topic Re: Individual Control Chart in Discussions

Individual Control Chart

faustoG — Thu, 03 Oct 2024 13:30:08 GMT

here you find 54 individual data, exponentially distributed.

JMP analyses the data and provides a STRANGE Control Chart

Why?

See the attached file

Fausto Galetto

Re: Individual Control Chart

statman — Thu, 03 Oct 2024 14:31:40 GMT

Welcome to the community. Sorry I can't provide specific feedback as your post lacks context. You have attached a Word document with a data set and an X, MR chart. Someone who was analyzing the data must have run (requested) that control chart platform. If the data is in a logical series (e.g., time) and you don't have any rational subgroups, then looking at the data with that chart is a good idea. Control charts do not assume any particular distribution to use them.

Re: Individual Control Chart

faustoG — Thu, 03 Oct 2024 15:37:11 GMT

Dear statman,

thank you for your reply.

I try to give you some more information:

the 54 numbers are UTI (Urinary Tract Infection)
collected in a Hospital
they are SINGLE data to be analysed as INDIVIDUALS
it is asked to assess if the "process" providing the data is IC (In Control) or OOC (Out Of Control)
the data distribution is EXPONENTIAL

In my opinion, the JMP Control Chart, shown in my attached file, is misleading...

Your statement

"Control charts do not assume any particular distribution to use them."

is not suitable.

faustoG

Re: Individual Control Chart

statman — Thu, 03 Oct 2024 16:07:01 GMT

What does this mean: "it is asked to assess if the "process" providing the data is IC (In Control) or OOC (Out Of Control)"

Is this a homework problem? How was the data collected? Is it in a time series? Is it in any rational order? If not, then perhaps X, MR charts are not appropriate. You can do some distributional analysis for outliers, but IC and OOC implies a rational series of(e.g., time).

Do you understand the meaning of IC and OOC? Both of these are a function of how the data was collected and what comparisons are being made. For example, an X, MR chart compares short-term variation as estimated by the range of consecutive data points (and shown as control limits on the X chart) to long term variation the X's plotted on the chart. If you were to have rational subgroups, the charts would compare within subgroup variation to the between subgroup variation.

For distributional assumptions related to control chart method (or lack thereof), please see:

Shewhart, Walter A. (1931) “Economic Control of Quality of Manufactured Product”, D. Van Nostrand Co., NY

Wheeler, Donald, and Chambers, David (1992) “Understanding Statistical Process Control” SPC Press (ISBN 0-945320-13-2)

Re: Individual Control Chart

dlehman1 — Thu, 03 Oct 2024 22:04:49 GMT

While I agree with statman's comments about additional context, I do think we can speculate a bit more here. If we assume that the data is in fact in a correct time series order, then the control charts don't look strange to me. It appears that something changed near the end of the series and appears to be "out of control." The precise meaning of "out of control" will depend on that missing context - I don't know much about urinary tract infections or about what exactly is being measured here, but there is a clear point at which what is being measured deviates significantly from the rest of the series.

I don't understand what you mean by the distribution is "exponential." I also don't understand your comment that the distribution-free control chart is "not suitable." I also don't understand what you find "STRANGE" about the control chart. Perhaps you can elaborate on those 3 points.

Re: Individual Control Chart

faustoG — Fri, 04 Oct 2024 07:58:57 GMT

Dear statman, Super User

it is NOT homework!
You seem to think I do not know Control Charts
I actually have a "profound" (see Deming!) knowledge of the THEORY of Control Charts
and I know the books that you cite
so that I can state that the JMP analysis of the data is WRONG!
I know well the meaning of IC and OOC!

I am not familiar with using JMP, so I started by analyzing the data in my file.

I wrote a letter to JMP (Chiappa) signaling the BIG problem that the CC made by JMP is WRONG!

Mr. Chiappa (of JMP) suggested asking the Community to get the answer....

I did it.

There is NO within subgroup variation and between subgroup variation; the data are INDIVIDUALS and must be analysed as such

IF YOU do not understand that the CC is wrong YOU cannot help me (new user of JMP)

faustoG

Re: Individual Control Chart

faustoG — Fri, 04 Oct 2024 08:14:06 GMT

Dear dlehman1

Level V

YOU say:

there is a clear point at which what is being measured deviates significantly from the rest of the series.

That point depends on the WRONG analysis by JMP.....

See my reply to statman.

YOU say:

I don't understand what you mean by the distribution is "exponential."

You have to read some probability books and look for "exponential distribution."

YOU say:

I also don't understand your comment that the distribution-free control chart is "not suitable."
I also don't understand what you find "STRANGE" about the control chart.

See my reply to statman: the JMP Control Chart is WRONG!

I am not familiar with using JMP, so I started by analyzing the data in my file.

I wrote a letter to JMP (Chiappa) signaling the BIG problem that the CC made by JMP is WRONG!

Mr. Chiappa (of JMP) suggested asking the Community to get the answer....

I did it.

.. and I am waiting for somebody tells me how to analyse correctly the data, using JMP

I am eager to learn how to do that with JMP

Yesterday | Posted in reply to message from faustoG 10-03-2024

Re: Individual Control Chart

Victor_G — Fri, 04 Oct 2024 08:49:23 GMT

@faustoG
Instead of telling everyone in this discussion they are wrong, you could perhaps provide the analysis you have done on the data ?
That would help other members of the forum understand the differences between your results and the outcomes from JMP control chart.

Please keep calm and stay respectful.

Re: Individual Control Chart

faustoG — Fri, 04 Oct 2024 09:28:59 GMT

Dear Victor_G

Super User

Thank you

I am calm and respectful.

Did you read my attached file?

IF NOT, please, read it and notice that I wrote to JMP about the WRONG Control Chart:

I am not familiar with using JMP, so I started by analyzing the data in my file.
I wrote a letter to JMP (Chiappa) signaling the BIG problem that the CC made by JMP is WRONG!
Mr. Chiappa (of JMP) suggested asking the Community to get the answer....
I did it.
.. and I am waiting for somebody tells me how to analyse correctly the data, using JMP
I am eager to learn how to do that with JMP

I do not have my solution:

I want to find the TRUE CC, with EXPONENTIALLY distributed data using JMP!

I do not tell the JMP Community they are wrong: I tell all of them that the analysis (made by JMP that you can find in my file) is WRONG: it does NOT consider that the data are EXPONENTIALLY distributed.

WHY all think that this point is NOT important?

faustoG

Re: Individual Control Chart

Victor_G — Fri, 04 Oct 2024 11:20:26 GMT

Ok, some points to answer and clarify (I did look at your file) :

The letter is written in Italian. As I don't speak/write/understand Italian (and many other users in the Forum may be in a similar situation) I may be lacking some context crucial to the understanding of the problem.
You mentioned a BIG problem, but never explains how/why/what is the problem. How/why is the calculation of control chart and/or control limits wrong ? Is it because few samples are detected out of the control limits calculated (and you were expecting more) ? What are your expectations/results ? Do you have specifications limits you would like to compare to (since you seem to imply the goal of the analysis is to check the measurement process) ?
I would suggest reading the post from @jthi . This post will help you frame the questions so that the discussion can lead to a solution for you. In this example, we don't have any reference/analysis to compare to the one from JMP, and this last one (JMP) isn't satisfying for you. We will never be of any help if we don't know what you're looking for, and/or if you don't provide an example of the analysis and the "correct" answer/results you expect.
In the meantime, since you don't seem to be familiar with JMP and how the calculations are done, you can read the documentation about the Control Chart Builder.

No need for exclamation points, bold sentences and words and capital letters in your post, please avoid them.

We are a respectful Community of JMP Users, willing to help any JMP users in our free time. If you can't respect other people, nobody is going to help you.

Hope that you can specify your context, correct answer and analysis in more details so that we can all focus on the statistical part.

Re: Individual Control Chart

dlehman1 — Mon, 07 Oct 2024 12:27:46 GMT

I want to echo Victor_G's comments. I realize there may be misunderstandings due to different languages, so little patience on everyone's part would be helpful. What I don't understand from your comments is exactly what you find wrong with JMP's control charts. I honestly don't know, so you should tell us so that we can either help you or see what JMP is doing wrong. Further, I am quite familiar with the exponential distribution, but I'm not sure what that is relevant to the control chart. As was said, the control chart assumes not particular distribution. If you know your data is supposed to come from an exponential distribution, then there are ways to see how close the data is to that distribution - but the control chart is examining the data over time rather than a time-invariant distribution. I think to combine the two (a known distribution and a control chart) might benefit from some processing of the data before making the control chart. For example, you might examine the deviations from a particular exponential distribution and plot these in a control chart - I don't have the medical background to know what the supposed exponential distribution would look like.

Re: Individual Control Chart

faustoG — Sun, 06 Oct 2024 07:16:22 GMT

Dear All,

I think I found a possible cause of my JMP version: it is

JMP Student version

In my opinion, my JMP lacks a feature.

If some of you want, with your version, you can try the following:

Control Charts, Rare Event Chart, T chart

You should find a chart that is different from mine in my uploaded documents.

Hoping you want do that het my regards

faustoG

Re: Individual Control Chart

dlehman1 — Sun, 06 Oct 2024 12:02:33 GMT

I have JMP Pro 18 and I produced the Rare Event Chart as well as the normal IR chart. Both are identical and identical to the one in your document (which you say is wrong). I still don't understand what you find wrong about it. I also tested your data against an exponential distribution and the values indeed do look like they come from an exponential distribution. As pointed out, that distribution is not relevant to the control chart - which is distribution free. So, I am still puzzled by what you find "wrong" about the control charts JMP is producing.

Re: Individual Control Chart

dlehman1 — Sun, 06 Oct 2024 12:39:51 GMT

I'm also still confused as to whether the data is in a meaningful time sequence. I did a time series analysis of the data (assuming it is in sequence) and there does not appear to be any autocorrelation. Also, fitting an exponential distribution to the data shows a very close fit to an exponential with a scale parameter of 0.2143. It would help if you could clarify your initial question: is it really a control chart that you are interested in or are you wishing to see if the data looks like it really came from an exponential distribution. If the question is the latter, you can't prove it came from any particular distribution but when you test whether it is exponential, you are far from rejecting that hypothesis.

In other words, the data does look to me like it came from an exponential data generating process. If it is in a time sequence, and you are interested in investigating whether it is deviating from meaningful control limits, I'd say it mostly look like it is within those limits. Of course, with additional information about what is being measured and what meaningful control limits would be, more can be said. But just from a data point of view, that is what I would conclude.

Re: Individual Control Chart

faustoG — Sun, 06 Oct 2024 14:12:27 GMT

you write:

As pointed out, that distribution is not relevant to the control chart - which is distribution free.
So, I am still puzzled by what you find "wrong" about the control charts JMP is producing.

The control chart is not "distribution free".

As I said previously, Shewhart's formulae for normal distribution are used.

Due to the Exponential distribution, I expected that JMP Pro 18 would produce a different chart using the T Chart...

I am sorry about that.

Thank you for your try.

faustoG

Re: Individual Control Chart

faustoG — Sun, 06 Oct 2024 14:26:40 GMT

You say:

It would help if you could clarify your initial question: is it really a control chart that you are interested in...?

YES.

You say also:

If it is in a time sequence, and you are interested in investigating whether it is deviating from meaningful control limits, I'd say it mostly look like it is within those limits.
Of course, with additional information about what is being measured and what meaningful control limits would be, more can be said. But just from a data point of view, that is what I would conclude.

The Control Limits found by JMP are not meaningful.

The additional information is that the data distribution is Exponential.

See my previous reply: Normal Distribution ... used by JMP.

Re: Individual Control Chart

dlehman1 — Sun, 06 Oct 2024 14:32:29 GMT

I think I am now understanding your question - I'm not an expert with control charts so I'll give my nonexpert response and let someone else be more precise. While the Shewhart control chart does not assume a normal distribution - the control limits are calculated from the data - it looks like there is an implicit assumption of a normal distribution for the random effects that drives the number of standard deviations used to set the control limits. The T chart apparently uses a Weibull distribution to establish control limits. Since your data appears to come from an exponential distribution, are you looking for a control chart whose control limits are based on an exponential distribution? If so, I'm not aware of an option for that, but perhaps someone else is.

I do think it is worth thinking about control limits more generally. Regardless of what assumption is made about the underlying distribution, control limits are established from the data, not from the subject matter. Specification limits may be more appropriate in your context. Based on appropriate medical knowledge, it might be relevant to see if a series of measurements fall outside of a meaningful limit of variability - based on medicine and not on the particular data series. I think it may be worthwhile thinking about the limits make more sense driven by the data versus being driven by subject area knowledge.

Re: Individual Control Chart

statman — Sun, 06 Oct 2024 15:24:28 GMT

Not exactly, Shewhart's arguments fundamentally are about the utility of the mean and standard deviation as useful estimates regardless of the underlying distribution. In fact he states in his book:

"...we can make use of the average and standard deviation of a statistic, even when the underlying distribution is not known."

He uses Tchebycheff's theorem to support establishing limits that reasonably identify "when trouble exists" and empirical evidence regarding economy of concluding there is trouble when there is not.

See previously referenced: Shewhart, Walter A. (1931) “Economic Control of Quality of Manufactured Product”, D. Van Nostrand Co., NY, Chapter XIX, p.275-278

Re: Individual Control Chart

dlehman1 — Sun, 06 Oct 2024 15:26:42 GMT

I found this reference that appears to address your need: https://brunochassagne.wordpress.com/2011/10/02/control-charts-for-exponential-distributions/. I can't speak to its accuracy, but on the attached file of your data I manually set the LCL and UCL according to what that document says (note that my file uses decimal points rather than the European commas). Since the data was so close to an exponential distribution, I think that explains why the data is so far within the control limits in the control chart. The enclosed scripts: one is for the distribution fit (which gave me the scale parameter of 0.21, which I used to derive the UCL as specified in the document), and the other is for the control chart with manually set control limits.

Re: Individual Control Chart

faustoG — Sun, 06 Oct 2024 15:31:32 GMT

Dear dlehman1 (Level V),

you say:

While the Shewhart control chart does not assume a normal distribution -
the control limits are calculated from the data

If you read the Shewhart books you will find the truth: from Shewhart book (1931), on page 294 , you will find

which is based on the Nromal Disti.rbution

The Control Limits MUST be calculated from the data.

You say also (VERY IMPORTANT)

The T chart apparently uses a Weibull distribution to establish control limits.

It was exactly what I hoped for when I suggested the T Charts (that my JMP Student Edition does not show, unfortunately).

The Exponential distribution is a WEIBULL distribution with shape parameter =1.

So, please, try "Rare Events" with "T Chart" "Weibull" ... and see ...

Thank you

faustoG