Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, i.e.,design,deployment and phase out.Most safety assessment methods consider only system parameters,such as configuration,hazard rate,coverage,repair rate,etc.along with periodic proof-tests (or inspection).Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants,chemical plants,etc.In this paper,a basic model of IEC 61508 is used.The basic model is extended to incorporate process demand and behavior of electronic- and/or computer-based system following diagnosis or proof-test.A new safety index,probability of failure on actual demand (PFAD) based on extended model and demand rate is proposed.Periodic proof-test makes the model semi-Markovian,so a piece-wise continuous time Markov chain (CTMC) based method is used to derive mean state probabilities of elementary or aggregated state.Method to determine probability of failure on demand (PFD) (IEC 61508) and PFAD based on these state probabilities are described.In example,safety indices of PFD and PFAD are compared. Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, ie, design, deployment and phase out. Host safety assessment methods consider only system parameters, such as configuration, hazard rate, coverage, repair rate, etc.along with periodic proof-tests (or inspection) .Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants, chemical plants, etc.In this paper, a basic model of IEC 61508 is the basic model is extended to incorporate process demand and behavior of electronic and / or computer-based system following diagnosis or proof-test. A new safety index, probability of failure on actual demand (PFAD) based on extended model and demand rate is proposed. Periodic proof-test makes the model semi-Markovian, so a piece-wise continuous time Markov chain (CTMC) based method is used to derive mean state probabilities of elementary or aggregated state. Method to determine probability of failure on demand (PFD) (IEC 61508) and PFAD based on these state probabilities are described. In example, safety indices of PFD and PFAD are compared.