# test input
_x = [1,1,2,4,2,4,6,8,9,1,2,3,1,2,1,5]
_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)):
    # calc cumulative value, store in temp value
    cumulative_value = new_array[index] + input_array[index] - my_mu

    # take max of cumulative value and zero
    max_value = max(0, cumulative_value)

    # append to the the array
    new_array.append(max_value)

  # return new array, first 0 is S0 that we set to 0 by default
  # you can optionally pop this off before return if you need to
  return new_array

# print result with test array
print(add_by_one(_x, _mu))