Make your requirements less dumb. Doesn't matter who gave them to you, or how smart they are. Requirements don't come from departments, they come from people.
Delete the part or process step. If you're not occasionally adding them back in, you're not deleting enough.
Simplify and optimize. However, don't optimize a part that shouldn't exist.
Accelerate cycle time. Don’t get complacent with your current pace.
Automate. Good automation is often unnoticed due to it’s high efficiency.
If you do these in the wrong order, you will inevitably suffer.
Requirements
Making your requirements less dumb is maybe too harsh a way of putting it, especially if someone else wrote them. But this step is the most important to start with as requirements are the ground truth for your designs.
Delete the Part or Process Step
As entropy grows in a system or design we end up with components that are redundant or no longer necessary. A switch that is never used, a screen that is never looked at, or code that is never executed. Always stay hungry to delete these components as they are the necessary overhead that stops you from working on things that matter. Generally, if you are not putting back components your removed at least sometimes, you are not deleting enough.
Simplify and Optimize
But don't optimize a part that shouldn't exist (see step 2).
Sometimes the right components are arranged in the wrong way caused by evolution in need of revolution. Always be mapping and learning to see the inefficiencies at every layer of abstraction.
Always spend your engineering time according to the theory of constraints. The component that requires optimization is the one with the largest effect on the total system. This is most clear in serialized processes: the step that takes the longest is the one that gains the most from a proportional improvement.
Accelerate
Often the best way to find the constraint in a system, especially a procedural one is to accelerate until something breaks or is at least showing signs of over-stress. This may also be referred to as benchmarking.
The same goes for engineering processes. Fast feedback loops with many iterations always net better products.
Don't let expectations set your goals too low. A production line is better spent at half utilisation than at half speed. Forget mantras like "Time to lean? time to clean. " and promote up-skilling and continual improvement.
Automation
Automation is the most alluring of all steps and is often the one that is mistakenly attempted first. However a system that is not well understood by applying the proceeding four steps will fall fowl to automating the wrong part or process.