A small electrical appliance is to be produced on a single$-$model assembly line.

The work content of assembling the product has been reduced to the work

elements listed in Table $15\mathrm{.}4.$ The table also lists the times for each element

and the precedence order in which they must be performed. The line is to

be balanced for an annual demand of $100,000$ units$/$yr$.$ The line will operate

$50$ wk$/$yr$,5$ shifts$/$wk$,$ and $7\mathrm{.}5$ hr$/$shift$.$ There will be one worker per station.

Previous experience suggests that the uptime efficiency for the line will

be $96\%,$ and repositioning time lost per cycle will be $0\mathrm{.}08$ min. Determine

$($a$)$ total work content time Twc$,($b$)$ required hourly production rate Rp to

satisfy the annual demand, $($c$)$ cycle time Tc$,($d$)$ theoretical minimum number

of workers required on the line, and $($e$)$ service time Ts to which the line must

be balanced.

$410$ Chap. $15/$ Multi$-$Station Manufacturing Systems: Manual Assembly Lines

Measures of Line Balance Efficiency. Owing to the differences in minimum rational

work element times and the precedence constraints among the elements, it is virtually

impossible to obtain a perfect line balance. Measures must be defined to indicate how good

a given line balancing solution is$.$ One possible measure is balance efficiency, which is the

work content time divided by the total available service time on the line:

Eb $=$

Twc

wTs

$(15\mathrm{.}14)$

where Eb $=$ balance efficiency, often expressed as a percent; Ts $=$ the maximum available

service time on the line $($Max$\{$Tsi$\}),$ min$/$cycle; and w $=$ number of workers. The denominator

in Equation $(15\mathrm{.}14)$ gives the total service time available on the line to devote to the

assembly of one product unit. The closer the values of Twc and wTs$,$ the less idle time on the

No$.$ Work Element Description Tek $($min$)$ Must be Preceded By

$1$ Place frame in work holder and clamp $0\mathrm{.}2$

$2$ Assemble plug, grommet to power cord $0\mathrm{.}4$

$3$ Assemble brackets to frame $0\mathrm{.}71$

$4$ Wire power cord to motor $0\mathrm{.}11,2$

$5$ Wire power cord to switch $0\mathrm{.}32$

$6$ Assemble mechanism plate to bracket $0\mathrm{.}113$

$7$ Assemble blade to bracket $0\mathrm{.}323$

$8$ Assemble motor to brackets $0\mathrm{.}63,4$

$9$ Align blade and attach to motor $0\mathrm{.}276,7,8$

$10$ Assemble switch to motor bracket $0\mathrm{.}385,8$

$11$ Attach cover, inspect, and test $0\mathrm{.}59,10$

$12$ Place in tote pan for packing $0\mathrm{.}1211$

TABLE $15\mathrm{.}4$ Work Elements for Example $15\mathrm{.}1$

Solution: $($a$)$ The total work content time is the sum of the work element times in Table $15\mathrm{.}4.$