$8$ Project network diagram

a Duration, ES$/$EF$,$ LS$/$LF$,$ and slack for each project phase

$9$ Probability of completion within $55$ days

a Crashing plan to ensure completion within $55$ weeks to within $90\%$

$10$ Revised system failure rate with back$-$ups installed

a If failure rate is greater than $1\%,$ which additional component$($s$)$ should have back$-$up

installed?

Can you answer these with this data set

Initial reports have determined that the failure rate of the system is too high. An improvement project is

undertaken to try to reduce the failure rate. Details are given below in Table $5.$ Based on the data, calculate

the expected time for each phase and construct the network diagram. Calculate the early start$/$early finish,

late start$/$late finish, and slack times for each phase. How long is the entire project expected to last?

Table $5,$ Project Timeline Data

Management would like to see the project completed within $55$ days. What is the probability the project will

finish in that time frame? What phase$($s$)$ must be crashed to ensure a greater$-$than$-90\%$ chance of finishing

within $55$ days?

As a result of the improvement project, back$-$up components were installed on sections charlie, delta, echo,

foxtrot, and hotel. The back$-$ups have the same reliability rates as the components they cover. Is that

sufficient to reduce the failure rate below $1\%?$ If not, what additional component$($s$)$ should have a back$-$up

installed? Assume all switches are $100\%$ reliable.