FLT ATTENDANT RPT; B767-ER; LAX GATE; INADVERTENT SLIDE DEPLOYMENT DUE TO FLT ATTENDANT FATIGUE.

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WHEN WE ARRIVED AT THE GATE IN LAX; A FLT ATTENDANT INADVERTENTLY DEPLOYED THE R REAR DOOR SLIDE. WHEN I WENT BACK TO INVESTIGATE THE SIT; I FOUND HER IN TEARS. THROUGH HER TEARS SHE SOBBED; 'IN 20 YRS WITH THE (COMPANY) I'VE NEVER DONE ANYTHING LIKE THIS.' SHE CONTINUED; 'I TOLD THEM I WAS TOO TIRED TO TAKE THIS FLT; BUT THEY WOULDN'T LISTEN AND NOW THIS HAS HAPPENED.' CHKING INTO THIS SIT; I LEARNED THAT ON THE PREVIOUS DAY THIS FLT ATTENDANT HAD AN UNBELIEVABLE 10 HRS 55 MINS OF BLOCK TIME INCLUDING CLOSE TO 7 HRS ON THE GND; TAKING CARE OF IRATE PAX 'TRAPPED' ABOARD THE ACFT DURING AN INCREDIBLE GND DELAY AT DFW. DURING A SUBSEQUENT CREW REST; SHE GOT VERY LITTLE SLEEP DUE TO TRANSPORTATION AND HOTEL PROBS. UPON ARRIVING AT HER HOME BASE; SHE WAS EXPECTING TO BE RELEASED BUT SHE WAS TOLD SHE HAD TO CONTINUE FLYING AND TAKE THE FLT TO LAX (MY FLT). SHE TOLD THE SCHEDULER HOW EXTREMELY FATIGUED SHE WAS; NEVERTHELESS THEY MADE HER TAKE THE FLT. (SHE TOLD ME SHE WAS AFRAID TO LITERALLY 'REFUSE' TO TAKE THE FLT.) I DID NOT LEARN HOW FATIGUED THIS FLT ATTENDANT WAS UNTIL AFTER THIS MISHAP. IF I HAD KNOWN ALL OF THE ABOVE-MENTIONED FACTS; AS CAPT; I WOULD NOT HAVE ALLOWED HER TO WORK ABOARD MY FLT; BECAUSE HER FATIGUE MADE HER UNSAFE. THE SAFETY ISSUE HERE IS FATIGUE. WHEN A CREW MEMBER (ESPECIALLY A VERY DEDICATED LONG-TIME EMPLOYEE; AS IN THIS CASE) SAYS SHE IS VERY FATIGUED; SHE NEEDS TO BE LISTENED TO AND BELIEVED; AND SCHEDULES NEED TO BE MODIFIED BEFORE SAFETY IS COMPROMISED.