ACR X DSCNT THROUGH OCCUPIED ALT TCASII TA HAD LTSS FROM ACR Y. SYS ERROR.

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ZOB CLRED ACR X FROM 3500 FT TO 3100 FT. WE STARTED AN INITIAL DSCNT OF ABOUT 500-800 FPM. AS WE PASSED 33000 FT; TCASII STARTED TO DISPLAY A TA AT OUR 12 O'CLOCK POS; BUT OFF SCALE; INDICATING IT WAS PAST 6 MI RANGE. ABOUT THIS TIME; CTR TOLD US TO 'INCREASE DSCNT RATE.' WHICH WE DID UP TO 1000 FPM. THE TCASII NOW INDICATED TFC AT ABOUT 12 O'CLOCK AND 6 MI AT PLUS 1000 FT CLOSING FAST. WE WERE AT ABOUT 32000 FT NOW AND CTR ADVISED US TO 'DSND AT 3000 FPM.' WE DID AND AS WE LEVELED OFF AT 31000 FT; ACR Y PASSED OUR 3 O'CLOCK POS AT 33000 FT. POTENTIAL CAUSE OF PROB: FO MISCONCEPTION THAT WE CAN DSND AT ANY REDUCED RATE TO OUR CLRED ALT VERSUS DSNDING AT OPTIMUM RATE. SUPPLEMENTAL INFO FROM ACN 268395: X GIVEN A CLRNC TO DSND AND MAINTAIN FL310 FOR TFC. DURING THE DSCNT (ABOUT 700-800 FPM; AT APPROX 33300 FT) THE CTLR GAVE US FURTHER INSTRUCTIONS TO GO 40 DEGS L AND INCREASE DSCNT RATE TO 3000 FPM. AT THAT TIME I INCREASED DSCNT TO 3000 FT WHILE INITIATING TURN. AT 32800 FT TARGET APPEARED 12 O'CLOCK ON TCASII. THE NEXT QUESTION WAS ASKED BY THE CTLR AS WE LEVELED AT 31000 FT AND ACR Y PASSED 900 FT ABOVE AND ABOUT 3 NM TO THE R ON TCASII.