# How to tell if something happened in a data set which monitors a value over time

I have a data set where a series of measurements are being taken each week. In general the data set shows a +/- 1mm change each week with a mean measurement staying at about 0mm. In plotting the data this week it appears that some noticeable movement has occurred at two points and looking back at the data set, it is also possible that movement occurred last week as well. What is the best way of looking at this data set to see how likely it is that the movements that have been seen are real movements rather than just some effect caused by the natural tolerance in the readings.

Edit

Some more information on the data set. Measurements have been taken at 39 locations which should behave in a similar way although only some of the points may show signs of movement. At each point the readings have now been taken 10 times on a bi-weekly basis and up until the most recent set of readings the measurements were between -1mm and 1mm. The measurements can only be taken with mm accuracy so we only receive results to the nearest mm. The results for one of the points showing a movement is 0mm, 1mm, 0mm, -1mm, -1mm, 0mm, -1mm, -1mm, 1mm, 3mm. We are not looking for statistically significant information, just an indicator of what might have occurred. The reason is that if a measurement reaches 5mm in a subsequent week we have a problem and we'd like to be forewarned that this might occur.

I think you need look at statistical control charts. The most common of which are cusum and Shewhart charts.

Basically, data arrives sequentially and is tested against a number of rules. For example,

1. Is the data far away from the cumulative mean - say 3 standard deviations
2. Has the data been increasing for the last few points.
3. Does the data alternate between positive and negative values.

In R you can use the qcc package.

For example,

#Taken from the documentation
library(qcc)
data(orangejuice)
attach(orangejuice)
plot(qcc(D[trial], sizes=size[trial], type="p"))


Gives the following plot, with possible problem points highlighted in red.

control chart http://img805.imageshack.us/img805/5858/tmp.jpg

What kind of movement are we talking about?

You could of course fit a distribution over your data and see whether the new weeks fit in this distribution or are in the tail of it (which means it is likely something significant, real that you are observing)