An electrical system consists of multiple devices in series or parallel connecti

Question

An electrical system consists of multiple devices in series or parallel connection. For a system to work, all devices in series must work while at least one device in parallel is required to work.

Assume the independent devices A, B, C, D have reliability (probability that the device is working) of 0.95, 0.90, 0.85, 0.80 respectively.

2.1. Find the reliability of a system S1 with A, B in series;

2.2. Find the reliability of a system S2 with C, D in parallel;

2.3. Find the reliability of a system S12 with S1, S2 in series;

2.4. If the system S12 does not work, what is the probability device C does not work?

Explanation / Answer

2.1)reliability of a system S1 with A, B in series =P(A will work and B will work) =0.95*0.90=0.855

2.2) reliability of a system S2 with C, D in parallel =P(at leaast one of C and D will work)

=1-P(none of C and D work) =1-(1-0.85)*(1-0.8)=0.97

2.3) reliability of a system S12 with S1, S2 in series =0.855*0.97=0.82935

2.4)probability that system S12 does not work =1-0.82935=0.17065

probability that S12 does not work as well C does not work =0.15*0.2=0.03

therefore probability device C does not work given S12 does not work =0.03/0.17065=0.175798

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.