Weibull distribution of fiber strength

The Weibull distribution is called a parametric distribution, i.e. it is an empirical distribution and does not concern itself with the origin of the defects. The Weibull distribution for the strength (cr) of a brittle material takes the following form 

Consider a fiber that follows the strength distribution given by Eq. (10.2). We can obtain an expression for the mean strength as follows  

Values of T(n) can be found in mathematical handbook tables. Some important values of T(n) are as follows  

Using the gamma function as defined above, we can write the mean or average strength of the fiber as 

Substituting the value of =()8+ l)/j8, we have the mean strength given by 

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