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
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.
Dear statman,
thank you for your reply.
I try to give you some more information:
In my opinion, the JMP Control Chart, shown in my attached file, is misleading...
Your statement
is not suitable.
faustoG
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)
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.
Dear statman, Super User
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.
IF YOU do not understand that the CC is wrong YOU cannot help me (new user of JMP)
Dear dlehman1
.. 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
@faustoGInstead 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.
Dear Victor_G
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.
Dear Mark_Bailey (Staff)
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.
Thank you
Now it remains a problem:
THEORY is important
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.
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:
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
@ statman Super User
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"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
IF my JMP Student Edition
PLEASE
In the meantime, see this from the Montgomery’s book
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
