I see now that there's a different problem. The array is badly defined. It needs to be:
var aFields = ["CheckBox1", "CheckBox2", "CheckBox3"];
Also, I think there's a logical error in your code. Since you want to check if any of the fields has the "Failed" value you should break the loop once you discover that one of them has that value. Otherwise, you're in effect only checking the last field. So your code should actually be:
// array of field names to check
var aFields = ["CheckBox1", "CheckBox2", "CheckBox3"];
// clear the field's value
event.value = '';
// loop through the check boxes and test for 'Failed"
for(i = 0; i < aFields.length; i++) {
if(this.getField( aFields[i] ).value == "Failed") {
// set event value to "Failed" and stop
event.value = "Failed";
break;
} // end match field
} // end loop of check boxes
