ENGG*3070 – Assignment No. 3 (Due
Nov 10, 2021, 11:59 Dropbox)
Multiple Stations
1. A six-station dial indexing machine is designed to perform four assembly operations at
stations 2 through 5 after a base part has been manually loaded at station 1. Station 6 is
the unload station. Each assembly operation involves the attachment of a component to
the existing base. At each of the four assembly stations, a hopper-feeder is used to deliver
components to a selector device that separates components that are improperly oriented
and drops them back into the hopper. The system was designed with the operating
parameters for stations 2 through 5 as given in the table below. It takes 2 sec to index the
dial from one station position to the next. When a component jam occurs, it takes an
average of 2 min to release the jam and restart the system. Line stops due to mechanical
and electrical failures of the assembly machine are not significant and can be neglected.
The foreman says the system was designed to produce at a certain hourly rate, which takes
into account the jams resulting from defective components. However, the actual delivery
of finished assemblies is far below that designed production rate. Analyze the problem and
determine the following: (a) The designed average production rate that the foreman
alluded to. (b) What is the proportion of assemblies coming off the system that contain one
or more defective components? (c) What seems to be the problem that limits the assembly
system from achieving the expected production rate? (d) What is the production rate that
the system is actually achieving? State any assumptions that you make in determining your
answer.
Station Assembly time Feed rate f Selector q m
2 4 sec 32/min XXXXXXXXXX
3 7 sec 20/min XXXXXXXXXX
4 5 sec 20/min XXXXXXXXXX
5 3 sec 15/min XXXXXXXXXX
Single Station
2. A single-station assembly cell uses an industrial robot to perform a series of assembly
operations. The base part and parts 2 and 3 are delivered by vi
atory bowl feeders that
use selectors to insure that only properly oriented parts are delivered to the robot for
assembly. The robot cell performs the elements in the table below (also given are feeder
ates, selector proportion θ, element times, fraction defect rate q, and probability of jam
m, and, for the last element, the frequency of downtime incidents p). In addition to the
times given in the table, the time required to unload the completed subassembly is 4 sec.
When a line stop occurs, it takes an average of 1.8 min to make repairs and restart the cell.
Determine (a) yield of good product, (b) average hourly production rate of good product,
and (c) uptime efficiency for the cell? Assume the feeders continue to operate and deliver
parts into the feed track even when a jam occurs during assembly and the low-level
quantity nf1 is sufficient to eliminate possibility of a stockout. (d) Solve the problem again
assuming the feeder stops when jam occurs.
Partial Automation
3. A partially-automated production line has three mechanized and three manual
workstations, a total of six stations. The ideal cycle time is 57 sec, which includes a transfer
time of 3 sec. Data on the six stations are listed in the table below. Cost of the transfer
mechanism is $0.10/min, cost to run each automated station is $0.12/min, and labor cost
to operate each manual station is $0.17/min. It has been proposed to substitute an
automated station in place of station 5. The cost of this new station is estimated at
$0.25/min and its
eakdown rate = 0.02 per cycle, but its process time would be only 30
sec, thus reducing the overall cycle time of the line from 57 sec to 36 sec. Average
downtime per
eakdown of the cu
ent line, as well as for the proposed configuration, is
3.0 min. Determine the following for the cu
ent line and the proposed line: (a) hourly
production rate, (b) proportion uptime, and (c) cost per unit. Assume that when an
automated station stops, the whole line stops, including the manual stations. Also, in
computing costs, neglect material and tooling costs.
4. Reconsider Problem 4 except that both the cu
ent line and the proposed line will have storage
uffers before and after the manual stations. The storage buffers will be of sufficient capacity
to allow these manual stations to operate independently of the automated portions of the line.
Determine (a) production rate, (b) proportion uptime, and (c) cost per unit for the cu
ent line
and the proposed line.
Group Technology
5. he following table lists the weekly quantities and routings of ten parts that are being
considered for cellular manufacturing in a machine shop. Parts are identified by letters and
machines are identified numerically. For the data given, (a) develop the part-machine
incidence matrix, (b) apply the rank order clustering technique to the part-machine
incidence matrix to identify logical part families and machine groups, and (c) for each
machine group identified, apply the Hollier method to determine the most logical sequence
of machines for this data.
Part Weekly quantity Machine routing
A 50 3 → 2 → 7
B 20 6 → 1
C 75 6 → 5
D 10 6 → 5 → 1
E 12 3 → 2 → 7 → 4
F 60 5 → 1
G 5 3 →2 → 4
H 100 3 →2 → 4 → 7
I 40 2 → 4 → 7
J 15 5 → 6 → 1