Suppose I have N amount of sensors. One of them is faulty. I can detect that there is a faulty sensor by getting the variance of all the sensors. If the variance is large I can assume the data isn't similar which should be the case in a normal sensor.
How do I then detect which sensor is faulty?
Example: Let's say, S1, S2, and S3 have detected values of 10,10,10 respectively, In this case, the variance is 0.
But let's say S3 failed and gave value 2. In that case, the variance is 21.333... By setting a threshold for variance. Let's say, 20 we can detect that we have fault in sensors. (The values aren't close to the same)
How do I then detect which one is faulty? Can mean or standard-deviation help in anyways? Or do I need something else?