RWY TRANSGRESS. MISUNDERSTOOD TAXI INSTRUCTIONS; FLC CROSSED ACTIVE RWY.

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THE ACFT WAS PARKED AT (FBO-X) RAMP IN LAS. BOTH MYSELF AND THE OTHER PLTS ARE RATED CAPTS; AND ALT SEATS AND RESPONSIBILITIES ON EVERY OTHER LEG. I WAS IN THE L SEAT COPYING THE ATIS (WITH MY HEADPHONES ON) WHILE THE OTHER PLT CALLED FOR TAXI. THE ATIS SAID 'EXPECT (TURBO JETS) RWY 25 FOR DEP; ALL OTHERS EXPECT RWY 19. AS I SWITCHED RADIOS OVER TO GND CTL I THOUGHT I HEARD THE CTLR CLR US TO 'B' TXWY. I CONFIRMED WITH THE OTHER PLT THAT WE WERE CLRED VIA TXWY B TO RWY 25.' AT THE SAME TIME I ASKED THE QUESTION; THE 'DOOR UNSAFE' LIGHT ILLUMINATED. I STARTED TAXIING FORWARD TO TXWY B. AS WE NEARED THE INTXN OF TXWY B AND RWY 19; I AGAIN ASKED THE OTHER PLT IF WE WERE CLRED TO RWY 25 BECAUSE I COULD SEE ALL ACFT ON EXTENDED FINAL FOR RWY 19. HE SAID THAT 'YES WE ARE.' I CROSSED RWY 19 AND THE GND CTLR INFORMED US THAT WE HAD CROSSED AN ACTIVE RWY. CAUSES AND CONTRIBUTING FACTORS THE CREW HAD STARTED THE DUTY DAY AT XD00 (XA00 LAS TIME) FOR A TOTAL OF APPROX 15 1/2 HRS OF DUTY TIME AND 4.3 HRS OF FLT TIME. BOTH PLTS WERE ON DIFFERENT RADIOS. 1) A POSSIBLE SOLUTION TO THE PARTICULAR PROB WOULD BE TO INSURE THAT OPERATORS UNDER FAR 91 HAVE SET DUTY TIME LIMITATIONS. 2) STRESS BETTER STANDARDIZATION OF COCKPIT PROCS FOR SPECIFIC ACFT TYPES.