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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2.3. Step 3: Estimation of global probabilities

The first difficulty to overcome in the joint assessment of experimental samples comprising heterogeneous specimen geometry or size, consists in the results ranking because the critical value of the generalized parameter reached at each test is related to its size or geometry. For this reason, the global probability of failure related to each test must be initially estimated from Eq (1) in order to proceed to the next step.

   

   

   

   



   

   

S

GP







 1 (1   



ij

ij

P

P

    1 exp ) 1

(1)

Int

 fail S ,

S



ij

ref

ref

In the first iteration, the Weibull parameters could be randomly estimated although this may lead to saturated values of the global probabilities, i.e. 0 or 1, for all specimens. Therefore, an initial estimation of the Weibull parameters resorting to only one homogeneous test size and geometry would be advisable. Figure 4 shows the relation between the critical values of the GP and the global probabilities after the first iteration.

Fig. 4. Maximum values of GP and global probability of failure obtained from each test (after first iteration)

2.4. Step 4: Rank order assessment and allocation of probability The failure results are ranked in increasing order according to the global probability of failure obtained for each test. After that, a new probability of failure ( i fail P , ) is associated to each of them using a plotting position rule, such as that given by Bernard (1955):

(2)

n i

0.4 0.3



P



, i fail



2.5. Step 5: Transfer all results to the reference size

It is important to notice that each critical value of the generalized parameter GP is associated with an equivalent size in such a way that if this equivalent size is subjected to such a GP value the same probability of failure occurs as the experimental one for the component when subjected to this critical value of the GP. In order to perform a joint assessment, each result must be referred to its corresponding reference size. To do this, the critical values of the