Here are some ideas that have worked out for us in speeding up our new product development process. Note that some of these ideas increase cost and others increase risk. However for many projects, the biggest cost is the cost of the project delay.
Make sure the development engineers have spare capacity
Break new product development process into small tasks
Start doing a development task as soon as enough information, material and parts are available for meaningful work to take place
Reuse technology and product modules as far as possible
Separate out product development tasks from technology development tasks
Use rapid prototyping techniques
They convey the full impact of the product to all the people involved. Quite a few people are unable to visualize the finished product from the CAD drawings or even the solid model.
Many tests can be performed or approximated in the lab. See the article Quick free product testing for Environmental and ESD issues
Get prototypes in the hand of users as soon as possible
Have the development team in one location