P2 – Listas Engenharia da Qualidade
Confiabilidade do Sistema
𝑅𝑇=𝑅1*(1− 1−𝑅2
( )
* 1−𝑅3
( )[ ]
𝑅𝑇=𝑅1* 1− (1−𝑅3−𝑅2+𝑅2𝑅3
[ ]
)
( )
𝑅𝑇=𝑅1*(𝑅3+𝑅2−𝑅2𝑅3)
𝑅𝑇=𝑅1𝑅3+𝑅1𝑅2−𝑅1𝑅2𝑅3
𝑅𝑇= 0,95*0,9( )+ 0,95*0,99( )− 0,95*0,99*0,9( )=0,94905
A)Importancia de Birnbaum
Para 𝑅1𝐼𝐵𝑡()=∂𝑅𝑠(𝑟𝑡())
∂𝑅1(𝑡) =∂(𝑅1𝑅3+𝑅1𝑅2−𝑅1𝑅2𝑅3)
∂𝑅1(𝑡) =𝑅3+𝑅2−𝑅2𝑅3=
𝐼𝐵𝑡()=𝑅3+𝑅2−𝑅2𝑅3=0,9+0,99− 0,99*0,9( )=0,999
Para 𝑅2𝐼𝐵𝑡()=∂𝑅𝑠(𝑟𝑡())
∂𝑅2(𝑡) =∂(𝑅1𝑅3+𝑅1𝑅2−𝑅1𝑅2𝑅3)
∂𝑅2(𝑡) =𝑅1−𝑅1𝑅3=
𝐼𝐵𝑡()=𝑅1−𝑅1𝑅3=0,95− 0,95*0,9( )=0,095
Para 𝑅3𝐼𝐵𝑡()=∂𝑅𝑠𝑟𝑡()( )
∂𝑅3𝑡() =∂𝑅1𝑅3+𝑅1𝑅2−𝑅1𝑅2𝑅3
( )
∂𝑅3𝑡() =𝑅3−𝑅1𝑅2
𝐼𝐵𝑡()=𝑅3−𝑅1𝑅2=0,95− 0,95*0,99( )=0,0095
