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13 June, 00:43

3. Determine the expected failure rates, f, and mean time between failures (MTBF), 1/f, for control systems with SIL1, SIL2, and SIL3 ratings with PFDs of 10-2, 10-3, and 10-4, respectively.

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  1. 13 June, 03:51
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    SIL1, SIL2, and SIL3 ratings with PFDs of 10-2, 10-3, and 10-4, respectively.

    PFD is the failure probability denoted as P.

    Let's define R as its inverse.

    Therefore, R = 1 - P

    The failure Rate f is given by

    f = - In R.

    The mean time between failures (MTBF), 1/f

    For SIL1,

    P = 2/10 = 0.2

    R = 1 - 0.2 = 0.8

    failure rate f = - In (0.8) = 0.2231

    MTBF = 1/f = 4.481

    For SIL2,

    P = 3/10 = 0.3

    R = 1 - 0.3 = 0.7

    failure rate f = - In (0.7) = 0.3367

    MTBF = 1/f = 2.804

    For SIL3,

    P = 4/10 = 0.4

    R = 1 - 0.4 = 0.6

    failure rate f = - In (0.6) = 0.5108

    MTBF = 1/f = 1.9576
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