Control chart/R chart of temperature data in response to stress

Question

Hello,

I have monitored the leg temperature of a chicken for 1 day. The temperature data I am working with is 4min 40sec long. On the 2nd minute, I introduced a loud noise, and expected the temperature of the leg to change. So my data consists of:

- 2 minutes baseline

- 40 seconds of stress

- 2 minutes post-stress

Every datapoint in my dataset represents 2 seconds of measurement (so sampling frequency is 0.5 Hz). I've divided my temperature data into 7 subgroups, and expected temperature to change around subgroup 4-5. When you look at the chart I created (see attachments) with the 'Range' as Statistic, this is indeed the case.

For [Points 1] in the chart, I understand the 'Range' Statistic. But I don't get quite the difference between the Sigma-section in [Limits 1]... What is the meaning of the 'Range', 'Standard deviation', 'Moving range' and 'Median moving range' sigma limits in my particular case here?

Thank you!

control_chart.png

statman · Answer

First I am going to paste some of what I wrote in another discussion. Control chart analysis and interpretation is completely dependent on how the data was acquired and how the data is organized (e.g., how the data is subgrouped.)

1. The RANGE chart answers the question: Is the variation within subgroup (due to the variables, x's changing within subgroup) consistent, stable?  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 e.g., frequency of measures within subgroup.  The range chart will answer the question as to whether those sources are acting randomly, common cause like (Deming).  If they are, then that source (subset of variables) can act as a basis of comparison to the other sources of variation included in your study.   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. Conversely, if ALL of the x's change within subgroup, then the average average range will be large and the control limits wide. For your situation, the choice of subgrouping seems to be arbitrary, not based on hypotheses (why create 7 subgroups?). Try changing your subgrouping strategy and you will change the control limits and thus the interpretation.  Re-thinking your subgrouping strategy is appropriate.

2. The X-bar chart answers the question: 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).  The other sources of variation captured in your study (a subset of variables chosen again as a function of your hypotheses) will have their variation exposed in the sampling between subgroups.  The key is to select sampling intervals that increase the likelihood those other variables will indeed change.  The X-bar chart is the comparison chart.  It compares the within subgroup (represented by 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.

Without rational sampling and subgrouping you can draw just about any conclusion you want to.

“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

I recommend 2 columns written by Donald Wheeler:

https://www.qualitydigest.com/inside/quality-insider-column/060115-rational-subgrouping.html

https://www.qualitydigest.com/inside/statistics-column/070115-rational-sampling.html

I don't know how you got the charts you did (using control chart builder). The charts shown in your attachment are the same charts.  These appear to be a function of how you subgrouped your data, but only the range chart is displayed (no average chart).

The moving range (absolute value of previous-current measure) is a surrogate to calculate a range when you don't have rational subgroups.  It is not very useful for separating and assigning variation, but does give you some ability to assess consistency of short-term variation.  The median is often used as a statistic to estimate central tendency when the distribution is not normal (which is not an assumption of Shewhart control charts).

Mark_Bailey · Answer

Select the rows that include the data for the readings when the stress was introduced and exclude them. Build the chart - the limits are based on the observations before the stress was introduced. Click the red triangle at the top and save the limits to the data column. Now un-exclude the rows. The chart should include all the rows but the limits are based on the first half of the data.

I suggest that you see Help > JMP Documentation Library > Quality and Process guide to see the definition of these terms.