# Find the reliability function and mean lifetime of a series system of 2 components, if the components lifetimes are uniformly distributed on (0,1) and (0,2)respectively. Repeat for a parallel system....

Find the reliability function and mean lifetime of a series system of 2 components, if the components lifetimes are uniformly distributed on (0,1) and (0,2)respectively. Repeat for a parallel system.
Note that if the component lifetime T has a uniform distribution on (a,b) then f(t)=1/(b-a).
Where a

## Solution

Robert answered on Dec 20 2021
1. Let and be the component lives.
We know that ( ) ( ) and ( ) (

)
If the components are connected in a series system then system reliability is,
( ) ( ( )) ( (

))
Hence the reliability function is
( ) ( ) (

)
As the first component fails after T=1, so the reliability will be zero for T>1.
Hence, ( )
( )(

)

(

)

Hence, ( ) ∫ (

)

If the components are connected in a parallel system then system reliability is,
( ) ( ( )) ( (

))
Hence the reliability function is
( ) (

) and (

)
As the second component fails after T=2, so the reliability will be zero for T>2.
Hence, ( ) and

Hence, ( ) ∫ ( )

∫ ( )

(

)

2. Given R=.8855
Out of 4
akes one front
ake and one rear...
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