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Additional resources for A Bayesian analysis of colonic crypt structure and coordinated response to carcinogen exposure incor

Example text

3. Re-estimating the model parameters but considering the data associated with real failures plus the expected ones associated with the run-outs. 4. Repeating Steps 2 and 3 until convergence of the process takes place. 5. 5 49 A fatigue model for varying stress range and given stress level If some specimens are tested to fatigue failure with loading cycles ranging from σm to σM for three different constant values of σm and a given fixed value σM = σM1 , we obtain the data indicated by crosses in Fig.

2 Parameter estimation . . . . . . . . 3 Alternative methods for dealing with run-outs . 5 Model for varying range and given stress level . 1 Derivation of the model . . . . . . . 2 Some weaknesses of the proposed model . . . 3 Parameter estimation . . . . . . . . 4 Use of the model in practice . . . . . . 5 Example of application . . . . . . . 6 Model for varying stress range and level . . 7 Dimensional Weibull and Gumbel models . . 8 Properties of the model .

5) S-N curve. 1: Dimensional analysis of the initial set of variables involved in the fatigue problem. M L T N 0 0 1 N0 0 0 1 Δσ 1 −1 −2 Δσ0 1 −1 −2 p 0 0 0 Fortunately, the Π-Theorem allows us to represent any relation between these variables in terms of a reduced set of dimensionless variables. 1 Thus, the initial set of five variables reduces to a set of three dimensionless variables. Though there are other alternatives, it seems convenient to choose N0 and Δσ0 as the normalizing variables, leading to the reduced set 1 In Sect.

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