When you insult something how will it respond

In early October, I, along with a colleague of mine, gave a talk at the joint American Statistical Association and American Society for Quality Fall Technical Conference in Kansas City.  The purpose of this conference is to share ideas among Statisticians and researchers in the engineering and physical sciences, though there is a high concentration towards industrial engineering (which I think is a drawback to this conference and would like to see other areas of science represented).

The talk that my colleague and I gave, I felt, totally stood out at this conference.  Most talks focused on how to improve the quality of items (quality being a broad term) and designing experiments in an industrial setting.   Ours, on the other hand, focused more on incorporating the current scientific knowledge about a nonstandard experiment (which isn't much) into some parsimonious (simplest equation that describes the science) model (though it is hard to say if it is).  I am not trying to discount the other talks, I would have just liked to see more nonstandard problems and the researchers approach to solving them.

I will spend the rest of this entry describing our talk which I hope you find interesting and clear if you are not a statistician (and if all goes well, this work will be submitted to the Journal of the American Statistical Association...boo yeah).

There is a safety group at my "place of business" whose job is to think up different scenarios that would cause a detonator (det) to "Go" (explode) when they do not want it to.  Typically, these scenarios involve either the environment that the det resides in or the workers who "tinker" with these dets accidentally insulting the det (oops I dropped my sandwich on the det. It always amazes me how calm people are who work around explosives.  One guy was even having me smell some them...which was pretty AWESOME.  They remind me of Coroners eating around corpses.  Sorry random tangent haha).  The researchers are interested in how the det will respond to such insults.  Below is a data set from such an experiment.  

The data represents an experiment where the researchers insulted a det with what they called electrostatic discharge.  They controlled this discharge by varying different levels of voltage and capacitance (i.e., they paid grad students to rub their feet on carpet and touch the det HAHA).  They then continued to insult the det until it either responded with a Go or degraded past a point that it will never Go. 

The researchers are interested in Go probabilities for a certain number of insults (usually 1).  They are then really happy if the Go probabilities are extremely small (there are issues with this type of estimation and if you are interested leave me a comment).  My colleague and I then needed to develop a class of models (equations that we pretend produced the data) that we think approximately is the "machine" that created the data and captures the current scientific knowledge for detonators.  

The current believe in the scientific community is that for a det to Go (probability of a Go is very large), the voltage and the energy (energy = .5 times capacitance times voltage^2) that the det was exposed to needs to be larger than some threshold value (which of course are unknown, the researchers didn't want to make this too easy for us).  Our job as statisticians is to take this scientific information and develop models that capture this information.     In other words, when I look at probabilities as a function of voltage and energy, the proposed model should somehow capture this notion of voltage and energy thresholds.

If we can find or develop a class of models that capture the already mentioned information then we can use the data to fit the models to the data.  Fortunately, my colleague and I developed a models which we think does a decent job of explaining the data and the science.  The following figure shows our estimates of one-insult probabilities (using our models) as a function of energy and voltage (for you stats nerds the left plot represents the lower credible bound, the middle plot is the median (posterior) estimate of one-insult probabilities and the upper plot represents the upper credible bound.  The contours represent log 10 probabilities).  Notice that the middle plot has an "L" shape in the contours.  This shape represents the notion of thresholds values.  

How you say does this plot capture the current science?  Great question, please let me explain.  Notice that for a fixed voltage, the probability of Go (for a single insult) increases as energy increases.  As the energy continues to increase, however, notice that the probability quits increasing (the vertical and roughly parallel lines towards the top of the plot).  In other words, it is not enough to keep pumping energy into the det, but we also need to expose it to a large voltage in order to get the probability to approach one.   


The left and right plots are used to represent our uncertainty in the shape of Go probabilities.  This statement means that we never really know what the true shape is, the best we can do is estimate this shape using the data and current scientific knowledge.  These estimates will never be correct so we use the other plots to give a range of "plausible shapes" and hope that this range covers the truth.


I will eventually provide a link providing the statistical mechanics that produced all these results.  But that will have to wait until the work is published.  Leave me a comment if you are interested in the mechanics and I can at least send the talk which gives a little more detail.