Mystery novels and research papers aren’t all that different.
When a local bottle factory was accused of making defective bottles, two unlikely detectives entered the scene—mechanical engineering professor Michael Miles and statistics professor Scott Grimshaw.
The mystery? The bottles were collapsing in on themselves.
The distributor of the bottles blamed the company that filled the bottles with energy drink, while the energy drink company blamed the bottle company.
To prove their innocence, the bottle company had to show that their bottles had the same thickness all the way around to prove that they were not at fault.
After creating a huge dataset of thicknesses of thousands of bottles, the real challenge was how to combine data from different locations on the same bottle and data from different bottles to determine the quality of manufacturing.
“If you gather all this data and treat it wrong, that’s when you get a false sense of confidence,” Dr. Grimshaw said.
Data on the same bottle have different degrees of correlation depending on how far apart the measurement locations are. Ignoring this spatial correlation results in process monitoring that would falsely identify bottles as poor quality when in fact they met specifications.
While this correlation is new to the high-tech instruments in modern manufacturing, it is well-known in environmental statistics and geostatistics.
To better understand this idea, instead of thinking about manufacturing let’s imagine a weatherman trying to find the average temperature of Utah. He puts a thermometer in every city and then ten thermometers in Provo.
For an accurate average temperature of Utah, a weatherman must modify the computation to recognize that the measurements taken in Provo were taken close together and yield more similar temperatures than the other weather stations. The Provo measurements would be very correlated, just like measurements taken very close to each other on a bottle are very correlated.
Miles and Grimshaw created a new equation to summarize all the data and compare to the specifications of uniform thickness while taking into account the correlation of spatially close samples.
The first thought was that the spatial correlation was a nuisance, but preliminary investigation into the statistical properties indicated the correlation made it better at detecting poor quality. These investigations were computationally intensive, and they decided they needed to call in another detective.
Natalie Blades, a statistics professor and expert in biostatistics, provided the computational expertise to further investigate the statistical properties for datasets larger than provided by the manufacturer.
With her added experience, the three professors were able to propose efficient data collection strategies and to conclude that spatial correlation offers improved sensitivity to detecting defective bottles.
While it seems overwhelming to make statements about the quality of every bottle the manufacturer produces, the evidence from thickness measurements taken on different bottles at different locations showed the distributor that the bottle manufacturer was not at fault.
After eliminating this suspect, further detective work found the energy drink company was the culprit. It appears that the company was at fault for putting the drink in the bottle while the liquid was still hot, which warped the plastic and distorted the bottle shape after the liquid cooled.
The case was cracked through the detective work of a mechanical engineering professor and two statistics professors. Let’s just say it was anything but elementary.