The first steps in improving machine safety and gaining its performance benefits begin with conducting a risk assessment (RA), and the most up-to-date standard that shows how is EN ISO 13849-1. This process and related calculations are described in ABB Jokab Safety's "Safety in Control Systems According to EN ISO 13849-1."
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While understanding EN ISO 13849-1's calculations isn't too hard, there are software and online tools that can help. The freely downloadable Sistema software utility provides developers and testers of safety-related machine controls with comprehensive support in evaluating safety in the context of ISO 13849-1. It's available from the German Social Accident Insurance organization's Institute for Occupational Safety and Health.