PSI - Issue 1

M. Muniz-Calvente et al. / Procedia Structural Integrity 1 (2016) 142–149 M.Muñiz Calvente/ Structural Integrity Procedia 00 (2016) 000 – 000

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2.7. Step 7: Convergence of Weibull parameters

The last step of the iterative process implies evaluation of the convergence rate of the Weibull parameters by comparing the values obtained in the preceding iteration with the last one using the expression:

                1 1 1 i i i i i i

(5)

If the change in the summation of the absolute values of the three parameters remains below a prescribed threshold value ε, the iterative process is stopped and the parameter values obtained from the last iteration are considered to be the final solution. However, if that change is higher than ε, the iterative process returns to step 3 in order to improve the calculation of the global probability by modifying the rank order assigned. Figure 7 shows the convergence process of the Weibull parameters for the example being handled

Fig 7. Convergence of Weibull parameters.

In order to check the quality of the primary failure cumulative distribution function PFCDF derived, an estimate of the experimental cumulative distribution function of failure ECDFF for each particular sample included in the test program may be found and compared this with the results experimentally obtained, see Fig. 8.

Fig 8. a) Comparison between the EFCDF estimated from the PFCDF and the simulated experimental results and b) EFCDFs for either test type.