# test input
_x = [1,1,4,8,9,5]
_mu = 3

# define function to handle CUSUM
def add_by_one(input_array, my_mu):

  # initialize new array that we will return with cumulative sum values
  new_array = []

  # S0 = 0 by definition
  new_array.append(0)

  # loop through the input array values, arrays start at 0

  for index in range(len(input_array) - 1):
    current_sum = new_array[index] + input_array[index] - my_mu
    current_value = max(0, current_sum)
    new_array.append(current_value)

  return new_array

print(add_by_one(_x, _mu))