Individual Control Chart

[#1]

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

[#2]

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.

[#3]

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

[#4]

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.

[#5]

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.

[#6]

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.

[#7]

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

[#8]

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.

[#9]

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

[#10]

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

[#11]

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.