B737-700 FLT CREW HAS AN ALTDEV DURING THE MAIER1 PT MAIER ARR TO PHX.

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I WAS PF THIS LEG TO PHX. WE WERE ASSIGNED THE MAIER ARR; THE FIRST TIME MY FO OR I HAD FLOWN THIS NEW ARR. THROUGH SUBSEQUENT PHONE CALLS AFTER LNDG; I LEARNED THIS WAS ALSO THE FIRST DAY PHX WAS USING THIS NEW ARR. DURING THE DSCNT ON THE ARR; WHILE AT 8000 FT ALT AND 180 KTS; AS DEPICTED ON THE STAR; I UNINTENTIONALLY STARTED THE NEXT DSCNT DOWN TO BE LEVEL AT KUCOO APPROX 2.5 MI EARLY; INITIALLY LOOKING AT THE -700 SITUATIONAL DISPLAY AND 'THOUGHT' WE WERE OVER EDDNA; BUT FAILED TO CONFIRM WE WERE OVER EDDNA WITH THE FMC. SINCE THIS WAS MY FIRST TIME DOING THIS ARR; I HAD BEEN ALSO LOOKING OUTSIDE A LITTLE MORE THAN USUAL DURING THE DSCNT FOR THE VISUAL REFS ON HOW THIS STAR WAS BRINGING US INTO THE PHX ARPT; AND INITIALLY COULDN'T FIND SKY HARBOR VISUALLY FROM THE N; PROBABLY DUE TO THE SUN ANGLE/SHADOWS. AT 7500 FT ON THE ALTIMETER; PHX TRACON GAVE US A CALL TELLING US OUR LOW ALT. I WAS UNAWARE OF MY DEV BELOW THE PRESCRIBED ALT AT THAT TIME; BUT MY FO NOTICED THE DEV JUST AS TRACON MADE THE CALL AND TOLD ME WE HAD STARTED DOWN FROM EDDNA A LITTLE EARLY; AND WERE 500 FT LOW. NEITHER OF US NOTICED ANY TFC CONFLICTS VISUALLY OR ON TCAS. THROUGH MY CALL AFTER LNDG; THIS WAS ALSO CONFIRMED BY TRACON. I ALSO MENTIONED TO THE TRACON REPRESENTATIVE ON THE PHONE AFTER LNDG THAT IT WAS TOTALLY MY ERROR ON THE NEW ARR. THE PROCS FOR THE NEW ARR ARE FINE.