Example $2$: A system has three components connected in series baving reliabilities $0\mathrm{.}40,0\mathrm{.}70,0\mathrm{.}80,$ respectively, for a mission of $400$ bous. Whar is the percentage increase in the reliability of the system in each of the follioning cases?

of Sophesytes

$($i$)$ Reliability of the first component is increased by $0\mathrm{.}1$ and then of the samol and third components remains the same.

$($ii$)$ Reliability of the second component is increas by by $0\mathrm{.}1$ and that of the finst and third components remains the same.

$($iii$)$ Reliability of the third component is increaced by $0\mathrm{.}1$ and that of the fint and second components remains the same.

Solution: First of all. we calculate the reliabilitv of the sisten as ax the virem