Using two sensors instead of one: Statistically meaningful? We are using resp. manufacturing a certain device which measures, among others, the humidity of liquids. I got asked by a colleague if it makes sense to use two sensors instead of one (which a competitor is apparently doing). Mainly, in a statistical manner.
My ideas are:
Redundancy: In a technical manner, just a backup. Or to use the one that provides more meaningful measurements (but I guess this is not possible because how can you know which is (more) true?).
Statistically: Using the mean of both. Maybe even with a sensor-specified weight (though I wouldn't).
One could define a kind of deviation band in which the sensors must be within. In case their signals differ too much, one knows that something is going on.
Are there some facts which become improved by going from one sensor to two? I'd say, e.g., the confidence is increasing but I don't know how to underline this (statistically).
Finally, I'd simply say: The more, the better.
Unfortunately, this isn't solid argument.
 A: Intuitively, if the noise and measurement errors from your sensors are independent and have zero mean, then using multiple sensors will improve the signal to noise ratio because the noise and errors will tend to cancel each other out as you increase the number of sensors.
There is an interesting parallel to be made with the concept of ensembling in machine learning: Averaging the output of multiple models will improve accuracy for similar reasons (They reduce the variance that is inherent in a single model).
So you can check the math underlying ensemble prediction methods to figure out a similar mathematical justification to using multiple sensors. Look for example at how Random Forests work as ensembles of high variance decision trees.
But, but...this only works if the noise and errors are independent and zero mean. Often times in lab and industrial instrumentation situations, the noise and errors have some systemic environmental cause or are due to flaws in the measurement process which is introducing a non-zero mean bias to your model, so a more in-depth analysis is necessary than simply averaging the output of multiple censors.
A: Sensor fusion via a Kalman filter takes 2 (or more) separate measurements, combines them within the filter calculations, and outputs a smoother/more accurate measurement of the underlying.
Some good stuff online about this, e.g. https://simondlevy.academic.wlu.edu/kalman-tutorial/the-extended-kalman-filter-an-interactive-tutorial-for-non-experts-part-14/
