Six sigma is a systematic approach to improvement. See here for some introduction. One of the basic models used in six sigma improvement projects is DMAIC model: Define, Measure, Analyse, Improve and Control. This basic model can be easily applied to safety management.
In the context of safety management, the organisation need to DEFINE what safety problem they are trying to tackle. This could be a unsafe behaviour that the organisation is trying to minimise. Then the organisation need to MEASURE the safety problem to understand the issue at hand thoroughly. This could involve observation of operators, or collecting samples of inspection records. The data collected must then be ANALYSED to identify the underlying causes. The team can also create time series plots (in systems thinking terms, this are the “behaviour over time plot”) of the key parameters and understand the qualitative relationship between the parameters. This might lead on to a causal loop diagram (one of the tools used in systems thinking) being drawn.
Subsequently, solutions must be identified and then implemented to IMPROVE the situation. Whatever solution implemented must then be monitored to ensure that they are effective in CONTROLling the safety problems that the project is meant to reduce. This might involve the use of control charts or perhaps further observations.