When problems arise there are great tools to attack them, specifically root-cause analysis and DMAIC. There are also excellent tools to stimulate creativity to develop new products, improve current products, and build innovative solutions. An excellent technique to help solve tough problems is Reverse Brainstorming.
Sorry to burst your bubble, but brainstorming is not very effective for developing new ideas. Most research on idea generation has shown brainstorming typically does not result in valuable ideas (Schirr, 2012). Most brainstorms are usually just a group of people haphazardly sharing ideas (Jones, 1995). Even with all the research on the flaws of brainstorming, it is still widely used in most organizations (Sutton & Hargadon, 1996).