I’m running some websites with shared hosting providers for /month. I’ve been experiencing some down times. The tech support tell me there’s nothing wrong with my site. The server experienced heavy loads from other accounts sharing the same space. If I purchased VPS, would I experience the same problem?

It depends. Keep in mind that a VPS does not guarantee resources and therefore stability. Because a VPS is another word for shared! A VPS is one virtual server amongst many on the same physical server. If another VPS on the same server starts consuming more resources, the whole server will under perform, including your VPS.
Get your own dedicated server if you need stability. You can find dedicated servers for less than $100 dollars. Feel free to get in touch if you have any questions or comments.
Best
joe@unixy.net
shared hosting is bad compared to your own server. get your own server and DNS space and so one. load times is all up to how many people are on the server at any given time and actions performed. you may still experience down time by it will be your traffic that does it.
It completely depends on the quality of the provider. Any technology can be done properly or bungled badly. A virtual private server can be as oversubscribed as shared hosting.