EPS Homework - HackMD

# EPS Homework ## 1. Dependability: ### a.) S1, S2 -> Sensors P1 -> Processor ![](https://i.imgur.com/ehrcMu8.png) RS1 = 0.89 RS2 = 0.95 RP1 = 0.85 RSYS = (1-(1-RS1)×(1-RS2)) × RP1 RSYS = (1-(1-0.89)×(1-0.95)) × 0.85 RSYS = (1-(0.11)×(0.05)) × 0.85 RSYS = (1-0.0055) × 0.85 RSYS = 0.9945 × 0.85 RSYS = 0.845325 ### b.) S1, S2 -> Sensors Pnew1, Pnew2 -> Processor ![](https://i.imgur.com/7ImnXyt.png) RS1 = 0.89 RS2 = 0.95 RPnew1 = 0.80 RPnew2 = 0.80 RP_Parallel = 1 - (1-RPnew1)×(1-RPnew2) RP_Parallel = 1 - (1-0.8)×(1-0.8) RP_Parallel = 1 - (0.2)×(0.2) RP_Parallel = 1 - 0.04 RP_Parallel = 0.96 RSYS = (1-(1-RS1)×(1-RS2)) × RP_Parallel RSYS = (1-(1-0.89)×(1-0.95)) × 0.96 RSYS = (1-(0.11)×(0.05)) × 0.96 RSYS = (1-0.0055) × 0.96 RSYS = 0.9945 × 0.96 RSYS = 0.95472 The setup from b.) is more reliable. ### c.) S1, S2 -> Sensors P1 -> Processor λS1 = 0.5 × 10-5 λS2 = 0.8 × 10-5 λP1 = 0.3 × 10-5 λsys = λS1 + λS2 + λP1 λsys = 0.5 × 10-5 + 0.8 × 10-5 + 0.3 × 10-5 λsys = (0.5 + 0.8 + 0.3) × 10-5 λsys = 1.6 × 10-5 MTTF = 1/λ MTTF = 1 / (1.6 × 10-5) MTTF = 1 / (1.6 × 10-5) MTTF = 105 / 1.6 MTTF = 6.25 × 104 t = 1 year = 365 × 24h = 8760h Rsys(1 year) = e-λsyst Rsys(1 year) = e-1.6 × 10-5×8760 Rsys(1 year) = e−14016 × 10-5 Rsys(1 year) = e−0.14016 Rsys(1 year) = 0.869219149 = 86.9219149%