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]

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

[#3]

@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

[#4]

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

[#5]

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...) 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.

[#6]

Create Rare Event and change sigma

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

[#7]

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

[#8]

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

[#9]

@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?

[#10]

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."

[#11]

@jthi 

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

faustoG