A B737-800 MISSED AN ALT CONSTRAINT ON THE LAX CIVET STAR FOLLOWING A LATE RWY CHANGE AND THE ACFT FMA INDICATING VNAV PATH WITHOUT HOLDING THE PATH.

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OUR FLT PLAN INCLUDED THE CIVET 5 ARRIVAL INTO LAX. WE NORMALLY RECEIVE CLRNC FOR AN ILS 25L/R SO WE SET UP THE FMS AND THOROUGHLY BRIEFED THE ARR AND APCH. NEAR GRAMM AT FL180 WE WERE SWITCHED TO SOCAL APCH AND WERE SUBSEQUENTLY CLRED TO DSND VIA CIVET 5 ARR RWY 24R TRANSITION. WE SET UP THE ACFT TO DSND VIA VNAV AND SET IN 7000 FT IN THE ALT WINDOW AS BRIEFED. WHILE I MONITORED THE ACFT MY FO CHANGED OUR EXPECTED TRANSITION/APCH TO RWY 24R. AS WE APCHED CIVET WE BOTH NOTICED THAT THE VNAV HAD A HIGHER RATE OF DSCNT THAN NORMAL PASSING THROUGH 15000 FT. WE BOTH VERIFIED THE PLANE WAS STILL IN VNAV AND FMC STILL SHOWED THE FMS WAS GOING TO PASS CIVET BETWEEN 14000 FT AND 15000 FT. AS THE ALT APCHED 14000 FT IT WAS VERY EVIDENT THE PLANE WAS NOT GOING TO LEVEL OFF AT 14000 FT SO I DISCONNECTED THE AUTOPLT AND CLB BACK UP TO THE CROSSING ALT. ALT DEV WAS LESS THAN 500 FT IN THE CORRECTION MANEUVER. AFTER CIVET WE CONTINUED ON THE ARR AND APCH -- REENGAGING THE AUTOPLT AND VNAV AND THE SYSTEM WORKED JUST FINE. THERE WAS NO ACFT IN THE VICINITY AND ATC DID NOT MENTION ANYTHING DURING OUR DEV. DEBRIEFED THE EVENT; WE ARE NOT TOTALLY SURE WHAT CAUSED THE VNAV ANOMALY; EXCEPT THAT WHEN THE NEW TRANSITION AND APCH WERE PUT IN THE FMC SOMETHING HAPPENED WITH THE VNAV. IT WAS SUBTLE AS ALL INDICATIONS VNAV/VNAV PATH AND CORRECT CROSSING RESTR AT CIVET WERE ALL DISPLAYED IN FMS/FMC/GLARE SHIELD AND ADI. NEXT TIME IF AN APCH CHANGE OCCURS; I WILL TAKE ACFT OUT OF VNAV AND FLY VERTICAL SPEED; UNTIL ALL CHANGES IN FMC'S ARE COMPLETE. SECONDLY I WILL DISCONNECT AUTOPLT EARLIER IF VNAV APPEARS TO BE IN ERROR.SUPPLEMENTAL INFO FROM ACN 726380: WHILE THIS CASE RESULTED IN A MINOR (RELATIVELY) DEVIATION IN ALT; THE POSSIBILITY EXISTS TO HAVE A SIGNIFICANT ERROR EVEN THOUGH VNAV PATH IS ON THE FMA. GOOD CRM AND 'ONE GUY FLYING' AND 'ONE GUY TYPING' MINIMIZED THE IMPACT OF THE FMS/VNAV PATH ERROR. BOTTOM LINE: FLY THE AIRPLANE FIRST -- TYPE/REPROGRAM SECOND.