What would you prefer: The carrot or the stick? Punishment works and is frequently used in less mature safety programs as a reaction to some incident that hurt someone. But there are negative side effects: greater absenteeism, more waste & damage, and less pleasantries. Supervisors feel like police officers rather than leaders. Moreover, you'll not get a culture where workers feel they can freely report hazards, close calls, and minor injuries which blinds you to the risks out there.
Reward can be a double-edged sword too. Incentives, where we give money or some valuable item for achieving a certain number of days without a recordable incident too often result in the hiding of hazards, close calls and minor injuries too. Noone wants to lose the incentive.
A company must have a consistent discipline program but it should be designed so supervisors have an opportunity to coach their workers in safe practices first. Any reward program should celebrate the identification through reporting of hazards, close calls, minor injuries and at-risk behaviors (through peer-to-peer observations).