Example $10\mathrm{.}2$

At the end of each stage of a three$-$stage production process, all items will be inspected. The probability that it will be junked is p$,$ that it will be reworked is q$,$ and that it will pass is r$,$ with p$+$q$+$r$=1.$ Consider the following states:

$0$: item junked

$1$: item completed

$2$: item in first manufacturing stage

$3$: item in second manufacturing stage

$4$: item in third manufacturing stage