No idea about otb, but on chess.com blitz it took me about 2 years, while being a student.
How much much time for a person to reach 1500 to 1800?

I think that if you want to reach 1800 then you must start build up a opening repertoire and try to play that opening in every game. This will give you good idea about the certain middlegame positions which you will always reach by playing that particular opening. You can select some openings by analyzing your style of play , whether you are attacking player or a bit positional. You may also see whether you play better in closed positions or in open positions. All this will help you to select the ideal opening for you. After selecting the opening you can learn that opening in detail through the resources available on YouTube and also you can see the master games of that opening on chessgames.com. In this way your opening and middle game will surely improve . And for the endgame you can check out the end game exclam! series by st Louis chess club which is available on YouTube. Also you should play players which are higher rated than you because it is said that if you want to reach higher rating then you must play higher rated players. I started playing on chess.com 6 months ago and at that time my rating was arround 800. In 6 months I have tried all those things I mentioned above and this helped me to improve my rating to 1450. So you may reach the 1800 mark within 6 months time if you work hard . I know you have the potential and ability to do it. Good luck.

I think that if you want to reach 1800 then you must start build up a opening repertoire and try to play that opening in every game. This will give you good idea about the certain middlegame positions which you will always reach by playing that particular opening. You can select some openings by analyzing your style of play , whether you are attacking player or a bit positional. You may also see whether you play better in closed positions or in open positions. All this will help you to select the ideal opening for you. After selecting the opening you can learn that opening in detail through the resources available on YouTube and also you can see the master games of that opening on chessgames.com. In this way your opening and middle game will surely improve . And for the endgame you can check out the end game exclam! series by st Louis chess club which is available on YouTube. Also you should play players which are higher rated than you because it is said that if you want to reach higher rating then you must play higher rated players. I started playing on chess.com 6 months ago and at that time my rating was arround 800. In 6 months I have tried all those things I mentioned above and this helped me to improve my rating to 1450. So you may reach the 1800 mark within 6 months time if you work hard . I know you have the potential and ability to do it. Good luck.
"... This book is the first volume in a series of manuals designed for players who are building the foundations of their chess knowledge. The reader will receive the necessary basic knowledge in six areas of the game - tactcs, positional play, strategy, the calculation of variations, the opening and the endgame. ... To make the book entertaining and varied, I have mixed up these different areas, ..." - GM Artur Yusupov

"... This book is the first volume in a series of manuals designed for players who are building the foundations of their chess knowledge. The reader will receive the necessary basic knowledge in six areas of the game - tactcs, positional play, strategy, the calculation of variations, the opening and the endgame. ... To make the book entertaining and varied, I have mixed up these different areas, ..." - GM Artur Yusupov
Sad just sad...

I heard Nigel Short tell a story recently about when he was the Iranian National chess coach, and particularly working with one player who was struggling to improve (I think it was Atousa Pourkashiyan, but I can't remember 100%). Short told her to spend a couple of hours a day doing tactics, so she did, and her performance shot up. I know, everyone says "tactics, tactics, tactics" but don't underestimate how many Elo points this could bring you, so you should definitely include this in your study plan. Indeed, if you have time, try a book like Grandmaster Preparation: Calculation by Jacob Aargaard - each puzzle is designed to be tough and at times you'll have to spend hours on an individual puzzle. Even if you don't get the full answer, just studying a position that in-depth for that long will certainly help improve your chess and the way to evaluate your candidate moves.
Good luck, keep us up to date with your progress!

Everybody says tactics, and rightly so. "Up to a certain level chess is 99% tactics."
You're wrong! If you don't know some basic endgames you won't get anywhere.

I think that if you want to reach 1800 then you must start build up a opening repertoire and try to play that opening in every game. This will give you good idea about the certain middlegame positions which you will always reach by playing that particular opening. You can select some openings by analyzing your style of play , whether you are attacking player or a bit positional. You may also see whether you play better in closed positions or in open positions. All this will help you to select the ideal opening for you. After selecting the opening you can learn that opening in detail through the resources available on YouTube and also you can see the master games of that opening on chessgames.com. In this way your opening and middle game will surely improve . And for the endgame you can check out the end game exclam! series by st Louis chess club which is available on YouTube. Also you should play players which are higher rated than you because it is said that if you want to reach higher rating then you must play higher rated players. I started playing on chess.com 6 months ago and at that time my rating was arround 800. In 6 months I have tried all those things I mentioned above and this helped me to improve my rating to 1450. So you may reach the 1800 mark within 6 months time if you work hard . I know you have the potential and ability to do it. Good luck.

I heard Nigel Short tell a story recently about when he was the Iranian National chess coach, and particularly working with one player who was struggling to improve (I think it was Atousa Pourkashiyan, but I can't remember 100%). Short told her to spend a couple of hours a day doing tactics, so she did, and her performance shot up. I know, everyone says "tactics, tactics, tactics" but don't underestimate how many Elo points this could bring you, so you should definitely include this in your study plan. Indeed, if you have time, try a book like Grandmaster Preparation: Calculation by Jacob Aargaard - each puzzle is designed to be tough and at times you'll have to spend hours on an individual puzzle. Even if you don't get the full answer, just studying a position that in-depth for that long will certainly help improve your chess and the way to evaluate your candidate moves.
Good luck, keep us up to date with your progress!
... if you have time, try a book like Grandmaster Preparation: Calculation by Jacob Aargaard ...
http://www.qualitychess.co.uk/ebooks/CALCULATION-excerpt.pdf
http://www.jeremysilman.com/shop/pc/Grandmaster-Preparation-Calculation-77p3705.htm
You should first precisely assess Your level, then find appropriate books. Studying middlegames (strategy and tactics) and endgames You learn more chess than with openings. Polishing the opening repertoire can be left for later. Anyway, it requires serious time investment over a good number of months.
Some forums with analyses are okay to read, and many YouTube videos are okay.
(PM me for more or more precise info.)