Two alternative treatment trains are being considered. Train $1$

includes three treatment processes, each of which, when operating

normally, reduces the target pathogen by two orders of magnitude $($a

$2$ log reduction$).$ Train $2$ includes four independent unit processes in

series. Two of the processes reduce the target pathogen by two orders

of magnitude $($a $2log$ reduction$)$ Each of the other two processes

reduce the target pathogen by one order of magnitude $($a $1log$ reduc$-$

tion in each step$).$ If each of the seven unit processes listed above fails

to perform, at random, about one percent of the time and if$,$ when a

unit process fails, the removal it achieves is half of what it normally

achieves, estimate: $($a$)$ the overall removal for trains $1$ and $2$ when all

the unit processes are operating normally and $($b$)$ for each train the

frequency $($in days per year$)$ of various levels of removal assuming that

process failures occur randomly.