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## Q. 17.2

Multistation Automated Assembly System
A 10-station in-line assembly machine has an ideal cycle time = 6 sec. The base part is automatically loaded prior to the first station, and components are added at each of the stations. The fraction defect rate at each of the 10 stations is q = 0.01, and the probability that a defect will jam is m = 0.5. When a jam occurs, the average downtime is 2 min. Cost to operate the assembly machine is \$42.00/hr. Other costs are ignored. Determine (a) average production rate of all assemblies, (b) yield of good assemblies, (c) average production rate of good product, (d) uptime efficiency of the assembly machine, and (e) cost per unit.

## Verified Solution

(a) $T_{c} = 6$ sec = 0.1 min. The average production cycle time is $T_{p} = 0.1 + (10)(0.5)(0.01)(2.0) = 0.2$ min. The production rate is therefore

$R_{p} = \frac{60}{0.2}= 300$ total assemblies/hr

(b) The yield is given by Equation (17.7):

$P_{ap} = (1-q+mq)^{n}$

$P_{ap} = \left\{1 – .01 + 0.5 (0.01)\right\}^{10} = 0.9511$
(c) Average actual production rate of good assemblies is determined by Equation (17.15):

$R_{ap} = P_{ap}R_{p} = \frac{P_{ap}}{T_{p}}= \frac{(1-q+mq)^{n}}{T_{p}}$

$R_{ap} = 300(0.9511) = 285.3$ good assemblies/hr
(d) The efficiency of the assembly machine is

E = 0.1/0.2 = 0.50 = 50%

(e) Cost to operate the assembly machine $C_{o} = \ 42/hr = \0.70/min$

$C_{pc} = (0.70/min)(0.2 min/pc)/0.9511 = \0.147/pc$