I suspect you are going to be battle errors in multiple places.
This section of code has 2 significant problems
array_city(i) = Range("A" & i).Value
array_rank(i) = Range("E" & i).Value
array_assign(i) = Range("F" & i).Value
First you are trying to assign values to array that do not have any dimensions. You decleared the arrays but you left them dimensionless. You need to define the dimensions before you try to assign values to the array
Something like
Redim array_city(1 to count)
Next you are trying to get a value from Range("A" & i) when the value of i is zero. Cell "A0" does not exists and will also throw an error.
So to rewrite your code as written, you would need to make a few changes:
Sub DistSystem()
Dim count As Integer
Dim i As Integer
Dim array_rank() As Variant
Dim array_city() As Variant
Dim array_assign() As Variant
count = Sheets("111").Range("Y2").Value
Redim array_rank(1 to count)
Redim array_city(1 to count)
Redim array_assign(1 to count)
For i = LBound(array_rank) To UBound(array_rank)
array_city(i) = Range("A" & i).Value
array_rank(i) = Range("E" & i).Value
array_assign(i) = Range("F" & i).Value
Next
For i = 1 To 10
MsgBox array_rank(i)
Next
End Sub
However, you are over complicating how you are reading the values into the array. You can simply read the entire range directly into the array
Sub DistSystem()
Dim count As Integer
Dim i As Integer
Dim array_rank As Variant 'Notice the arrays are not longer declared with ()
Dim array_city As Variant ' -> this is necessary
Dim array_assign As Variant
count = Sheets("111").Range("Y2").Value
array_city = Range("A1:A" & count).Value
array_rank = Range("E1:E" & count).Value
array_assign = Range("F1:F" & count).Value
For i = 1 To 10
MsgBox array_rank(i, 1)
Next
End Sub
The resulting array with be 2 dimensions, with the Row value as the first dimension and the column as the 2nd dimension. since all of the ranges are a single column, you would access any value by calling array_rank(Row,1) or array_city(Row,1) or array_assign(Row,1).
