First step in optimising Tukey Chart

I have now written a simple Monte Carlo routine in Octave script to loop through a series of sine waves of periods 10 to 50 inclusive, with an amplitude of 1, to extract a series of optimised ucl and lcl multipliers such that each multiplier ensures that the ucl and lcl for that particular sine wave has a value of 1, i.e. perfectly encloses said sine wave between the control limits. The code is certainly "clunky" and not optimised for speed, but this is not important as it will only need to be run a few times. I calculate that it will take about 10 hours to obtain a total sample of 3000 multipliers for each sine wave period. I shall run this overnight tonight while I am sleeping and have the results ready for analysis from tomorrow.