Question

In: Statistics and Probability

Which system, (a) or (b), has the higher reliability at the end of 100 operating hr?...

Which system, (a) or (b), has the higher reliability at the end of 100 operating hr? The higher reliability in the answer put it in the answer box using five decimals.

(a) Three CFR components in parallel, each having an MTTF of 1000 hr.

(b) A Weibull component with a shape parameter of 2 and a characteristic life of 10,000 hr in series with a CFR component with a failure rate of 0.00005.

Expert Solution

ANSWER

i)

The relaibility of system wit exponential failure time is

and .

The reliability of a single componet after 100 hours is

The reliability of the Three components connected in parallel is

R1(100)=1-(1-R(100))3

R1(100)=1-(1-0.9048)3

R1(100)=0.99914

ii)

Reliability function of Weibull distribution is

The shape parameter is /

The reliability of the Weibull component after 100 hours is

The reliability of the component connecetd in series with the above component is

The reliability after 100 hours of the series system is

So the second system has higher rteliability since .

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orchestra answered 2 years ago

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