In your control chart, if you use $+-2$ sigma limits for your control limits instead of the traditional $+-3$

sigma limits$,$ what would be the outcome?

You run the risk of calling the process in control when it is really out of control$-$Type II error

Nothing, because about $95\%$ of the data should fall within $+2$ standard deviation.

You run the risk of calling a process out of control when it really is not out of control$-$Type I error

Nothing, because your control limits are determined by your customer and not the process.