PSI - Issue 47

Anass Gouya et al. / Procedia Structural Integrity 47 (2023) 448–453 Author name / Structural Integrity Procedia 00 (2019) 000–000

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reliable. The method of variance-based sensitivity indices developed by Sobol is based on the ANOVA decomposition and has the following unique decomposition: ( )= 0 + ∑ ( ) =1 + ∑ ( , ) 1≤ < ≤ + ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ + 1 , 2 , ∙∙∙∙∙∙∙ , ( 1 , 2 , ∙∙∙∙∙∙∙∙∙∙∙∙ , ) (2) The variance of the output variable can therefore be shown as : = ∑ =1 + ∑ 1≤ < ≤ + ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ + 1 , 2 , ∙∙∙∙∙∙∙∙∙ , (3) 4.4. The variance of contribution result The Taguchi approach involves employing statistical techniques for analyzing the experimental data in order to define the optimal levels of various factors of control. One important statistical tool that has been used in the Taguchi method is ANOVA, a technique which is used to assess the contribution made by each control factor towards the overall variability of the response item. This variance of contribution serves as a measure of the comparative importance of each control factor at determining the success of the product or process.

Table 2:The analysis of variance results

Degree of freedom

Contribution P (%) 26,31777581 1,388578999 3,43097742 3,294001649 34,43133388 31,13733223

F-Variance ratio

Symbol

Sum of square

Variance

A B C

2 2 2

66,126942 3,488991 8,620791 8,276621 86,513345 78,236724

79,8961 4,2155 10,4158

33,063471 1,7444955 4,3103955 0,41383105 3,327436346

Error Total

20 26

- -

Model

6

13,039454

31,5091

The variance and contribution of each factor on the response of the variable. The ANOVA has the ability to give information on certain statistical parameters, such as the sum of squares, variance, contribution and F-variance ratio[11]. The table 2 gives a summary of the values of these parameters for each factor. The statistical parameters that are obtained from different equations have been written by other groups.

Fig 4:Graph of the contribution (%) according to the factors used for the failure stress

The table and figure show that Young's modulus (Factor 1) has a significant effect on the breaking stress for wire ropes followed by Friction (Factor 2) which has a relative effect, while the Temperature (Factor 3) has a very small