Safety and Reliability of Embedded Systems - Software Engineering ...
Safety and Reliability of Embedded Systems - Software Engineering ...
Safety and Reliability of Embedded Systems - Software Engineering ...
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General Formulas for AND / OR with n Inputs, NOT, XORAND-Gate:OR-Gate:n∏P out= P ii=1∏ ( 1 − )P out= 1 − P ini=1Precondition for these formulas:Stochastically independentevents! NOT-Gate: P = 1 − (only one input)outP inXOR-Gate:Pout=n∑i = 1P ⋅in∏j = 1j ≠ i(1 − P )j XOR is normally defined for 2 inputs only The n-out-<strong>of</strong>-m Voter can be replaced by a combination <strong>of</strong> AND / OR gates The Inhibit-Gate can be replaced by an AND <strong>and</strong> a NOT gate The Priority-AND has no static combinatorial formula<strong>Safety</strong> <strong>and</strong> <strong>Reliability</strong> <strong>of</strong> <strong>Embedded</strong> <strong>Systems</strong>© Pr<strong>of</strong>. Dr. Liggesmeyer, 8Calculation <strong>of</strong> Top-Event ProbabilityLaptopunavailable0.154 Apply gate formulas in a bottom-upfashion Stop if top-event is reached>=10.06 Bottom-up calculation is not efficient forlarge FTs&There are two practical algorithms...0.2 0.3 0.1Battery emptyNo socketaroundHardwaredefective<strong>Safety</strong> <strong>and</strong> <strong>Reliability</strong> <strong>of</strong> <strong>Embedded</strong> <strong>Systems</strong>© Pr<strong>of</strong>. Dr. Liggesmeyer, 95
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