PLTS OF C560 SPLIT THEIR FLT CREW RESOURCES FOR ADMINISTRATIVE PURPOSES AND PASS THROUGH ALT RESTR AT KEPEC ON RNAV ARR TO LAS. A TCASII RA WITH B737 TFC RESULTS.

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WE WERE GIVEN THE KEPEC RNAV 1 ARR TO RWYS 25L/R AT LAX. THE ARR CALLED FOR XING KEPEC AT 12000 FT AND THE IPUMP AT 11000 FT. AFTER SKBER WE STARTED THE DSCNT TO 12000 FT FOR KEPEC. THE SIC ASKED ME TO TAKE COM #2 WHILE HE CALLED THE FBO AT LAS. I AGREED. (COM #2 IS USED FOR ATC.) AS THE ACFT APCHED 12000 FT; I SAW WHAT I THOUGHT WAS THE AUTOPLT CAPTURING THE ALT. I THEN SET 11000 FT IN THE AAD FOR THE IPUMY XING. ATC CALLED OUT TFC AT 11 O'CLOCK POS; I CALLED TFC IN SIGHT. THEN ATC CALLED TFC AT 2 O'CLOCK POS. I LOOKED; FOUND THE TFC (B737) AND CALLED IT IN SIGHT. ATC THEN CALLED SAYING; 'YOU SHOULD BE AT 12000 FT.' I LOOKED BACK AT ALTIMETER AND SAW WE WERE DSNDING THROUGH 11500 FT. I DISENGAGED THE AUTOPLT AND CLBED THE ACFT BACK TO 12000 FT. ATC INFORMED ME THAT THE OUTBOUND B737 HAD AN RA AND ATC WOULD BE FILING AN ALTDEV. AFTER LNDG; I REVIEWED COMPANY SOP'S WITH THE SIC. WE FELT THAT BY FOLLOWING COMPANY SOP'S MORE CLOSELY THE ALTDEV WOULD HAVE BEEN AVOIDED; IE; THE PNF SHOULD HAVE SET THE AAD FOR NEXT FIX. COMPANY SOP'S CALL FOR A STERILE COCKPIT BELOW 10000 FT. HOWEVER; WHEN GIVEN A CLRNC TO 'DSND VIA ARR' FLT CREWS SHOULD FOLLOW THE STERILE COCKPIT RULE FROM THE BEGINNING OF THE ARR.