Problem 24E

One design for a system requires the installation of two identical components. The system will work if at least one of' the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9,and if the components function independently! Which design has the greater probability of functioning?

Solution 24E

Step1 of 3:

Let us consider a design in that a system requires the installation of two identical components. The system will work if at least one of' the components works.An alternative design requires four of these components, and the system will work if at least two of the four components work.

P(component works) = 0.90.

P(none works) = 1 - P(component works)

= 1 - 0.90

= 0.10

We need to check which design has the greater probability of functioning.

Step2 of 3:

Consider,

P(at least one work) = P(X > 1)

=

=

= 1 - 0.01

= 0.99

Hence, probability that at least one work is 0.99.

Step3 of 3:

Consider a four components design.

P(at least 2 works) = P(X > 2)

= 1 -

= 1 - {0.0001+0.0036}

= 1 - 0.0037

= 0.9963

Hence, probability that at least 2 works is 0.9963.

Conclusion:

From step 2 and step 3, we can say that the an alternative Design has the greater probability of functioning.