Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human-Machine Interface; Troubleshooting
Aircraft Equipment Problem Less Severe
Flight Crew Returned To Gate; General Release Refused / Aircraft Not Accepted; General Maintenance Action
Aircraft
VNAV (vertical navigation) would not arm before takeoff. Because I was flying the Max for the first time I considered this may be something different or weird about the new airplane. After writing this up on the ground the mechanics did a reboot of the airplane and these problems seemed to go away but now we experienced the failure of the Captain's FMC multiple times.  Upon arrival at the airplane that morning I found the FMC switch in the 'R' position instead of the normal 'BOTH.' During preflight; with the FMC programmed; I engaged LNAV (lateral navigation) and VNAV with the Master on my (First Officer) side. A few minutes later I noticed VNAV disengaged. I reengaged it. A few minutes later I noticed it disengaged again. This time I told the Captain and he said he noticed it as well. This was my first flight in the Max so I chalked it up as a Max-ism. I thought it would 'fix itself' airborne. The Captain and I discussed it and decided to just proceed and attempt to engage it airborne after multiple attempts on the ground to keep it engaged. This was the only discrepancy I noticed on the ground. Once airborne we did attempt to engage VNAV but it would disengage within a couple seconds. I climbed out in LVL CHG (level change mode) all the way to FLXXX when ALT HLD (altitude hold) engaged. After a few minutes at cruise the Captain decided we should try switching everything to his side so we switched to CMD A and engaged VNAV. After this we had no further issues with VNAV. We agreed I would continue to be pilot flying utilizing the A autopilot and the master on his side.  During cruise shortly after engaging VNAV as previously discussed I began noticing weird things on my ND (navigation display) and PFD. On the PFD on my speed tape the minimum and maximum maneuvering amber bars would simultaneously shoot out.  The minimum would jump up about 8 knots while the maximum would simultaneously shoot down about 2 knots and then immediately retract. Also the ND would ratchet instead of making smooth movements. This was especially noticeable in turns. Lastly we noticed ANP (actual navigation performance) going as high as 1.3. By the end of the flight I would say it was back in the normal range; less than 0.1. I flew the STAR in LNAV/VNAV to the bottom and performed a visual [approach] with no other issues. We wrote this up on the ground doing our best to explain this to Maintenance. The Captain and I decided if we set up the box and selected the master on my side and engaged VNAV and it stayed engaged we would be satisfied and then switch everything to his side. After boarding was complete and we were just about to shut the door both FMC's blanked with a MAP and VTK (vertical track) on Captain's PFD. We called Maintenance back out for another 'reset'. We then closed the door and pushed back. As I began to start the engine we had the same failure again on the FMC. Captain called Maintenance and they told us to return to gate.  By this point the Captain and I agreed we would not be taking this airplane. With its previous history that we learned about in previous log pages; along with the multiple issues we experienced; combined with the complicated process involving an MEL for both FMCs and an early wake up we agreed it would not be the safest course of action. Hindsight is 20/20 and looking back armed with the information I have now I would have never left the gate in ZZZ.
During my preflight I noticed the FO (First Officer) engaging VNAV and it disengaging a few minutes later. He tried a couple of times and it would not stay engaged.  He told me he found the FMC switch in the Both on R and switched it back to normal. We discussed waiting for final numbers and trying again.  It continued not to engage after final numbers and I decided to push back and start and try again on taxi.  A couple times during taxi we tried to engage it and would only last seconds. We discussed departing old school bug up N1 flaps 1 and try again airborne knowing the jet can fly without VNAV.  We both were comfortable with that decision. It was his leg and the F/D (flight director) was on his side.  There were no other discrepancies. As we rolled out on the runway and were cleared for take off I engage VNAV and it stayed on until 500 feet and disconnected. I am guessing it held on with TOGA (takeoff/go-around). We tried engaging VNAV a couple times in climb and after level off at FLXXX with no success.  We were on autopilot CMD B (command B). At that point I selected CMD A and then engaged VNAV and it stayed on. We decided to leave it on CMD A.  The remainder of the flight VNAV remained engaged. It was the FO's first time in the Max and my second leg so he remained the pilot flying using CMD A. About the same time we were switching sides we noticed on his speed tape the minimum and maximum amber bars would jump up from the bottom about 5 knots and down from the top about 2-3 knots. Also the ND (navigation display) would glitch from left to right 5-7 degrees. Both of those continued the entire flight; the ND would glitch more in a turn. All 3 airspeeds were matched the entire flight and Captain's side had no issues of glitching and we received no cautions about airspeed.  A little while later we received a scratch pad message that I don't remember exact wording but was about FMC position when I looked at all latitude and longitudes FMC; IRSL (left inertial reference system); IRSR; GPSL (GPS left); GPSR were normal within a couple of decimal points looking normal to me. I then noticed the ANP was 1.3 and bouncing between 1.2 and 1.3.  I monitored that and it started to decrease back to normal around .03; .02 but it took 20 to 30 minutes and would move between .02 and .11.  Towards the end of the flight it seemed to be more steady around .03; .02. No other scratch pad messages and the flight had no other issues. We landed [and] I wrote up the problems and we both talked to the 3 maintenance technicians to relay as much info as we could. I know that they powered down the aircraft and did operation tests that all passed and signed off the aircraft. We boarded the passengers for [our next] flight.  We discussed that we would check both sides for VNAV engagement; also monitor all speed tapes and ND's for any glitching before takeoff.  As we were about to close the door both FMC's blanked out and Map flag; VTK flag; and no runway flag on my side only appeared. No FMC prompt on either FMC screens only ACARS; ACMS (aircraft condition monitoring system); SAT (satellite).  I called Maintenance and they came out and talked about that they had Captain's FMC history. I asked about it and we looked it up in the previous logbook; first I had heard about that. I was thinking new airplane I did not realize that there was an entire logbook already used below the current logbook.  They then switched the FMC switch to both on R and the flags on my side went away and FMC prompts returned. I told them I cannot takeoff like that.  They called Maintenance Control I believe and they did a circuit breaker reset which fixed the flags and returned the FMC prompts and the FMC switch back to normal. We closed the door and started the pushback. As the FO was about to start engine 2 the same flags returned on my side and no FMC prompts on both sides. Maintenance Control told us to return to the gate because he could not MEL it. We returned to the gate and Maintenance again did the circuit breaker reset that only lasted a few minutes before the flags returned. They decided to MEL the FMC with my approval. The FO and I did not want to continue with this aircraft because of our history with it and that it had only been powered down and 2 circuit breaker resets.  We now would be manually setting bugs and thrust for the entire flight in an aircraft we both had very little time in and had an early morning show to start the day and it was now late afternoon.
B737 MAX 9 flight crew reported multiple autoflight anomalies that ultimately resulted in their refusal to accept the aircraft.