what should be the course of action in case of Dual FMC failure in Boeing 737 ng ?
You do the "FMC Fail" non-normal checklist of course:
1 Resume conventional navigation. Without an operating FMC, LNAV and VNAV are not available.
2 When preparing for approach: Use the manual N1 set knobs to set the N1 bugs.
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I had the pleasure of this a few weeks ago. With a "dual" FMC failure in a classic. Well... actually there is only one FMC in most classics, but the result is the same as a dual fail in an NG = "FMC FAIL" written on both CDUs and loss of map mode on both sides.
ATC was informed and we got vectors for the remaining 1 1/2 hour flight, since our route was mostly RNAV points. The checklist was read and approach speed and go-around N1 was looked up in the QRH. Flight progress was checked by looking in the Jeppesen charts and finding appropriate VORs where our flight plan points could be located with a radial and DME distance, so that we would have an idea when passing abeam them. During descend it started working again with the message "select active waypoint" which is normally assosiated with a power loss - probably condensation somewhere in the wiring I would guess - it was bloody cold that night.
We didn't have endless amounts of fuel so without the FMC prediction for fuel at destination, it was a bit uneasy feeling until we got a system going with VORs for cross checking our position. Otherwise it's no big deal.