and  I  am a  Control  Chart  Developer  for  JMP .

I  am  here  today  to  talk  with  you   about  the  new  in  JMP  version  17

Laney  P '  and  U '  control  charts .

Let 's  review.

The  control  charts   are  intended to  show  the  stability  of  your  process .

If  your  process  is  not  stable , then  you  can 't  reliably  make  the  same  size

or  the  same  parts ,   and  customers  will  get  upset

and  not  want  to  purchase  from  you  again .

In  this  case ,  we 're  talking  specifically about  attribute  charts ,

which  are  based  either  on  the  Binomial or  the  Poisson  distribution ,

and  they  assume  a  constant  variance,

a  constant  variance  because   both  the  Binomial  and  the  Poisson

are  a  one  parameter  distribution .

You  got  one  parameter  for  the  mean and  then  manipulations  on  that

for  the  variance .

But  what  happens  if  your  variance   is  not  constant  over  time ?

When  you  have  a  non -constant  variance ,

in  other  words ,

if  you  have  more  variance  in  your  model or  in  some  cases ,  less ,

more  variance  in  your  model   than  you 're  currently  describing ,

that 's  referred  to  as  overdispersion .

One  parameter  model   cannot  model  overdispersion .

David  Laney  proposed   that  we  normalize  the  data

and  we  account  for  varying  subgroup  sizes , we  compute  a  moving  range ,

and  average  that ,   and  then  we  insert  that  into  our  model ,

into  our  limits  for  the  control  charts .

Let 's  take  a  look  at  this  in  JMP .

Let 's  keep  in  mind  this  assumption  is  that  for  the  regular  P  and  U  charts ,

we  have  this  assumption of  the  probability  of  nonconformity

is  the  same  for  each  sample .

In  other  words ,  we  have  assumption that  our  variance  is  constant .

Let 's  look  briefly  at  our  limits  formulas .

For  the  P  chart ,   it 's  the  average  plus  or  minus  3

times  our  standard  error and  the  same  with  the  U  chart .

Again ,  remember , we  have  this  one  parameter .

There 's  not  much  that  we  can  do if  our  limits  are  not  constant  here

or  if  our  variance  is  not  constant .

What  do  we  do  if  we  have  overdispersion ?

This  is  the  big  question .

What  Laney  proposed was  basically  we  standardize  our  data ,

we  take  the  moving  range , we  compute  an  average  moving  range ,

and  then  we  adjust  that and  form  a  sigma  sub  Z .

These  limits  that  Laney  is  proposing look  very  similar  to  the  other  limits .

We  were  just  inserting  the  sigma  sub  Z into  the  formula

right  before  the  standard  error for  both  the  P  charts  and  the  U  charts .

Let 's  take  a  look  at  an  example .

I 'm  going  to  start  with  a  data  set from  the  JMP  sample  data  folder .

We  have  lot  sizes that  are  not  terribly  large .

F or  our  first  example , let 's  look  at  this  one .

I 'm  going  to  go  through the  interface  for  this  first  one .

We 'll  use  dialogs  for  future  ones .

We  have  the  number  of  defective washers  that  we 're  going  to  model .

I 'm  going  to  change the  chart  type  to  attribute .

Before  we  go  to   Poisson ,  I  have  my  lot as  my i dentifier  for  our  X -axis ,

and  we 're  just  going  to  use the  constant  lot  size  of  400 .

Drop  that  in  the   n Trials  drop  zone .

Now ,  Laney 's  charts  are  only  available when  our  statistic  is  proportioned ,

so  I  have  to  change  that   back  to  proportion .

When  the  statistic  is  proportion ,   then  we  have  four  choices

for  our  sigma  value .

I 'm  going  to  choose  Laney  P '. But  first ,  let 's  take  a  look  here .

We  see  we  have  two  points  out  of  control on  this  P  chart,

which  is  indicating  to  us   that  this  is  not  a  stable  process .

We  can  certainly  turn  on  the  limits , and  that  just  affirms  what  we  spotted .

If  we  change  the  Laney  P '  chart , that  sigma  sub  Z

was  clearly  greater  than  1 ,   because  now  our  limits

have  jumped  up  considerably .

While  the  points  being  plotted   are  the  same  as  they  were  on  the  P  chart ,

the  upper  limit  in  particular

has  gotten  larger .

There 's  a  fairly  simple  example .

Let 's  move  on  to  another  example .

This  is  again ,  another  data  set   out  of  this  JMP  sample  data .

In  this  case ,  we 're  looking at the  number  of  defects  out  of ...

We  have  several  units   that  are  being  tested ,

several  braces that  are  being  tested  in  each  unit .

Each  unit  isn 't  the  same  size .

This  is  another  scenario  where

this  problem with  the  non -constant  variance  pops  up.

We  can  count  the  number  of  defects .

We 're  not  counting the  number  of  defectives.

We 're  counting the  number  of  defects  per  unit .

In  this  case , our  unit  size  is  varying .

Let 's  choose  a  U  chart under  the  Control  Chart  menu.

We  have  our  number  of  defects , and  we  have  our  date

as  our  subgroup  identifier ,   and  we  have  our  unit  size

as  our   n Trials .

We  talked  about  having that  non -constant  unit  size ,

so  we  have  varying  limits.

We  do  see  some  of  the  points are  out  of  control  here .

Again ,  this  appears  to  be   a  non -stable  process,

which  is  cause  for  panic or  having  to  readjust  everything .

Now ,  if  we  show  the  control  panel , since  we  have  proportion  as  a  statistic ,

we  can  change  this from  a  Poisson  or  CNU  to  a  Laney .

Again ,  the  limits  have  now  increased .

We  now  realize  we  have  a  stable  process . We  don 't  have  any  points  out  of  control .

This  is  better  characterizing our  scenario ,  our  data  here .

Now ,  let  me  show  you  a  third  example , which  is  a  little  bit  more  complex .

The  picture  in  my  background  here is  actually  a  picture  I  took

from  Acadia  National  Park .

A  couple  of  summers  ago , I  was  working  at  the  Schoodic  Point

and  volunteering  to  study microplastics  in  the  water  up  there .

We  were  taking  samples  of  one  liter of  water  per  week  at  different  locations .

We  would  take  that  water , and  we  would  pour  it  through  a  filter ,

and  then  we  take  the  filter and  look  under  a  microscope

and  physically  count   the  number  of  micro  beads  and  microfibers

that  were  appearing  on  the  filter that  we  poured  the  water  through .

Let 's  analyze  this  as  a  control  chart .

The  principal  investigator   for  this  particular  study

is  trying  to  form  a  nice , complex  model  over  time

to  find  out  whether  or  not the  water  plastics  were  increasing .

But  in  order  to  do  that , you  really  want  to  know

that  you 're  modeling  your  data  correctly

and  whether  or  not we  have  actual  stable  data .

This  is  an  example where we  could  run  a  P  chart ,

so  let 's  try  that .

Being  the  control  chart  developer , I 'm  always  looking  for  more  opportunities

to  model  control  charts .

We  want  to  look  at  the  total  plastics.

For  our  subgroup ,  we  have  week ,

and  for  our   n Trials ,   we  have  total  volume ,

and  then  we  have  different  site  IDs as  a  phase .

Here  we  see  we  have  three  different  points that  we  were  taking  the  measurements  from .

Some  were  better  than  others ,

but  they  all  seemed to  be  really  out  of  control .

He 's  going  back  to  the  drawing  board   and  like ,  "What  should  I  do ?

Should  I  take  more  data ? How  do  I ..."

I  thought ,  "Hmm ,  let 's  see  if  this   really is  characterizing  the  situation ,

the  process  here  very  well. "

Let 's  run  this  again  through  a  dialog ,

and  you  see  there  are  two new  entries  on  the  menu ,

one  for  Laney  P ' and  one  for  Laney  U  control  chart .

Again ,  let 's  look  at  our  total  plastic as  the  Y ,

and  the  total  volume  is  our   n Trials .

Our  week  is  our  subgroup , and  the  site  ID  is  the  phase .

We 've  got  the  same  points  again , but  suddenly,  our  limits  are  much  wider .

We  can  conclude  from  this  that ,  well , we  actually  have  a  pretty  stable  process .

This  is  good  data .

He  can  go  ahead  and  start  to  form his  larger  model  on  this  data .

While  it 's  a  calming  thing , also,  it  makes  a  lot  more  sense .

In  closing ,  I  would  like  to  recommend that  everyone  use  the  Laney  P '  and  U '

control  charts when  monitoring  your  proportion

of  non -conforming  or  defects ,

especially  when  you  see  a  difference between  the  P  and  the  P '  chart .

Thank  you  very  much .