derived  in  a  way  that  when  you  select  a  plan  from  those  standards,  these  risks  are  going  to  be  balanced.   That's  what  we  talk  about  the  generation  of  the  lot  acceptance  sampling  plan.

We  have  these  two  risks.  Again,  we  can  say  that  a  good  lot  is  going  to  be  rejected  and  there's  also  a  chance  that  a  bad  lot  may  be  released  like  the  false  positive.   We're  going  to  assign  some  probabilities  to  this  risk.   One  thing  we  want  to  make  sure  is  that  if  it's  good,  we  want  to  accept  that  most  of  the  time.   How  do  we  define  that?

Well,  standard  practice  is  used  95%.  A gain  that  sounds  like  95%  confidence  when  you  use  some  type  of  statistical  test.   What  we're  saying  is  we're going  to  pre define  a  fraction  defective  for  that  lot  and  we  are  going  to  select  a  plan  that  guarantees  that  or  almost  guarantees  that  95%  of  the  time,  a  good  lot  is  going  to  be  accepted. A  good  lot  is  going  to  pass.

On  the  other  hand,  we're  going  to  also  say  that  we're  going  to  have  a  high  chance  of  rejecting  a  bad  lot.  Or  if  you  flip  that,  you  can  say  there's  a  small  chance  of  passing  a  bad  lot.   90%  here  transforms  itself  to  a  10%.   We're  saying  there's  a  95%  of  accepting  a  good  lot,  but  only  a  10%  chance  of  accepting  a  bad  lot.   Those  are  standard  numbers  in  sampling  plans,  in  the  standards  and  the  way  people  use  those  sampling  plans.

You  were  talking  about  the  user.  The  user  has  the  option  of  changing  those  numbers.   Rather  than  use  95%,  we  can  use  99%.  Rather  than  using  10%,  we  can  use  5%.  However,  if  we  get  too  greedy,  then  as  some  of  you  may  know,  the  sample  size  is  going  to  increase  and  that's  part  of  that  balance.  We  want  to  find  a  sample  size  that  is  small  enough  that  it's  going  to   guarantee  these  probabilities.

Should  we  do  some  examples?  Are  there  things  we  could  do  to  explain  some  of  the  balance  that  you're  talking  about  between  these  two  competing  risks?

Yes.

It  sounds  like  one  might  be  on  the  consumer  side,  and  maybe  one  of  the  risks  is  on  the  producer's  side.

Exactly.   The  first  chance  of ...  If  you  look  at  the  95%  chance,  that  means  there's  a  5%  chance  that  a  good  lot  is  going  to  be  rejected.  That's  on  the  producer  side.   Because  as  a  producer,  you  don't  want  your  good  lot  to  be  rejected.  The   loss  of  material  or  good  product.

On  the  other  hand,  the  10%  chance  of  accepting  a  bad  lot,  that's  on  the  consumers  because  we  don't  want  the  consumers  to  receive  something  that  is  bad.  Now,  in  order  to  do  this,  there's  this  tool  that  we  use  in  sampling  plans  which  is  called  the  operating  characteristic  curve  or  OC  curve.  Some  people  may  be  familiar  with  that.   Those  curves,  I'm  going  to  show  you  some  examples,  are  the  ones  that  are  used  to  find  that  balance  between  this  risk  and  probability.  Risk  and  probability.

What  is  an  OC  curve?  An OC  curve  is  essentially  a  plot  that  shows  you  the  probability  of  accepting  a  lot  as  a  function  of  that  fraction  defective  in  the  population.   You  look  at  these  two  curves,  the  blue  line  here  on  the  Y- axis,  we  have  the  probability  of  accepting  the  lot,  and  the  X- axis,  we  have  the  proportion  defective  in  the  population.

As  you  can  see,  when  the  proportion  defective  is  very  small,  there's  a  high  probability  of  accepting  the  lot.  A s  soon  as  that  probability  starts  increasing,  then  the  probability  of  accepting  that  lot  decreases,  and  that's  the  shape  that  we  want  to  see  in  an  OC  curve.

Now,  remember  we  have  two  probabilities  and  two  risks.   We  want  a  95%  chance  of  accepting  a  good  lot  and  a  10%  chance  of  accepting  a  bad  lot.  Now,  the  definition  of  good  and  bad  is  in  terms  of  that  proportion  defective  in  the  population.   We  as  users  of  sampling  plans,  we  have  to  define  what  is  a  good  fraction  defective.  Of  course,  ideally,  the  good  fraction  defective  should  be  zero,  but  that  will  throw  a  [inaudible 00:17:22]   in  the  math.  If  you  know  that  zero  divide  by  zero,  you  get  infinity,  meaning  you  have  to  sample  everything  if  you  want  perfection.   What  we  do  is  define  a  small  number,  and  that  is  called  the  AQL,  the  acceptable  quality  level.

On  the  other  side,  we  define  the  RQL  or  rejectable  quality  level.  Granted,  there  are  many  terms  that  people  use.  Sometimes  you  may  see  the  LTPD  instead  of  RQL.  That's  the  lot  tolerance  percent  defective,  the  maximum  percent  defective  that  you  can  accept  in  your  population.   With  the  probabilities  and  those  fraction  defectives,  you  define  two  points  in  this  curve.  H ere,  the  AQL  is  1.8%,  and  we  have  a  95%  probability  of  accepting  that.

What  that  means  is,  as  long  as  the  fraction  defective  in  the  lot  is  less  than  2%,  let's  say,  then  there's  a  high  chance  of  accepting  that  lot.  But  as  long  as  it  goes  higher,  like  2%,  then  we're  going  to  accept  that  lot  very  infrequently.   These  two  points  are  the  ones  that  you  look  at  in  the  OC  curve,  and  those  are  the  ones  that  are  going  to  determine  the  sample  size  and  the  acceptance  criteria.

Got  it.

I  think  it  will  help  Julio  if  we  run  some  example.

I  think  Julio  is  texting  and  he  said  that  would  be  great  if  we  could  do  an  example.  Okay,  let's  do  that.  Why  did  you  develop  or  why  did  we  produce  a  JMP  add-in?

Yes,  Julio,  what  we're  going  to  do  is  we're  going  to  show  you  an  app  to  do  this.   People  sometimes  ask  us,  "Why  did  you  do  this?  Why  do  you  spend  a  lot  of  time  for  writing  code  and  package  it  in  an  add- in?"  Well,  to  tell  you  the  truth,  [crosstalk 00:19:30] .

That  is  really  tiny.  I'm  going  to  have  to  get  a  new  set  of  readers  or  a  giant  magnifying  glass.  Is  that  really  how  people  do  this?

Now  it may  seem  weird,  but  still,  I  believe  in  some  industry,  people  may  use  a  standard.  Granted,  it may  not  be  the  old  book  that  they  use,  maybe  a  pdf,  but  sometimes  they  still  use  this.  But  these  are  very  tedious  and  they're  discreet  in  the  sense  that  they're  just  approximations  to  the  plans.

T here's  a  process  to  do  that.  Of course, there  are  multiple  tables  that  you  have  to  go  through  in  order  to  find  the  appropriate  sample  size.  W hat  we  wanted  to  do  is  make  our  life  easier,  actually,  because  to  be  truthful  here,  we  use  sampling  plans.  We're  also  tired  of  using  these  tables.  So  we  wanted  to  automate  the  generation  of  the  LASPs.

Okay,  got  it.  What  else  do  we  need  to  know  before  we  do  some  examples?

This  is  JMP,  which  is  one  of  the  greatest  pieces  of  software  out  there  for  doing  statistics  and  getting  insights  out  of  your  data.  A nother  thing  that  we  did  is  that  not  only  we're  automating  the  generation  of  the  plans,  making  life  easier,  but  we're  using  all  the  visualization  tools  in  JMP,  like  the  profilers,  to  understand  these  OC  curves.  Remember,  we  just  showed  you  that  the  way  we  determine  or  generate  the  plans  is  via  an  OC curve.  The  OC curve  is  also  very  important  to  evaluate  plan.  How  do  we  know?  If  someone  gives  us  a  sampling  plan,  how  do  we  know  if  that's  good?  T hat's  part  of  this.

Let's  look  at  an  example.  T his  comes  from  Professor  Montgomery's  book.  A gain,  here a  shameless  PR  for  us.  We  wrote  a  companion  book.  You  saw  that  book  at  the  beginning  for  this.  It's  called   JMP  Base .  I f  you  look  at  this  figure,  this  is  in  chapter  15, P rofessor  Montgomery  also  shows  another  approximation.  It's  another  way  of  generating  sampling  plan,  which  is  using  a  nomo graph.  A  nomo graph  is  this  figure  that  you  see  here.  Here,  you  have  to  figure  out  what  your  AQL  and  RQL  are,  the  probabilities,  and  that  you  have  to  go  in  there  and   approximate  that.

Here,  they  give  you  an  example  where  they  say  the  acceptable  quality  level  is  2%  or 0.02 ,  the  rejectable  quality  level  is  8%  or 0.08 .  The  probability  of  accepting  a  lot  that  has  an  AQL  of  2%  of  less  is  0. 95.  As  we  say,  that's  high.  T he  probability  of  accepting  a  lot  that  has  RQL  of  8%  or  more  is  only  10%.  A gain,  these  0. 95  and  0.1  are  our  standard  value  in  industry.

Y ou  notice  this  diagram  here,  they  put  the  0.02,  they  draw  a  line  here  to  intersect  the  0. 95.  The  0.08  intersects  at  that,  and  then  you  intersect  those  two  lines  and  you  guess  at  that.  Okay,  that's  a  93  plan.  Meaning,  out  of  an  infinite  population,  you  take  90  samples,  you  inspect  them  all,  and  you  can  accept  up  to  three  defectives.  If  you  see  more  than  three  defectives,  you  reject  the  lot.  If  you  see  three  or  less,  then  you  accept  the  lot.  T hat's  sampling  plan.  A  little  cumbersome  too .

Yeah,  it  looks  a  little  difficult  to  line  up  exactly.   I  hope  we  could  get  away  from  doing  that  with  the   add-in.

Well,  let's  show  Julio  how  we  can  do  that  with  JMP.

Okay,  sounds  like  a  good  idea.  All  right,  Julio,  let's  jump  over  to  some  examples  here.  H ere  is JMP  and  to  get  to  the   add-in,  you  just  go  to  your   add-in,  JMP  Sampling  Plans,  and  let's  look  at  attribute  sampling  plans.  T hen  this  particular  one,  we're  going  to  do  just  a  single  lot  acceptance  sampling  plan.  W e  have  the  menu.

After  we  make  that  choice,  it  comes  up  and  it  gives  us  three  options.  We  can  evaluate  an  attributes  plan,  we  can  generate  or  create  an  attributes  plan,  or  we  can  compare  plans.  The   add-in  gives  us  the  ability  to  compare  up  to  five  different  plans.  There's  an  option  to  keep  the  dialogue  open  in  case  you  want  to  look  at  more  than  one  plan.  L et's  go  ahead  and  generate  that  plan  that  you  were  just  sharing  here  from  Dr.  Montgomery's book.

I'll  give  you  the  numbers.  Let's  see.

All  right.

This  is  the  interface. [inaudible 00:24:51] AQL.

Right. Y ou  have  the  couple  of  different  sections  in  the  interface.  You  get  to  put  in  your  quality  levels,  your  probabilities,  and  then  you  have  the  optional  area  about  the  type  of  lot  sampling  you're  going  to  do.  T hat  lot  sampling  is  based  on  a  distribution.  S o  we  could  either  do  a  hypergeometric  distribution  or  a  binomial  distribution.

Lets put Montgomery's  numbers  there.  The  AQL in  Professor  Montgomery's  book  is  0.02  or  2%.  The  RQL  he  has  is  0.08.

All  right.

Oh,  they're  pre- populated.  Yes,  those  are  the  standard  values, 0.95.

The  standard  values.  So  we  keep  the  default  there.   I  think  you  told  me  there  was  no   theoretical  lot  size  here.  So  we're  going  to  do  type  B.

Actually,  in  Montgomery's book,  it  says  that  he's  using  a  binomial  nomograph,  so  it's  meaning  he's  using  the  binomial  distribution.  So  yes,  that's  the  right  choice.

Then  all  we  have  to  do  is  hit  okay,  and  then  what  happens?  JMP  gives  us  this  curve  here  and  an  output  window  and  a  report.  T here's  three  sections  to  the  report.  You  get  a  little  at  the  top  of  summary,  you  get  a  summary  of  the  plan.  I t  shows  you  your  input  parameters  and  then  what  the  plan  generated  as  a  sample  size  and  acceptance  number.  T hen  it  gives  you  some  information  on  how  to  interpret  the  plan.

That was helpful.

O ut  of  the  plan  recommendation  here,  of  the  98  samples,  it  says  you  can  accept  the  lot  here  as  long  as  the  number  of  defectives  is  less  than  or  equal  to  four  out  of  that  98  sampled.  O therwise,  you  reject  it  if  it's  greater  than  that.  T hen  it  tells  you  some  additional  information  there.  I f  we  look  at  that  OC  curve,  I  think  this  is  what  you  were  showing  us  earlier.

Yes.

So  we  have  a  probability  at  95%  and  the  quality  level  of  2%.  But  if  I  recall,  you  told  me  in  the  literature  that  this  was  a  plan  of  90 and 3.  So  I'm  confused  again  here  or, should I say, Julio texted  me  and  said  he's  confused.  How  is  it  different  here? Or  why  is  this  different?

We're  getting  98  and  4.   Professor  Montgomery,  in  his  book,  he's  showing  the  nomo graph  and  he's  getting  90 and 3.  Let  me  go  back  there  just  1  second.  R emember,  what  we're  using  is  this  graph  here  where  you  have  all  these  approximations.  You  have  a  line  that  goes  200,  300,  you  go  between  70 and 100.

Got  it.

There's  not  really  a  93  or  94,  anything  like  that.  A s  I  say,  you  had  to  approximate  these.  T his  nomog raph  is  just  an  approximation.  What  we're  actually  trying  to  do  is  solve  these  equations  for   those  of  you  mathematically  inclined.  The  one  minus  alpha  is  the 0. 95,  the  beta  is  the 0.10 ,  p1  is  the  AQL  and  p2  is  the  RQL.  I f  we  put  all  those  four  things  in  here  and  we  solve  these  equations  to  try  to  find  the  minimum  n  that  satisfied  those  four  things. W hen  you  do  that,  actually, software  does  that  for  us,  the  code  that  we  wrote,  we  get  the  98  and  4.

I  get  that.

The  moral  of  the  story  here  is  that  the  nomograph  gives  approximate  lot  acceptance  sampling  plan  again,  because  it's  just  an  approximation  game.  T his  is  again  one  of  the  advantages  of  using  the   add-in,  because  you  get-

Sampling plan add-in,  of  course.

-more  exact  sampling  plan.  Y ou  show  that  we  can  evaluate  a  sampling  plan.  L et's  do  that.  Why  don't  we  evaluate  this  plan,  the  93?  Show us ho w  to  do  that.

Since  I  left  that  window  open,  we  don't  have  to  go  back  to  the  menu  again.  L et's  evaluate  a  plan  now.  W e  have  in  that  interface,  again,  we're  going  to  put  in  our  previous  0.02, 2%,  and  I  think  he  told  me  the  RQL  was  8%.

Yes.

This  time,  though,  instead  of  a  sample  size  of  20,  we're  going  to  do  90  and  evaluate  three.  Again,  it's  a  binomial.

Here,  you're  entering  the  four  quantities  that  we  talked  about  in  the  generation,  but  you  also  enter  the  actual  sampling  plan  that  you  want  to  evaluate.

Exactly.  Now  when  I  say,  okay,  it's  going  to  look...  Sorry  about  that. I'll j ust  redo  that  quick.

[inaudible 00:30:31],  no?

Yes,  sorry.  I  want  to  evaluate  that plan,  you get 90 and 3.

Three, yes.

When  I  rerun  that,  we  get  the  exact  same  style  of  report,  but  the  information  is  slightly  different,  I  see  here.  I  noticed  also  down  in  this  table,  there's  some  color  coding  and  direction  of  the  arrows.

Yeah,  I see some  red  there.  I  see some  red,  yes.  That's  an  issue.

Is  this  an  indication  that  the  specified  quality  level  is  better?

Actually,  no.  I  think  that  the  reason  that  it's  red  is  because  what  happens  here  is  what  this  is  telling  us.  If  I   use  a  sample   size  90  with  an  acceptance  number  of  three,  you  can  see  the  associated  probability  of  acceptance  is  0. 89.  Remember,  we  wanted  that  to  be  0. 95.

So  it's  actually  lower.

It's lower and that's  why  that  is  red.  T his   add-in  is  giving  you  a  signal  that  your  probability  of  acceptance  is  less  than  the  one  you  specify  and  that's  an  issue.  T hat's  why  the  98 and 4  is  a  better  plan.  A lso  you  can  see  at  the  bottom  that  the  probability  of  acceptance  for  defective  lot  is  6%  rather  than  10%.  I n  that  case,  it's  blue  because  it's  better,  that  probability  is  better.  Y ou're  going  to  have  a  smaller  consumer's  risk.  You  can  see  that  the  n  is  6.47  versus  the  10. 67.  T hat  is  what's  happening.

That  producers  risk  is  really  just  the  difference  between  that  one  minus  the  associated  probability  of  acceptance  there?

Exactly.

Got  it.

Exactly.  T he  producer's  risk,  we  want  it  to  be  5%,  and  in  this  case, it's  10%.  No w  this  is  something  that  I  haven't  seen  in  any  other  software.  Normally,  what  you  see  is  the  plot  on  the  lot.  You  get  that  for  the  associated  AQL  and  all  that,  and  they  assume  that  the  probabilities  are  the  ones  that  you  specify,  but  they're  not.

W hat  the  add-in  does  too,  is  it  flips  things  around  and  says,  okay,  if  rather  than  fixing  the  AQL  and  RQL,  I  fix  the  probabilities,  I  want  to  be  95  because  that's  what  it  is,   I'm  neurotic  that  way.  I  want  it  to  be  95  and  0.1.  Then  what  are  the  corresponding  AQL  and  RQL  for  that?  T hat's  what  that's  telling  me.

Okay.   I  wasn't  really  just  seeing  double.  It's  really  a  different  calculation  on  the  right  hand  side. Got it.

What  that  says  is  if  the  probability  of  acceptance  peaks  at  0. 95,  then  the  AQL  is  not  2%  but  1.53%.

Okay, got it.

It  has  to  be  way  less  than  that.

So it's a... Okay,  go  ahead.

A lso  at  0.1,  then  it's  not  8%  but  7%.

Okay.  7.3%,  roughly.

That's  why  both  cases,  they  are  blue.  They  are  blue.  A gain,  just  very  quickly  here  to  show  this.  In  summary,  for  this  one  is  that,  again,  the  nomogram  gives  an  approximate  lot  acceptance  sampling  plan.  The  90  and 3  plan  shows  you  that  we're  not  hitting  that.

Are  you  sharing?

Yes,  I'm  sharing.

Okay.

Hopefully,  people  can  see  that.  Our  producers  risk  is  now  10%  versus  5%.  But  there  is  one  more  thing  that  you  had  there,  which  is  compare.   I'm  curious,  can  we  use  that?  I'll tell  you  tell  can  tell  you   what  I  want  to  do.  I  want  to  use  the  add-in  to  compare  the  planning  Professor  Montgomery's  book  of  '93  with  a  plan  that  the  add-in  gave  us,  which  is  98,  4

All  right.  W e  did  mention  that  we  can  compare  up  to  five  different  plans.  Y ou  want  me  to  compare  the  two  plans  that  we  just  created.  All  right. Again,  that  8%  RQL.  In  this  case,  we  had  a  90  and  an  acceptance  of  three.

Yeah.

Then  I  think  you  told  me  it  was  98  and  4.

That's  what  they  do.  I  didn't  tell  you.  That's what  the   add-in  gave  us.  Yeah.

Wow,  that,  that  is  pretty  slick.  A gain,  if  you  wanted  to  do  more  than  two,  you  would  just  check  the  additional  rows  and  then  the   add-in  will  calculate  up  to  five  different  comparisons  here.  I'm  going  to  go  ahead  and  click  OKay.  N ow  it  looks  a  little  bit  different,  Jose,  here.  Now  I'm  seeing  two  OC  curves.  I'm  getting  a  comparison  of  both  of  my  OC  curves  on  the  same  plot  I  see  here.

Exactly.  H ere  the  blue  one  is  the  plan  93 and he red line is-

T he  blue  is  the  93.  Yeah,  exactly.  I  see that.

The  red  line  is  the  98, 4 .  Y ou  can  see  that  the  red  line or  curve,  is  on  top  of  the  blue  curve.  T hat's  what  you  want  to  see.  You  want  the  curve  to  be  on  top,  literally.  T his  shows  you  that  you  have  higher  probabilities  of  acceptance  according  to  the  parameters,  the  IAQL  and  RQL  that  we  prespecified  with  the  plan  98, 4  than  with  the  plan  93.

T his  is  very  helpful  because  you  may  be  in  situations  where  you  may  get  an  approximate  plan  from  a  book  or  someone  may  suggest,  "Hey,  why  don't  you  use  this  plan?"  With  this  one,  you  can  compare  them  all  and  see  which  one  is  better.  I t's  easier  to  negotiate  the  sample  size  using  these  tools  than  just  getting  into  an  argument  and  say,  "No,  we  should  use  93  because  that's  in  the  book  or  something  like  that.

"I  think  that's  a  great  feature  to  be  able  to  compare,  and  that  way  you  move  the  discussion  into  some  actual  information  and  rather  than  subjective,  individuals  can  now  compare  directly.  Ag ain,  if  you  want  the  reference  lines,  it  didn't  make  sense  to  show  all  the  reference  lines  across  five  different  curves.

W hat  we've  done  is  we  could  just  display  a  single  set  of  reference  lines  by  toggling  the  filter,  and  it  will  update  the  graphs  for  you  as  you  toggle  between  them.  That  way,  if  you  do  want  to  see  that  individually,  you  could  do  that,  and  then  you're  just  focused  in  on  the  table  and  the  graphs  for  that  particular  set  of  observations. That's,  I  think,  a  nice  feature,  Julio.

It  is.

All  right. It's time for one more.  [inaudible 00:38:32].

I  think  that  Julio  is  probably  getting  tired  there.

He  is  very  exhausted.

Julio, there's  some  other  things  that  the  add-in  can  do.  So  maybe  it should  be  a  follow  up  to  this.

Maybe  we  could  do  another  session  for  Discovery  Summit  Japan  or  Discovery  Summit  China.

We'll  continue  showing.  [inaudible 00:39:05].

I  think  I'm  getting  breaking  news  coming  across  here.  Just  into  the  news  center  here  of  the  show.  A nyone,  it  looks  like,  can  get  that  sampling  plan   add-in.  If  you  just  go  to  the  JMP  user  community  and  search  for  the  sampling  plan   add-in,  you  could  download  it  yourself.

And that's free. No? That's free?

Absolutely  free.  We  would  never  charge  for  that  on  the  community.  G o  ahead  and  download  that.  If  you  have  feedback  or  you  run  into  issues,  feel  free  to  message  me,  and  we'll  get  those  defects  entered  and  get  a  corrected  version  out  there  as  soon  as  we  can.  Other  things  just  before  we  wrap  up  here,  I  just  want  to  say  thank  you  to  Jose.  Thank  you  for  joining  us  on  the  JMP  sampling  plan  show  today.  It  was   great  to  have  you  here.  Really  great.  T hank  you  again.