Question

1. With the booming world economy, the 2x4 lumber consumed in the construction industry is considerably increasing. To obtain the 2x4's that meet the quality requirements the milling system for 2x4's needs to be effective. The following reliability diagram is established. What is the reliability of the milling system? 0.55 0.87 0.94 0.6 0.94 0.64 0.93 0.65 0.65 b) A system for milling 2x6's has four sensitive components connected in series with reliabilities of 0.92, 0.72, 0.84 and 0.85. According to the quality department of the lumber mill, the current system lacks reliability. At the manufacturing plant, the engineers have proposed to improve the reliability of the system. The new system still has the same four components, but the system has a backup for each component. The four backup components all have a reliability of 0.60. What is the reliability of the series (old) system? What is the reliability of the new (proposed) system? If you pay a premium, the manufacturer can improve all four of the backup units to 0.87 (the third option). What is the reliability of the third option?

Answer 1

Given: R1 = 0.94, R2 = 0.55, R3 = 0.6, R4 = 0.93, R5 = 0.87, R6 = 0.64, R7 = 0.65, R8 = 0.65, R9 = 0.94

R2 and R3 are in parallel

Hence R23 = 1 - (1-R2)*(1-R3) = 1 - (1-0.55)*(1-0.6) = 0.82

R6, R7, R8 are in parallel

Hence, R678 = 1- (1-R6)*(1-R7)*(1-R8) = 1 - (1-0.64)*(1-0.65)*(1-0.65) = 0.96

R4 and R678 are in series

Hence, R4678 = R4*R678 = 0.93*0.96 = 0.89

R23, R5 and R9 are in series

Hence, R2359 = R23*R5*R9 = 0.82*0.87*0.94 = 0.67

R4678 and R2359 are in parallel

Hence, R46782359 = 1 - (1-R4678)*(1-R2359) = 1-(1-0.89)*(1-0.67) = 0.96

R1 and R46782359 are in series

Overall reliability R = R1*R46782359 = 0.94*0.96 = 0.90

___________________________________________________________________________________________________

Since other question is not sub-part and is independent, it has to be posted separately