contestada

A design has an expected distribution of stress with a mean value of 1 MPa and a standard deviation of 0.3 MPa. The strength of the design is expected to have a mean value of 2 MPa and a standard deviation of 0.2 MPa. Both can be assumed to be normal distributions. What is the expected failure rate of the design?

Respuesta :

Answer:

P=0.0028

Explanation:

For x:

Mean = 1 MPa

Standard deviation = 0.3 MPa

For y:

Mean = 2 MPa

Standard deviation = 0.2 MPa

Let failure is denoted by F, then F will also follow normal distribution.

F= y-x

Mean

[tex]\mu _F=\mu_y-\mu_x[/tex]

[tex]\mu _F=2-1[/tex]

[tex]\mu _F=1\ MPa[/tex]

Standard deviation

[tex]\sigma_F=\sqrt{\sigma_x^2+\sigma_y^2}[/tex]

[tex]\sigma_F=\sqrt{0.2^2+0.3^2}[/tex]

[tex]\sigma_F=0.36\ MPa[/tex]

The failure probability given as

[tex]P(F<0)=P\left(\dfrac{0-1}{0.36} \right)=P(z<-2.77)[/tex]

Now from chart P=0.0028

Otras preguntas