I am speaking purely as a HR Manager, not as a Safety Pro. The last 23 years of my formal career I worked for a Corporation that is a National Defense Contractor, who considered themselves the premier manufacturer of all the products they made. For example, any aircraft built in North America has my companies’ control systems in it, including all military aircraft. Every year all employees must sign NDAs that included strict confidentiality clauses. We had explicit rules against employees taking pictures and sharing any of them with non-employees and forbid any non-employee to use cellphones or cameras in our facilities. We did not allow cell phones to be used in the plant due to confidentiality, not because we did not trust our employees wasting time on their phones. Every employee understood why confidentiality was so important to national security and to our customers.
The key word here is TRUST. You either trust your employees or you do not! Do not expect to get much cooperation from your employees if you do not TRUST them FIRST! If you have product and other issues that require confidentiality, ban cell phones, but tell your employees why. Make sure you enforce the policy justly. Which brings up the other issue, “Fairness!” If for whatever reason you are going to ban cellphones from the plant floor that means NO ONE can use cellphones. That includes CEOs, Owners, Managers, Supervisors, Visitors, and down the food chain. If you do not do that and for example, allow Managers and Supervisors to use cell phones and ban them from your employees, I do not care how you do it, that kind of policy will just add more bricks to the wall between Management and Employees! We should be tearing that wall down not up! That is why I always left my cellphone in my office when I went into the plant. If I had to take pictures I used a digital camera not a cellphone! Bottom line, If you ban cell phones that means EVERYONE!!

Can you install a cell phone blocker in the building to restrict cell signals within a certain area?

Policy is policy. If you excuse it forever, why would they follow any other rule? I like Ron's idea to make designated phone areas. This will give you time to communicate with the employees and their management, design and roll-out the new areas, and inform folks ahead of time that the policy will be enforced moving forward.

Our quarterly bonus ($100/person) is based on the adherance to safe practices in several categories. The entire dept. will lose 10% bonus if one employee is seen using cellphone. This way employees police themselves becase bonus audit is unannounced and can happened any time.