LGT ACFT ON ARR WAS CLRED TO HOLD AND RPTR CAPT THOUGHT THE HOLDING FIX WAS A CLOSER DME THAN THE CLRNC AND ATC INTERVENED WHEN SEEING ACFT CONTINUE PAST HOLDING FIX.

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WHILE FLYING THE KASPR 1 ARR INTO MSP; TSTMS NECESSITATED HOLDING FOR ALL MSP ARRS. UPON INTERCEPTING THE FARMINGTON 178 DEG RADIAL WE WERE GIVEN HOLDING INSTRUCTIONS FOR A HOLD AT KASPR INTXN. THE FO WROTE DOWN THE INSTRUCTIONS AND READ THEM BACK TO ATC. I IMMEDIATELY BEGAN FUEL CONSUMPTION COMPUTATIONS AND ASKED THE FE FOR THE PLANNED FUEL BURN TO OUR ALTERNATE. I THEN ASKED FOR THE FE TO FIGURE OUR PROPER HOLDING AIRSPD. KASPR INTXN IS AT THE 40 DME POINT ON THE 178 DEG RADIAL. IN THE MIDST OF MY COMPUTATIONS AND FE REQUESTS; I MISTAKENLY THOUGHT THAT THE HOLD WAS ASSIGNED AT THE BANNI INTXN (28 DME). UPON REACHING 38 DME; 2 MI PAST KASPR; ATC ASKED IF WE HAD STARTED OUR TURN OUTBOUND IN THE HOLD. THINKING THAT I STILL HAD 10 MI TO GO; AND THE FO MISTAKENLY THOUGHT SO TOO; HE RESPONDED 'NO.' AT THAT TIME; ATC TOLD US TO IMMEDIATELY TURN R TO 180 DEGS. ATC ALSO STATED THAT KASPR INTXN WAS 15 MI BEHIND US. I DO NOT KNOW WHY HE SAID THIS; BECAUSE IF WE WERE 15 MI PAST KASPR; WE WOULD HAVE BEEN 3 MI PAST BANNI; WHICH WAS WHERE I HAD PLANNED TO START THE HOLD. NONETHELESS; I DID MISS THE KASPR INTXN. THE MISTAKE WAS DISCOVERED WHEN ATC QUERIED US ABOUT STARTING THE TURN. THE CONTRIBUTING FACTORS WERE MY OWN APPREHENSIVENESS ABOUT THE TSTMS IN THE TERMINAL AREA; AND THE HIGH MENTAL AND PHYSICAL (FLYING THE AIRPLANE) DEMANDS THAT I PLACED UPON MYSELF. THE MOST OBVIOUS CORRECTIVE ACTION WOULD BE TO UTILIZE BETTER CREW MGMNT TECHNIQUES WHEN DEALING WITH SIMILAR SITS. I SHOULD HAVE GIVEN CTL OF THE ACFT TO THE FO AND VERBALLY CONFIRMED WITH HIM THE HOLDING INSTRUCTIONS. AFTER DOING THIS; I WOULD HAVE BEEN MORE CAPABLE OF COMPUTING MY EXPECTED FUEL BURN DURING THE HOLD; AS WELL AS BEING ABLE TO WORK WITH THE FE TO FIGURE A HOLDING SPD AND ANTICIPATED FUEL BURN TO THE ALTERNATE.