a) A product has five components in series as shown below: AB C D E The reliabil

Question

a) A product has five components in series as shown below: AB C D E The reliability of components A, B, C and D are the following: A: 92% B: 88% C: 85% D: 80% The product is to have an overall reliability of 60%. What must the reliability of component E be to satisfy this requirement? If it is not possible to satisfy the 60% reliability requirement, what is the best reliability possible for the product and what would the reliability of component E be to achieve this reliability?

b) BioTech Research Center is working to develop a new vaccine for the West Nile Virus. The project is so important that the firm has created three teams of experts working on the project from different perspectives. Team 1 has a 90% chance of success, Team 2 has an 85% chance of success, and Team 3 has a 70% chance of success. It is only necessary for one of the teams to succeed in developing the new vaccine. BioTech wants to make a statement about the reliability or probability that it will succeed in developing the new vaccine. What is this reliability or probability?  

Explanation / Answer

This is a question on series and parallel reliabilities. Now, in the first question, we have 5 components which are in series.

The overall reliability, if these components are in series, is given by:

R = R1 x R2 x R3 x R4 x R5

Now, we need the overall reliability to be 60%, and we are given the remaining reliabilities in the question. That is,

0.6 = 0.92 x 0.88 x 0.85 x 0.80 x R

This gives us R = 109%

This is clearly not possible. The maximum possible reliability of the system would be when Re = 100%.

In that case, the overall reliability of the system would be 0.92 x 0.88 x 0.85 x 0.80 x 1.0 = 0.55 or 55%

Hence, the maximum possible reliability is 55.05%

Now, let us move to the next question.

This is a question of systems in parallel.

Note that we are given that any one team's success is enough for them to develop a new vaccine. This is what helps us determine that this is a system which is in parallel, as the success of any one parameter is enough.

The reliability of a parallel system is given by:

Rp = 1 - (1-R1)(1-R2)(1-R3)

Rp = 1-(1-0.9)(1-0.85)(1.0.7)

Rs = 0.9955 or 99.55%

Hence, the required probability is 99.55% in this case.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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