$3.$ Failure statistics $(20$ points$)$

Repeat cyclic bending tests of cantilevers fabricated from an Ni alloy under the same loading conditions showed the following results:

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|\}$

$\backslash$hline Test number & Cycles to failure $\backslash \backslash$

$\backslash$hline $1$ & $661570\backslash \backslash$

$\backslash$hline $2$ & $283235\backslash \backslash$

$\backslash$hline $3$ & $467405\backslash \backslash$

$\backslash$hline $4$ & $439340\backslash \backslash$

$\backslash$hline $5$ & $157900\backslash \backslash$

$\backslash$hline $6$ & $12715\backslash \backslash$

$\backslash$hline $7$ & $18910\backslash \backslash$

$\backslash$hline $8$ & $15175\backslash \backslash$

$\backslash$hline $9$ & $72605\backslash \backslash$

$\backslash$hline $10$ & $123275\backslash \backslash$

$\backslash$hline $11$ & $155705\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$1)$ Determine whether or not the failure statistics associated with the tests shown above is consistent with Weibull statistics. $(10$ points$)$

$2)$ If your answer to $1)$ is yes, determine the Weibull modulus associated with the tests shown above. $(10$ points$)$