803401_en-US

liliconcom

Individual Control Chart

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

Quality and Process EngineeringWindowsRe: Individual Control Chart

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

Dear statman,

thank you for your reply.

I try to give you some more information:

1. the 54 numbers are UTI (Urinary Tract Infection)
2. collected in a Hospital
3. they are SINGLE data to be analysed as INDIVIDUALS
4. it is asked to assess if the "process" providing the data is IC (In Control) or OOC (Out Of Control)
5. 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

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

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

Dear statman, Super User

1. it is NOT homework!
2. You seem to think I do not know Control Charts
3.  I actually have a "profound" (see Deming!) knowledge of the THEORY of Control Charts
4. and I know the books that you cite
5. so that I can state that the JMP analysis of the data is WRONG!
6. 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

 

 

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

 

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
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

 

 

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:

1. I am not familiar with using JMP, so I started by analyzing the data in my file.
2. I wrote a letter to JMP (Chiappa) signaling the BIG problem that the CC made by JMP is WRONG!
3. Mr. Chiappa (of JMP) suggested asking the Community to get the answer....
4. I did it.
5. .. and  I am waiting for somebody tells me how to analyse correctly the data, using JMP
6. 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

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

1. 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.
2. 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) ?
3. I would suggest reading the post from @jthi Getting correct answers to correct questions quickly. 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.
4. 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

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

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

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

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

you write:

1. As pointed out, that distribution is not relevant to the control chart - which is distribution free. 
2. 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

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:

1. 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. 
2. 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

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

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

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

Dear dlehman1 (Level V),

you say:

1. While the Shewhart control chart does not assume a normal distribution -
2. 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

 

 

Re: Individual Control Chart

Dear statman (Super User),

see my previous reply to dlehman1.

True that Shewhart mentions the "Tchebycheff's theorem", but it use formulae based on the Central Limit Theorem...

Try, please the T Charts in JMP

Thanks

faustoG

Re: Individual Control Chart

Dear dlehman1 (Level V),

thank you.

Unfortunately, when I open your file I see only the data: my JMP Student Edition does not show anything else.

Can you, please copy the T Chart in a DOCX file or PDF file?

I know very well the document you mention...

Thank you

faustoG

Re: Individual Control Chart

Perhaps statman (or someone else) can help with a couple of questions here.  First, the JMP help does discuss the T chart (https://www.jmp.com/support/help/en/18.1/?os=win&source=application#page/jmp/statistical-details-for-t-charts.shtml#ww1149445) but I can't find any such option in the Control Chart Graph Builder (or elsewhere).  I do see the Rare Event control chart - it provides the identical picture as the Shewhart control chart.  I can manually create the LCL and UCL for the exponential distribution using the document that I had previously linked to.  I also fit both an exponential and Weibull distribution to the original data - the exponential fits slightly better, but both are very close.  The fitted Weibull distribution has a shape parameter of 1.03, not the value of 1 which would match the exponential distribution (which accounts for the slight difference in the goodness of fit tests).

 

So, one unanswered question is how to get the T chart that the JMP help refers to.  Another question - more conceptual - is the disparity between Shewhart's use of 3 standard deviations (based on the Normal distribution) and Shewhart's verbal description that no particular distribution is assumed.  That disparity might just be semantics:  you can construct a control chart using the estimated standard deviation and that can be useful without specifying a particular distribution, but the use of 3 suggests a reliance on the Normal distribution (at least in the default chart).

 

I attached the control chart I produced using the manually entered LCL and UCL from that earlier document.

Re: Individual Control Chart

Create Rare Event and change sigma

 

https://www.jmp.com/support/help/en/18.0/#page/jmp/rare-event-control-charts.shtml

 

Re: Individual Control Chart

Thank you.

I'll come back as soon as I analysed the Control Chart and the Bruno File

faustoG

Re: Individual Control Chart

Rare Event is grayed out in my file.  I suspect this is because it requires an additional variable for time between events?

Re: Individual Control Chart

Thank you, BUT it is not useful for my "JMP Student Edition".

I hope it is useful for other people in the Community.

faustoG

Re: Individual Control Chart

@dlehman1 I'm fairly sure it will get grayed out because your values aren't all integers.

Re: Individual Control Chart

@jthiI checked and you are correct that the option is only available for integer values.  Do you have any idea why?  And, given that, it would seem that this is not an appropriate chart for the data that FaustoG posted.  Is there a continuous option for building a control chart for data that comes from an exponential process?  Is the calculation for the LCL and UCL that I used (based on the document I linked) a correct way to model this?

Re: Individual Control Chart

I'm not really familiar with rare event control charts (or at least I don't remember them anymore) but I think the Y parameter selection is the important here:

"A T chart measures the time intervals elapsed since the last event. Each point on the chart represents a number of time intervals that have passed since a prior occurrence of a rare event."

 

 

Re: Individual Control Chart

@dlehman1 

@jthi 

In JMP Guide I found

• In the T chart, all points appear to be within the control limits. It is clear that the Individual & Moving Range chart was inappropriate for the analysis, as the limits were too narrow.

In my JMP Student Edition at Rare Events I see

1.  neither G Charts nor T charts
2. the G chart requires integer values, while T chart doesn't

faustoG

 

Re: Individual Control Chart

@jthi 

• the data for a T chart are "Time Between Events" (TBE) measures in hours, days, months, years, NOT Integer values

faustoG

Re: Individual Control Chart

To my knowledge, JMP Student Edition should be exactly the same as JMP Pro (except for different licensing) https://www.jmp.com/en_fi/academic/licensing-for-students.html . Which JMP version are you using? 18?

 

I have referred to this earlier https://www.jmp.com/support/help/en/18.0/#page/jmp/rare-event-control-charts.shtml

 

Re: Individual Control Chart

@dlehman1 

1. Since the data are Exponentially distributed with mean "theta", also the RANGES are Exponentially distributed with the same mean "theta"
2. then the control charts of the data and of the MR have almost the same Control Limits

Your charts in "Untitled.jmp" are not consistent between them.

The parameter betaW=1.03 has a Confidence Interval that includes the betaE=1.

Therefore the T Chart for the Weibull is adequate for the pourpose

faustoG

 

 

Re: Individual Control Chart

@jthi 

Yes: JMP Student version 18

you show

It IS NONSENSE, from JMP

I do not know how they justify that...

YOU can use "picosecond" and transform a fraction of a second into an integer value

Multiply the values in my document by 1000 and make the T Chart, IF you want.

Let's see what happens

faustoG

 

 

 

Re: Individual Control Chart

I can verify that, at least on my JMP Pro 18, the T chart does require integer values.  I'm not sure why - and I'm not clear on why that should be necessary mathematically or conceptually (perhaps it is a computational reason specific to JMP, but I don't know).  In any case, it isn't clear to me that your data is measuring the time between events.  You still haven't described what is being measured.  Nor do I understand what you are saying is wrong with the control limits I calculated in the file I attached.  Please refrain from the caps, bold fonts, and harsh words - it might be due to a language difference - but regardless I find it distracting and disturbing.  I don't use control charts much and so I don't have much background with anything but the most straightforward ones - which your case is not.  I'd like to understand what is appropriate for your data and I'm trying to help as well.  The section you quote that "a traditional plot of these data might contain many points at zero" also does not seem to match your data (which does not have this characteristic).  I know it would help me understand what is going on if you can say something about what these measurements are.

Re: Individual Control Chart

You write

• in  any case, it isn't clear to me that your data is measuring the time between events. 
• You still haven't described what is being measured
• I know it would help me understand what is going on if you can say something about what these measurements are.

This is taken from the document that shows the data

(I do not know anything more). So, please, ...

1. Data were provided from a large hospital system concerned with a very high rate of hospital-acquired urinary tract infections (UTIs). Specifically, the hospital would like to track the frequency of patients being discharged who had  acquired a UTI while in the hospital as a way to quickly identify an increase in infection rate or, conversely, monitor whether forthcoming process or material changes result in fewer infections. Because the root cause often differs based on gender, male and female patients are charted separately and this example focuses on males.
   The data, which can be seen in the appendix, appear to satisfy the distributional assumption for use of the t chart, with the mean time between male UTI patients at 0.21 days or about 5 hours. The data were plotted using the proposed t chart method and demonstrate statistical control.
2. The importance of tracking this and similar metrics in a health care setting is the quick identification of an increase in infection rates, which results in two significant costs to the hospital. The health cost to the patient is significant and made more severe by a higher rate of death among patients who contract infections while hospitalized. In 2002, the most recent year of Centers for Disease Control and Prevention reporting, there were an estimated 424,060 hospital-acquired UTIs among adults not in an intensive care unit in the United States, and 13,088 deaths (Klevens et al. 007). Further, the financial cost to the hospital is significant, with Medicare no longer covering the cost to treat hospital-acquired infections. Nearly 80% of the patients who acquired UTIs in this study were covered by Medicare or Medicaid, resulting in a very large expense to the hospital.
3. As can be seen from the chart, the data do not show any signs of process degradation or improve ment but the chart can be continuously monitored to detect such changes as quickly as possible.

====================================================================================

Does this help with the data analysis?

You say also:

• Nor do I understand what you are saying is wrong with the control limits I calculated in the file I attached.

As I said previously

1. the data are Exponentially distributed
2. therefore, the Ranges are Exponentially distributed, as well, with the same mean
3. so, the Control Limits cannot be very different in the two charts

You say, also:

• I can verify that, at least on my JMP Pro 18, the T chart does require integer values.

1. Multiply my data by 100000 and you get integer values.
2. Try to find the T chart
3. and see

faustoG

 

Re: Individual Control Chart

Dear: dlehman1 (Level V)

 

The fact that

• The fitted Weibull distribution has a shape parameter of 1.03, not the value of 1 which would match the exponential distribution (which accounts for the slight difference in the goodness of fit tests).   So, one unanswered question is how to get the T chart that the JMP help refers to. 

is important.

The fact that

•  the disparity between Shewhart's use of 3 standard deviations (based on the Normal distribution) and Shewhart's verbal description that no particular distribution is assumed.  ...useful without specifying a particular distribution, but the use of 3 suggests a reliance on the Normal distribution (at least in the default chart).   I attached the control chart I produced using the manually entered LCL and UCL from that earlier document.

depends, as I said before, on the Central Limit Theorem, ALWAYS (I know that you do not like caps, and bold letters! BUT they are important to highlight things).

About T Charts see the attached file

faustoG

 

 

 

 

 

 

Re: Individual Control Chart

You can fit your data using the exponential distribution in the Distribution platform. Use the Quantiles command in the red triangle menu of Fitted Exponential and specify 0.005, 0.5, and 0.995 for the desired probabilities. The estimated quantiles can then be used for user-specified control limits. Right-click in the Individuals chart in CCB and select Limits > Add Limits. Enter the quantiles here.

Re: Individual Control Chart

A P-chart seems appropriate for tracking the number of patients with UTI ('defectives'), with the sample size being the total number of patients discharged in the same period. The Poisson distribution is used for counts such as this case.

Re: Individual Control Chart

Your further explanation definitely helps me.  Your data is the time between events (I'm not sure why there was a description saying that such data often has many zeros - yours has no zeros and I would think zero time between events would be fairly unusual).  In any case, I did as you suggest and multiplied the data by 1000 and rounded it to integers, so I am able to get the T chart with sigma set from a Weibull distribution.  I'm attaching a picture of the T chart as well as the "standard" IR chart where I defined the LCL and UCL according to the formula in the document I had linked to.  The pictures are similar, although the control limits don't match.  I'm not sure why - and it could either be the document's formula being incorrect or it could be differences between the Weibull and fitted Exponential distributions.  Both show the same qualitative result - that the process seems to be stable.  But the large differences in the control limits means someone with more knowledge will need to comment.  And, yes, I don't like caps.

Re: Individual Control Chart

Dear  dlehman1 (Level V)

You say

 

• the process seems to be stable. 
• But the large differences in the control limits means someone with more knowledge will need to comment.

You should divide the values in the Control Chart by 1000 the factor that you used to get "almost integer values" needed for the T Chart.

Thank you

faustoG

 

Re: Individual Control Chart

Dear Mark_Bailey (Staff)

Preview

 

can you please show the Control Chart, according to you suggestions?

I tried, but I did not succeed: I am new to JMP Student Edition

Thank you

faustoG

 

 

 

Re: Individual Control Chart

Yes, I realized that last night.  Since I had multiplied the values by 1000, that requires adjusting the control limits.  They still don't match, though they are the correct order of magnitude.  So, I don't know what accounts for the difference.  But it does seem that there are 2 ways to get the control chart you want from JMP - either using the T chart based on the Weibull distribution (after making the data into integer values), or by manually setting the control limits in an IR control chart.

Re: Individual Control Chart

Note: The Quantiles command was replaced with a Quantile Profiler in JMP 18. Otherwise, the process is the same.

Here is a simulated sample of data from the exponential distribution, Response, and transformed Log[Response] data.

Here are the XmR charts for Response using Control Chart Builder.

We want to use probability limits based on the quantiles corresponding to 0.005, 0.5, and 0.995 for the desired probabilities. Here is the distribution analysis of both responses.

Here is the fitted exponential distribution model for Response with the Quantile Profiler turned on and set to probability = 0.005.

We will use 0.00406 as the lower control limit. Using this profiler, we can similarly find the other two quantiles.

Return to the CCB, right-click on the Individuals chart, and select Limits > Set Control Limits. Enter the three quantiles determined above.

The CCB immediately updates with the appropriate control limits.

Re: Individual Control Chart

Unfortunately, I do not know

faustoG

 

P.S.

We learned that

1. my JMP Student Edition cannot deal with Rare Events
2. it computes wrong control limits
3. the distribution of the data matters
4. the usual formulae for CC are based on the Normal distribution, due to the Central Limit Theorem

 

 

Re: Individual Control Chart

Thank you

Now it remains a problem: 

1. is the T Control Chart right
2. or the Control Limits are still wrong
3. because they are not computed according to the THEORY

faustoG

 

THEORY is important

 

 

Re: Individual Control Chart

@faustoG 

You seem intent on complaining about the JMP Student Edition.  I'm not sure why, but I don't think it is productive.  No software claims to do everything you want.  In any case, your points 2-4 all pertain to control limits.  I agree with point 4 - the usual control limits are set on the basis of a normal distribution - but there is the opportunity to override these based on some other distribution or other considerations.  I still think it is important to distinguish between control limits (a property of the data) and specification limits (a property of the problem).  In the case of medical issues (such as you have here), I would put more emphasis on the specification limits.  A process could well be in control yet hazardous to your health.

 

By the way, if it JMP's difficulty dealing with your specific data that you have problems with, you can always try to find a Python or R program that suits your purpose and run that within JMP.  Specialized methods are generally more available in R, given the relatively larger user base among statisticians.  And, if you can specify the exact problem you are trying to solve that JMP does not have the built in capability for, you can often get someone willing to write a script to accomplish what you need - I have used the Community this way in the past.

 

I did find this recent article that you might be interested in:  https://www.tandfonline.com/doi/full/10.1080/08839514.2024.2322362#d1e4814.  I haven't examined it in detail, but it appears to be a kind of hybrid of control and specification limits - at least that is my high level attempt to interpret this.  Inclusion of economic parameters seems like a way to introduce meaning into the control limits rather than just relying on a statistical calculation based on the data.  If anybody can digest this paper, please confirm (or refute) this, and expand the interpretation if possible.

Re: Individual Control Chart

Please feel free to completely ignore my post below.  No reply is asked for. I am hesitant on posting this...no offense is intended.  I have copied part 1 (of 3) of an earlier post by Fausto, describing the situation and motivation.  I have added questions.

 

1. Data were provided from a large hospital system concerned with a very high rate of hospital-acquired urinary tract infections (UTIs).

 

What is “a very high rate”?  How is it measured?  Has the measurement system been studied (e.g., determining it is a UTI and not some other infection or health issue)? How do they determine it was hospital induced/acquired and not some infection the patient already had, perhaps un-detectable or not measured before coming to the hospital or contracted by visitors to the patient, etc.?

 

Specifically, the hospital would like to track the frequency of patients being discharged who had  acquired a UTI while in the hospital as a way to quickly identify an increase in infection rate or, conversely, monitor whether forthcoming process or material changes result in fewer infections.

 

Why do they want to track this?  I  would think they want to reduce it. The main questions answered by control charting is:

1. How should the investigation proceed (special or common?) and
2. Where should you focus your investigative efforts (e.g., which components of variation dominate)? 

I assume their intention is to understand causal structure, perhaps running experiments or sampling to uncover causes and then ultimately suggesting potential solutions. It seems what they lack is a measurement that is capable of providing expedient measurement of the infection? How does plotting the current data lead to creating a  “better” measure?  I would think, based on the information provided in 2 (from the previous post), they want to understand and reduce the number of hospital induced/acquired health problems (of which one is UTI’s).  They don’t want to reduce UTI’s by replacing that infection with another health issue.

 

Because the root cause often differs based on gender, male and female patients are charted separately and this example focuses on males.

 

This is a hypothesis. Perhaps it has been studied?  How was it studied (one factor at a time?)? There is a lot of noise and hidden factors involved.  How was the noise accounted for in their studies? It seems directed sampling would be quite useful to separate components of variation.

The data, which can be seen in the appendix, appear to satisfy the distributional assumption for use of the t chart, with the mean time between male UTI patients at 0.21 days or about 5 hours.

 

Is this the best way to measure the phenomena? Does the severity of the UTI matter?  Can the amount of infection be measured? Are there other “Y’s” of interest (e.g., vitals, other infections, other health issues). How frequently are the patients tested to determine when, exactly, they got the infection?  Could other measures correlate or predict infection?

They really care about the hospital induced infection rate.  While mean time to UTI is a measure of the rate, it seems each event could be considered independent (each data point is a different patient with different underlying health conditions). It also seems there may be some similarities due to potential hospital effects (both common AND special causes).  How will plotting the metric distinguish between these different sources of variation?

 

The data were plotted using the proposed t chart method and demonstrate statistical control.

 

What is meant by statistical control?  Is a consistent, predictable amount of UTI’s a good thing? How are the control limits “created”.  Control limits are a function of the x’s (variables) changing at the designed sampling frequency.  Shewhart’s approach is to select a subset of the x’s and group them into a subgroup (for argument sake, relatively short term in time). Chose another set of x’s that will vary over a longer term (or some other rational condition). Use the subset of x’s as a basis for comparison.  First, is the subset of x’s consistent (range chart)? If they are, then a comparison can be made to the other set of x’s that vary in the study.  This is done using the X-bar chart.  The control limits are a function of the range (the subset of x’s) and the dots plotted on the X-bar chart are a function of the x’s changing between subgroup.  If this chart is “in-control” then the within subgroup x’s dominate the effect on the plotted Y.  If this chart is “out-of-control”, then the between sources dominate.

 

“The engineer who is successful in dividing his data initially into rational subgroups based on rational theories is therefore inherently better off in the long run. . .”

                                                                                                      Shewhart

 

Re: Individual Control Chart

@ statman Super User

 

=======================================================================

“The engineer who is successful in dividing his data initially into rational subgroups based on rational theories is therefore inherently better off in the long run. . .”

                                                                                                      Shewhart

 

"All models are wrong, some are useful" G.E.P. Box

=======================================================================

 

statman Super User

 

These statements do not help in this case!

 

YOU do not want to consider that

1. The data are individuals
2. And they are exponentially distributed
3. And the distribution MATTERS in making the Control Chart and computing the Control Limits

 

IF my JMP Student Edition

• would have worked correctly with Rare Events
• I would not bother the JMP Community
• With the problem explained in my letter

 

PLEASE

1. chose a case that you trust
2. with data exponentially distributed
3. and individuals
4. and inform us about your analysis (Control Chart)

 

In the meantime, see this from the Montgomery’s book

 

 

 

 

 

faustoG

Re: Individual Control Chart

dlehman1 Level V

 

IF my JMP Student Edition

• would have worked correctly with Rare Events
• I would not bother the JMP Community
• With the problem explained in my letter

 

Students must know how to analyse Rare Events

 

I will read the paper you suggested and I will come back

faustoG

Re: Individual Control Chart

 

 

Re: Individual Control Chart

@ dlehman1 Level V

 

In the paper, you suggested there is …

 

• It is NONSENSE,
• unless the Researcher (Scholar) be enlightened by the Holy Spirit
• who tells him the TRUE values of the quantities Theta_0, LCL and UCL:
• these quantities MUST be estimated by the data and are numbers
• (determinations) of Random Variables

Re: Individual Control Chart

@ Mark_Bailey, Staff

 

Thank you.

I am eagerly waiting for the TRUE case of Individual Control Charts (with exponentially distributed data) by

• statman Super User

faustoG

Re: Individual Control Chart

I'm so sorry that I have not been able to communicate my thoughts to you.  I'm still not sure why mean time to UTI is exponentially distributed....seems it should be randomly (normally) distributed, unless there are actions being taken on the process.

Re: Individual Control Chart

@ statman, Super User

YOU WRITE:

1. I'm still not sure why mean time to UTI is exponentially distributed....
2. seems it should be randomly (normally) distributed, unless there are actions being taken on the process.
3. "All models are wrong, some are useful" G.E.P. Box

 

YOU do not want to accept that

• The data are exponentially distributed....
• NOT “mean time to UTI”
• randomly distributed DOES NOT MEAN normally distributed
• some ideas on models are TOTALLY WRONG

 

I ask you again to find a case you trust …

 

faustoG

Re: Individual Control Chart

dlehman1 Level V

 

In the paper you suggested there is …

 

I do not find this result

Can you?

faustoG

Re: Individual Control Chart

dlehman1 Level V

2024-10-11

Dear colleagues,

Please find my analysis of the Car Seats data given in the paper suggested by dlehman1 Level V

 

I find it very strange that

• an Out Of Control (OOC) process is better than
• an In Control (IC) process

 

What do you think?

 

 

k1_A, k2_A,       k1_B, k2_B

are the Control Limits shown in the paper.

faustoG

Re: Individual Control Chart

Control (as defined by Shewhart) has nothing to do with good or bad.  That is a function of specification. Specifications are typically (sic. always) independently derived from actual process data and variation.

My suggestion, you should try to understand what Shewhart meant by control as he is the creator of the control chart method, take it or leave it.  I'm out.

Re: Individual Control Chart

@ statman, Super User with 769 Kudos

YOU WRITE:

• I'm out.
• "All models are wrong, some are useful" G.E.P. Box

It’s a real pity.

We will not see any case on the Control Charts you trust … (in spite that I asked you to find a case )

 

I think that, in spite of citing Shewhart and Box, you are unable to deal with “real” data and to make good Control Charts…

You did not analyse any data, you did not provide any data…

You made a lot of waffling

 

In my opinion, you should

1. Study the Shewhart and Deming books
2. Learn their “good” ideas
3. Study some “good” Statistical books
4. Learn that some ideas on models are TOTALLY WRONG

 

faustoG

Re: Individual Control Chart

Your posts on this forum are unacceptable.  You came here for advice and many have provided it.  Most of us are volunteering our time.  I suggest you take your rants to another forum.

Re: Individual Control Chart

It doesn't seem that this thread is going to progress in a positive manner so I am turning comments off.

Jeff Perkinson

JMP User Community Moderator