Problem $6$: $10$ points

An electronic missile guidance system at Mguide, Inc. consists of components A$,$ B$,$ C$,$ and D which have

reliabilities of $0\mathrm{.}98,0\mathrm{.}97,0\mathrm{.}91,$ and $0\mathrm{.}95,$ respectively $($see the following diagram$).$

a$)$ Calculate the Reliability of the entire system $($Hint Refer to slide $21$ and $23$ of Lecture $3.$ You can

calculate a partial reliability first. For example, calculate the reliability of $"$ C parallel with $C^{\text{'}})$

b$)$ Suppose customer requires a reliability off at least $0\mathrm{.}98.$ Find a configuration that meets this

requirement using the minimum number of components. Note that $A,B,C,D$ have to be in sequence