Take a close look at your inspections. Pay special attention to the reasons for the inspection and whether they should be permanent (i.e. regulatory) or if there is the potential to eliminate the need for the inspections.
Once you understand where you are checking, test the effectiveness of your inspections. Over an extended period of time, randomly check inspected units. To prevent the Hawthorne Effect from creeping in, only check items that were signed off on prior to the secondary inspectors showing up. This keeps the primary inspectors from adjusting their process based upon the check. The goal here is to highlight the shortcomings of inspecting quality into a process.
Armed with this information, work to get rid of inspections. The best way to eliminate them is to understand the problems that are being identified. Make sure you have an inspection log and are compiling data about the defects. With that information, you can do two things. The first is the best option. Build quality into the process where the error is occurring and eliminate the need for the inspection.
The second is to move the inspection closer to the point of origin. When the inspection id conducted at the end of a process, it has the unoriginal name of end-of-line inspection. Source inspections are done much closer to where the error actually occurred. Inspections can also be done at the next downstream process, which serves to get a second set of eyes on an item. Regardless of who find the problem, though, the operator gets the advantage of seeing the conditions that caused the error, often while they are still present. End-of-line inspections tend to give limited feedback that arrives too late to do a thorough investigation.