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After reading the answers I now know there are three independent sensors. I will leave the question as-is, to not take the answers out of context:

I do remember reading that airliners have two independent sensors and channels to deliver readings like airspeed and altitude to the cockpit (pitot-static system). If this is not the case my question will not make sense.

If the two systems show conflicting information, what is the standard procedure? If one of them is 'overspeed' or close to stall speed should the pilots assume this is the one to focus on? Or do the pilots reason based on each situation independently and all the other factors at play?

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The procedure used would depend on which information is conflicting/unreliable (and of course the aircraft type).

With one or more unreliable airspeed indications (which is one of the more critical ones), the initial action is NOT to start troubleshooting/figuring out which indicator is "the correct one", but to ensure safe speed/flight path by other means. The initial actions on Boeing aircraft is to disconnect automatics (auto throttle, autopilot, flight director) and control the aircraft given memorized combinations of pitch and thrust. With the aircraft under control, and when directed by the checklist, you start analyzing the situation, to see if you can rectify/isolate the faulty source. If a reliable source can not be determined, the aircraft continues to be flown by pitch/thrust settings given in the manual (based on altitude, if known, weight, flaps/gear, desired vertical profile etc).

In the case of unreliable altitude, in case you can't determine a reliable source, you can typically use radio altitude below 2'500 ft. A big caveat is that if the transponder is set to use an unreliable static pressure source, the altitude that ATC sees on secondary radar will also be unreliable. An example of this was seen in the Aeroperú 603 accident, where the aircraft took off, with the static ports taped over, and ATC was asked to assist with altitude and speed information: CVR transcript - Wikipedia

Erroneous airspeed/altitude indications often imply each other, as an unreliable static pressure source will affect both.

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There are at least three systems. You compare indicators with the standby system and know which one of the main systems failed. Sometimes all systems can fail due to icing or bird strikes. In this case there is an unreliable air speed procedure or checklist. Basically aircraft is flown by pitch and power settings.

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Avionics computers are generally (if not always) triple redundant to avoid the very situation you bring up. Form a pure logic standpoint you cant know which reading is correct if you only have 2 readings in a blind situation. However if you have 3 readings, 2 in agreement and 1 that differs you can statistically assume that the 2 agreed readings are correct. There is a nice summary here on Wikipedia. This Question on why there are multiple autopilots also addresses it nicely.

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  • $\begingroup$ Avionics sensors are, indeed, usually triple-redundant. It does not apply to avionics computers, where the redundancy (for the critical systems like FBW) relies on dissimilar systems instead. $\endgroup$
    – Jan Hudec
    Commented Jun 11, 2015 at 21:53
  • $\begingroup$ Interesting, my understanding of FWB was that it was also triple redundant but I learn something new every day. $\endgroup$
    – Dave
    Commented Jun 12, 2015 at 13:06
  • $\begingroup$ I don't know about Boeing, but in Airbus ELACs and FACs are only two and only SECs are three, but fault detection does not seem to use cross-checking between them anyway. Instead each unit is a pair of computers, one checking the other. See also aviation.stackexchange.com/a/15262/524. $\endgroup$
    – Jan Hudec
    Commented Jun 12, 2015 at 13:12

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