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A production machine that consists of three components connected in series. The first component follows Weibull probability distribution with shape parameter of 1.3 and scale parameter (characteristic life) of 24,000 hr. The second follows Weibull probability distribution with shape parameter of 1.9 and scale parameter (characteristic life) of 18,000 hr. The third component follows exponential distribution with MTTF= 48,000 hr. Find the reliability of the system at t = 6000

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Cricetus

Answer:

The correct solution is "0.66104".

Explanation:

Given:

Component 1,

[tex]\beta=1.3[/tex]

[tex]\gamma=24,000 \ hr[/tex]

Component 2,

[tex]\beta = 1.9[/tex]

[tex]\gamma=18,000 \ hr[/tex]

Component 3,

[tex]MTTF=48,000 \ hr[/tex]

Now,

At t = 6000 hr, the system reliability will be:

⇒ [tex]Rs(t=6000)=\frac{3}{\pi} R_1\times R_2\times R_3[/tex]

                         [tex]=[e^{-(\frac{6000}{24000} )^{1.3}}]\times [e^{-(\frac{6000}{18000} )^{1.9}}]\times [e^{-(\frac{6000}{48000} )}][/tex]

                         [tex]=0.66104[/tex]

Thus the above is the correct solution.

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