The trick is to detect conditions like this with virtually zero false positives. Say the sensor fails one in 100,000 times and your algorithm has a 1/100 change of flagging a false positive in the case where the sensor is in fact working properly. Then the chance of a real failure successfully detected is:

    0.00001 * 0.99 = 0.0000099

The chance of a false alarm is:

    0.99999 * 0.01 ~= 0.01

Thus:

    P(failure|alarm) =  P(alarm|failure)*P(failure)
                        ---------------------------
                                P(alarm)

                     =   0.99 * 0.00001
                        ----------------
                        0.0000099 + 0.01

                    ~= 0.001

 

So alerts from your seemingly ok-ish algorithm will be false alarms 99.9% of the time!