Student name: Ahmed Hassan Ibrahim

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Ain Shams University

MANF 487: Computer Applications in Industry Faculty Of Engineering Fall 2012

Manufacturing Engineering Credit Hours Engineering Programs

Time allowed : 90 Minutes

Answer all the following questions:

1- Choose the correct answer(s): (21 Marks)

Each correct answer is worth 1 point. Each omitted answer or wrong answer

reduces the score by 1 point, and each additional answer beyond the correct

number of answers reduces the score by 1 point.

Question Answer symbol(s)

Which of the following industries are classified as secondary

industries (three correct answers):

(a) beverages (b) financial services, (c) fishing, (d) mining,

(e) power utilities, (f) publishing, and, (g) transportation?

a

e

f

Mining is classified in which one of the following industry

categories:

(a) agricultural industry, (b) manufacturing industry,

(c) primary industry,(d) secondary industry, (e) service industry,

or, (f) tertiary industry?

C

A production planning and control department accomplishes

which of the following functions in its role of providing

manufacturing support (two best answers):

(a) Designs and orders machine tools, (b) develops corporate

strategic plans, (c) orders materials and purchased parts,

(d) performs quality inspections, and, (e) schedules the order of

products on a machine?

c

e

Which of the following rapid prototyping processes starts with

a photosensitive liquid polymer to fabricate a component (two

correct answers):

(a) Ballistic particle manufacturing, (b) fused deposition

modeling, (c) selective laser sintering, (d) solid ground curing,

and (e) stereolithography?

d

e

Which one of the following RP technologies uses solid sheet

stock as the starting material:

(a) Ballistic particle manufacturing, (b) fused-deposition

modeling, (c) laminated-object manufacturing, (d) solid ground

curing, or (e) stereolithography?

c

Student name: Ahmed Hassan Ibrahim

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Which of the following are problems with the current material

addition rapid prototyping technologies (three best answers):

(a) inability of the designer to design the part, (b) inability to

convert a solid part into layers, (c) limited material variety,

(d) part accuracy, (e) part shrinkage, and (f) poor machinability

of the starting material?

c

d

e

Fixed routing is associated with which of the following types

of manufacturing systems (two best answers):

(a) Automated production lines, (b) automated storage systems,

(c) cellular manufacturing systems, (d) flexible manufacturing

systems, (e) job shops, and (f) manual assembly lines?

a

f

Which of the following types of material handling equipment

are typically used in a process type layout (two best answers):

(a) Conveyors, (b) cranes and hoists, (c) fork lift trucks, and

(d) rail-guided vehicles?

c

d

Most parts classification and coding systems are based on

which of the following types of part attributes (two best

answers):

(a) Annual production rate, (b) date of design, (c) design,

(d) manufacturing, and (e) weight?

c

d

What is the dividing line between a manufacturing cell and a

flexible manufacturing system:

(a) Two machines, (b) four machines, or (c) six machines?

b

In a control chart, the upper control limit is set equal to which

one of the following:

(a) Process mean, (b) process mean plus three standard

deviations, (c) upper design tolerance limit, or (d) upper value of

the maximum range R?

b

The R chart is used for which one of the following product or

part characteristics:

(a) Number of rejects in the sample, (b) number of reworked

parts in a sample, (c) radius of a cylindrical part, or (d) range of

sample values?

d

Student name: Ahmed Hassan Ibrahim

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2- Why is the normal statistical table used in a Six Sigma program different from

the standard normal tables found in textbooks on probability and statistics? Use

a neat sketch in your answer. (4 Marks)

There are two reasons for this:

First, the values in table refer to only

one tail of the distribution, so that an appropriate

comparison with the standard normal tables would

only use one tail of the distribution (1350 DPM).

Second, and much more significant, is that when Motorola devised

the Six Sigma program, they considered

the operation of processes over long periods of

time, and processes over long periods tend to experience

shifts from their original process means. To

compensate for these shifts, Motorola decided

to adjust the standard normal values by 1.5σ. These effects

can be seen in the following figure.

Student name: Ahmed Hassan Ibrahim

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3- What is the common approach used in all of the material addition technologies

to prepare the control instructions for the RP system? Describe using a neat

sketch the RP technology called laminated object manufacturing. (13 Marks)

Steps to Prepare Control Instructions ≡ Part program

1. Geometric modeling - model the component on

CAD system to define its enclosed

volume. Solid modeling provide a complete

mathematical representation of the geometry.

2. Tessellation of the geometric model - the CAD model is

converted into a computerized format that

approximates its surfaces by triangles or

polygons.

3. Slicing of the model into spaced parallel

horizontal layers. As shown in figure (1).

Student name: Ahmed Hassan Ibrahim

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Solid physical model made by stacking layers

of sheet stock, each an outline of the cross-sectional

shape of a CAD model that is sliced into layers.

Starting sheet stock includes paper, plastic,

cellulose, metals, or fiber-reinforced materials.

The sheet is usually supplied with adhesive

backing.

After cutting, excess material in the layer remains in place to

support the part during building.

Used for large parts.

Student name: Ahmed Hassan Ibrahim

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4- Six samples of size n = 4 have been collected from a process in statistical

control, and the dimension of interest has been measured for each part. The

calculated values of �̅� for each sample are (mm) 9.15, 9.20, 9.19, 9.12, 9.24,

and 9.23. The values of R are (mm) 0.24, 0.26, 0.19, 0.21, 0.21, and 0.23,

respectively. (a) Determine the values of the center, LCL, and UCL for the �̅�

and R charts. (b) Construct the control charts and plot the sample data on the

charts. (20 Marks)

Constants for the �̅� and R charts Sample �̅�chart R chart Size n 𝐴2 𝐷3 𝐷4

4 0.729 0 2.282

For �̅� charts:

𝐿𝐶𝐿 = �̿� − 𝐴2�̅� and 𝑈𝐶𝐿 = �̿� + 𝐴2�̅�

For 𝑅 charts:

𝐿𝐶𝐿 = 𝐷3�̅� and 𝑈𝐶𝐿 = 𝐷4�̅�

𝑥 ̿ =∑ �̅�

𝑛𝑜.=

9.15 + 9.20 + 9.19 + 9.12 + 9.24 + 9.23

6= 9.188𝑚𝑚

�̅� =∑ 𝑅

𝑛𝑜.=

0.24 + 0.26 + 0.19 + 0.21 + 0.21 + 0.23

6= 0.2233𝑚𝑚

For �̅� charts:

𝐿𝐶𝐿 = �̿� − 𝐴2�̅� and 𝑈𝐶𝐿 = �̿� + 𝐴2�̅�

𝐿𝐶𝐿 = �̿� − 𝐴2�̅� = 9.188 − 0.729 × 0.2233 = 9.0252𝑚𝑚

𝑈𝐶𝐿 = �̿� + 𝐴2�̅� = 9.188 + 0.729 × 0.2233 = 9.3507𝑚𝑚

𝐶𝑒𝑛𝑡𝑒𝑟 (�̿�) = 9.188𝑚𝑚 For 𝑅 charts:

Student name: Ahmed Hassan Ibrahim

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𝐿𝐶𝐿 = 𝐷3�̅� and 𝑈𝐶𝐿 = 𝐷4�̅�

𝐿𝐶𝐿 = 𝐷3�̅� = 0 × 0.2233 = 0𝑚𝑚

𝑈𝐶𝐿 = 𝐷4�̅� = 2.282 × 0.2233 = 0.50957𝑚𝑚

𝑐𝑒𝑛𝑡𝑒𝑟 (�̅�) = 0.2233𝑚𝑚

8.8

8.9

9

9.1

9.2

9.3

9.4

1 2 3 4 5 6

Sample size, s

𝑥 ̅ charts

0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6

Sample size, s

R chart

Student name: Ahmed Hassan Ibrahim

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5- A foundry that casts turbine blades inspects for eight features that are

considered critical-to-quality. During the previous month, 1236 castings were

produced. During inspection, 47 defects among the eight features were found,

and 29 castings had one or more defects. Determine DPMO, DPM, and DUPM

in a Six Sigma program for these data and convert each to its corresponding

sigma level. (12 Marks)

Nd = total number of defects found = 47

Nu = number of units in the population of interest = 1236

No = number of opportunities for a defect per unit = 47

Ndu= number of defective units in the population = 29

𝐷𝑃𝑀𝑂 = 1,000,000𝑁𝑑

𝑁𝑢𝑁𝑜

𝐷𝑃𝑀𝑂 = 1,000,000 ×47

1236 × 8= 4754 (4.1 𝑠𝑖𝑔𝑚𝑎)

𝐷𝑃𝑀𝑂 = 1,000,000𝑁𝑑

𝑁𝑢

𝐷𝑃𝑀𝑂 = 1,000,000 ×47

1236= 38026 (3.3 𝑠𝑖𝑔𝑚𝑎)

𝐷𝑃𝑀𝑂 = 1,000,000𝑁𝑑𝑢

𝑁𝑢

𝐷𝑃𝑀𝑂 = 1,000,000 ×29

1236= 23463 (3.5 𝑠𝑖𝑔𝑚𝑎)

Student name: Ahmed Hassan Ibrahim

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6- A prototype of a part is to be fabricated using Stereolithography. The part is

shaped like a right triangle whose base = 15 mm, height = 6 mm, and thickness

= 10 mm. In application, the part will stand on its base, which is 15 mm by 10

mm. In the Stereolithography process, the layer thickness = 0.5 mm. The

diameter of the laser beam = 0.15 mm, and the beam is moved across the

surface of the photopolymer at a velocity of 400 mm/s. Compute the minimum

possible time required to build the part, if 8 seconds are lost each layer to lower

the height of the platform that holds the part. Neglect the time for post curing.

(30 Marks)

𝑻𝒊 =𝑨𝒊

𝒗 × 𝑫+ 𝑻𝒓

i w b area Ti

0 10 15 150 10.5

1 10 13.75 137.5 10.29167

2 10 12.5 125 10.08333

3 10 11.25 112.5 9.875

4 10 10 100 9.666667

5 10 8.75 87.5 9.458333

6 10 7.5 75 9.25

7 10 6.25 62.5 9.041667

8 10 5 50 8.833333

9 10 3.75 37.5 8.625

10 10 2.5 25 8.416667

11 10 1.25 12.5 0.208333

Total time 104.25

Student name: Ahmed Hassan Ibrahim

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Some useful relations:

𝐓𝐢 = 𝐀𝐢

𝐯 ∗ 𝐃+ 𝐓𝐫 𝐃𝐏𝐌 = 𝟏𝟎𝟔 ∗

𝐍𝐝

𝐍𝐮

𝐃𝐏𝐌𝐎 = 𝟏𝟎𝟔 ∗ 𝐍𝐝

𝐍𝐮 ∗ 𝐍𝐨 𝐃𝐔𝐏𝐌 = 𝟏𝟎𝟔 ∗

𝐍𝐝𝐮

𝐍𝐮

For �̅� chart LCL = �̿� - A2 �̅� 𝐚𝐧𝐝 𝐔𝐂𝐋 = �̿� + 𝐀𝟐 �̅�

For R chart LCL = D3 �̅� 𝐚𝐧𝐝 𝐔𝐂𝐋 = 𝐃𝟒 �̅�

********************************************************************

Constants for the �̅� and R charts

Sample Size �̅� Chart R chart

n A2 D3 D4

3 1.023 0 2.574

4 0.729 0 2.282

5 0.577 0 2.114

6 0.483 0 2.004

7 0.419 0.076 1.924

8 0.373 0.136 1.864

9 0.337 0.184 1.816

10 0.308 0.223 1.777

********************************************************************

Sigma Levels And Corresponding Defects Per Million In A Six Sigma Program

Sigma level Defects per

Million Sigma level

Defects per

Million Sigma level

Defects per

Million

6.0 σ 3.4 4.6 σ 968 3.2 σ 44565

5.8 σ 8.5 4.4 σ 1866 3.0 σ 66807

5.6 σ 21 4.2 σ 3467 2.8 σ 96801

5.4 σ 48 4.0 σ 6210 2.6 σ 135666

5.2 σ 108 3.8 σ 10724 2.4 σ 184060

5.0 σ 233 3.6 σ 17864 2.2 σ 241964

4.8 σ 483 3.4 σ 28716 2.0 σ 308538