Answer:
The overall reliability is 99.7402 %
Step-by-step explanation:
The overall reliability of the product is calculated as the product of the working probability of the components.
For components A,B,C and F we have :
[tex]P(failure)=\frac{1}{10000}[/tex]
⇒
[tex]P(Work)=1-\frac{1}{10000}=\frac{9999}{10000}=0.9999[/tex]
For components D,E,G and H we have :
[tex]P(failure)=\frac{3}{10000}[/tex]
⇒
[tex]P(Work)=1-\frac{3}{10000}=\frac{9997}{10000}=0.9997[/tex]
Finally, for components I and J :
[tex]P(failure)=\frac{5}{10000}[/tex]
⇒
[tex]P(Work)=1-\frac{5}{10000}=\frac{9995}{10000}=0.9995[/tex]
Now we multiply all the working probabilities. We mustn't forget that we have got ten components in this case :
Components A,B,C and F with a working probability of 0.9999
Components D,E,G and H with a working probability of 0.9997
Components I and J with a working probability of 0.9995
Overall reliability = [tex](0.9999)^{4}(0.9997)^{4}(0.9995)^{2}=0.997402[/tex]
0.997402 = 99.7402 %
