Control chart of continuous temperature data

Question

Hello,

I have conducted a stress experiment in chickens. I've monitored the leg temperature over a period of 7 days. For example, I introduced a loud sound to see what happens with the leg temperature (we expect it to drop after stressor induction).

I have extracted the temperature 2 minutes before stressor induction and 2 minutes after stressor induction. So I have a vector of 7001 datapoints, since the sampling frequency of the temperature sensor was 25 Hz. I am trying to build a control chart of this temperature vector, but it doesn't give good results... In attachment you can find my data vector and the control chart I've tried to build... Can anyone help me out please?

Thank you.

Kind regards,

Sam.

Byron_JMP · Answer

I'm not sitting here with your data, but something that might be interesting to try is this:

Analyze>Specialized Modeling>Fit Curve

Red triangle menu, Exponential Growth and decay>Fit Cell Growth 4p

Or maybe one of the pharmacokinetic models?

If you happened to have JMP Pro, I'd definitely look into trying to fit the curves with the Functional Data Explorer.

Then you could include things like intensity, frequency, duration between stimuli, and things like that as supplementary variables to study their effect on the response curve, rather than just the curve parameters.

statman · Answer

First, you need to understand what questions "Shewhart type" control charts answer.

1. Is the variation within subgroup (due to the variables, x's changing within subgroup) consistent, stable?  This question is answered with the range chart.  If there is little opportunity for x's to change within subgroup, then the average range (and hence the control limits which are a function of the range D4R-bar) will be very small and the corresponding control limits very tight.

2. Is the variation between subgroup variation (due to the variables changing between subgroup) more than that predicted by the within subgroup variation?  The control limits on the X-bar chart are a function of the within subgroup variation (+/- A2R-bar).  Or, in essence which source of variation is greater.

The concept of rational subgrouping is extremely important, although difficult to generalize (and hence teach).  If you are using control charts to partition and assign sources of variation (components of variation study) then you select the subgroup to portray a subset of the variables you think might affect the response (I recommend you have scientific hypotheses supporting your selection).  You do this by choosing the subgroup size and frequency of measures within subgroup.  The range chart will answer the question as to whether those sources are acting randomly, common cause like, per Deming.  If they are, then that source can be quantified and that source (subset of variables) can act as a basis of comparison to the other sources of variation you are interested in studying.  Those other sources of variation (another subset of variables chosen again as a function of your hypotheses) will have their variation exposed in sampling between subgroups.  The key is to select sampling intervals that increase the likelihood those variables will indeed change.  The X-bar chart (really more likely a Y-bar chart as you are likely charting Y's, not x's) is the comparison chart.  It compares the within subgroup (the control limits) to the between subgroup (plotted values for the averages).  Points "out-of-control" suggest the between sources of variation have greater leverage than the within sources.

For your situation, the choice of subgrouping seems to be arbitrary, not based on hypotheses.  The variation is so small, the control chart loses its utility of being able to separate sources of variation.  Re-thinking your subgrouping strategy is appropriate.

Mark_Bailey · Answer

A control chart might not be appropriate for this data.

* Control charts assume a stable process with constant variation.* Perturbations by special causes disturb the stability but are infrequent.
* Special causes are absent while the data is collected that will be used to establish the control limits.

* Control charts assume  majority of sub-groups exhibit only common cause variation. Would you expect that in this case?
* Control charts assume that the measurements are independent.* There is no way that the temperature readings are independent when sampled at 25 Hz.
* The real temperature fluctuations would have to occur at half that rate for independence.

* Control chart discrimination requires at least five level changes between the lower and upper control limits to be useful.* There are no levels between the control limits.

The collection of data over time naturally suggests using at least a run chart for visual examination of the data, but adding the control chart features does not seem appropriate.

You might try the Functional Data Explorer and treat the data as a function. This approach would provide functional principle components that could then be used as a new response versus treatment (normal versus shock) and random effects like bird (subject) and so on assuming that you have collected such data over multiple birds multiple times.

I don't have any other suggestions. There are a lot of smart people in the Community, though, so you might get some other ideas here.