Example 3614

For the deteriorating retaining wall beam in Example 36.13, use the hazard function to determine the probability that the retaining wall will fail in its 20th year if it has not failed earlier. Table 36.3 shows the hazard functions in 2-year increments based on the following computations:

ps(t) = ps(0) = 1.0 — pf (0) = 1.0 — 0.000946 = 0.999054

dps(t) _ dps(2) = (0 . 998844 — 0 .999054) = _0 000n dt dt 2 — 0 .

The graph of the hazard function is shown in Figure 36.8 Because the numerical differentiation causes uneven jumps in the curve, a best fit line through the points, often by fitting a Weibull distribution to the points, provides a smooth curve. Therefore, as shown in Table 36.3, the hazard rate at year 20, provided by best fit, is H(20) = 0.001951.

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