Item$-$by$-$item sequential sampling plan involves two frontiers, one is for acceptance and another is for reject.

$($a$)$ Derive an item$-$by$-$item sequential sampling plan for which $p1=0\mathrm{.}02,$ alpha $=0\mathrm{.}05,p2=0\mathrm{.}10,$ and beta $=0\mathrm{.}10.$

$($b$)$ Suppose the acceptance line reaches $0,$ it will stop and accept the lot. How large must $n$ be before sampling could be stopped with a decision to accept the lot?