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 .
