This is an old formula. The latter part -- 'NOT my will' -- is more important than the former part. If one starts repeating it non-stop, the first thing he will discover is in a matter of minutes he will stop it. It will stop by itself. He will forget it. He will forget that he undertook such an exercise and it was forgotten. It means he is unrelated to this formula or God. Such a person lives physically or vitally. Maybe he lives mentally. God is not part of his scheme of things.
Suppose he does not forget but continues to repeat it, he will find the words missing or jumbled. In cases of exact repetition it may be "Let My will be done; Not Thy will" which he may not notice for some time. This is exactly opposite. Human nature is perverse and even hostile to the Divine and that is why this inversion. Let us forget these insufficiencies and perversities and consider one who is capable of RIGHT, GOOD repetition. It is great. He is a devotee. On further examination, the repetition will be from the surface mind.
Make this repetition complete, let it go behind when you are at work. In TRUE cases, it will be only for a small part of the day. To increase its duration is like getting a promotion in an office each month or each week. But it is possible with persistence. A moment comes when the whole day is covered by that. There is an innermost centre in us where we live all by ourselves where the closest person has no access. Move this repetition to that centre and gradually spread it all over the day. Let is be your spiritual companion.
By filling the day with it on the surface, all one's problems will vanish. Repeating it from the deepest centre all day, MAN will be unable to think of problems or opportunities as he will be pervaded by the Spiritual Peace - Shanthi - or Light in his inner being. Though he may not rise to the position of a realised soul, he will radiate joy to all who come in contact with him. It will make for inner contentment unknown to him until then. That will be a good foundation and the first step for any spiritual progress he may aspire for.