Scenario:
You work as a production engineer for a company that manufactures engine and transformer parts. You have been investigating a number of issues in the production area and have been given access to a range of manufacturing data. Your manager has asked you to analyse the data in order to present this to nontechnical colleagues within the organisation.
Activity:
Part 1:
 Data has been gathered from a lifting system used to transport engine parts. The system consists of a drum and cable. The following data was obtained when the drum lowers the load (assume constant acceleration).
Drum diameter = 0.8m
Mass of load = 6kg
Initial velocity = 0 m/s
Time to descend = A secs
Distance travelled = 0.25m
You have been asked to use this information to determine:
a) The final linear velocity of the load
b) The linear acceleration of the load
c) The final angular velocity of the drum
d) The angular acceleration of the drum
e) The tension force in the cable
f) The torque applied to the drum
 The velocity of propagation of a pressure wave (u) through a liquid can be expected to depend on the elasticity of the liquid represented by the bulk modulus K, and its mass density ρ. Derive using dimensional analysis, the equation that determines u.
Hint: u = f (C K^{a} ρ^{b} ) where C is a nondimensional constant and bulk modulus is given by:
Pressure (P) is force per area
V is volume
Part 2:
a) You are investigating the electrical testing circuits and find that, in an inductive circuit, the relationship between instantaneous current i (amps) and the time t (secs) is given by:
i = 4.2(1e^{10t})
You have been asked to determine the time taken for the current to rise from 2350mA to B amps.
b) The drive system of a conveyor used to transport the engine parts is made up of an open belt which passes over two pulleys. The pulleys have diameters of 205mm and 325mm respectively and the distance between centres is T mm.
You have been asked to determine the length of the belt, using trigonometric techniques, assuming the belt is in tension.
c) The length l metres of an AAAC aluminium overhead line conductor at temperature t° C is given by
l = l_{0} e^{a}^{t}, where l_{0} and a are constants.
Measurements are taken of the length at various temperatures:
at 80°C, length = 3.55m
at 250°C, length = Lm
Find the lengths of the bar at room temperature, 24.5°C and at 46.5°C.
Evaluate the practical implications of your results given that there are weather forecasts that temperature would rise up to around 49.5°C in the summer.
Part 3:
1). A drill used in the manufacture of the engine parts is designed to have eight speeds. The range of hole sizes anticipated is from 5mm to 30mm.
You have been asked to determine the seven spindle speeds (rev/min) given that the cutting speed is 15m/min. These spindle speeds are to be arranged in:
a) arithmetic progression
b) geometric progression
Note:
Where, N = spindle speed (rev/min), s = cutting speed (m/min) and D = hole diameter (mm).
2). The following are the equipment life (in years) and dielectric strength (in MΩ) of the winding of 24 apparently new transformers after pressure testing during factory acceptance tests (FAT).
Dielectric
Strength (MΩ) (y)

Age (yrs) (x)

Dielectric
Strength (MΩ) (y)

Age (yrs) (x)

121
129
142
127
135
129
137
133
141
145
136
130

45
53
62
20
60
54
26
20
31
22
60
68

129
137
147
125
144
131
125
122
127
124
127
121

20
43
64
26
53
33
58
46
58
70
26
46

(a) Find the correlation between age of equipment and dielectric strength using:
 Simple (Pearson’s) correlation coefficients, and
 Spearman`s correlation coefficients, and comment on your results.
(b) Obtain the regression equation
(c) What is the predicted dielectric strength for a transformer aging 45 years?
(d) If the expected dielectric strength for a transformer to run for at least 40years is 132MΩ, is the quality control process adequate based on the data collected? Discuss your finding
LO1 Identify the relevance of mathematical methods to a variety of conceptualised engineering examples
Part 4:
The company considers itself to have quality processes in line with 6s principles
Measurement of inspection time, from a large sample of a specific engine part, gave the following distribution:
Time (sec)

5079

80109

110139

140169

170199

200229

Number

4

8

10

13

4

3

You have been asked to determine the mean inspection time and the standard deviation (in seconds). You should also present a graphical illustration of the distribution using appropriate computer software.
From the data gathered and processed you have been asked to determine:
a) the maximum and minimum limits that inspection time might take (assuming the distribution to be normal and 6s compliant (all times within mean ±3s)
b) the probability that a randomly chosen inspection time will be greater than 155 seconds
c) the probability that a randomly chosen inspection time will be shorter than 82 seconds
One of the machines is causing quality problems as P% of the engine parts produced on this machine have been found to be defective. Find the probability of finding 0, 1, 2, 3, 4and 5 defective parts in a sample of 25 parts (assuming a binomial distribution). You should also present a graphical illustration of the probabilities using appropriate computer software.
Measurement of inspection time, from a large sample of outsourced components, gave the following distribution:
Time (sec)

19

21

23

24

26

27

28

30

Number

2

4

3

4

5

4

4

5

Your manager thinks that the inspection time should be the same for all outsourced components. Using the data provided test this hypothesis and indicate whether there is a correlation or not.
Your manager has asked you to summarise, using appropriate software, the statistical data you have been investigating in a method that can be understood by nontechnical colleagues. LO1 Identify the relevance of mathematical methods to a variety of conceptualised engineering examples
Student

A

L

B

T

P

Initials

1

1.96

3.46

1.56

760

9.6

AH

2

1.97

3.47

1.57

770

9.7

SA

3

1.98

3.48

1.58

780

9.8

DB

4

1.99

3.49

1.59

790

9.9

DCo

5

2.00

3.50

1.60

800

10

DCr

6

2.01

3.51

1.61

810

10.1

KC

7

2.02

3.52

1.62

820

10.2

BD

8

2.03

3.53

1.63

830

10.3

AD

9

2.04

3.54

1.64

840

10.4

MD

10

2.05

3.55

1.65

850

10.5

JE

11

2.06

3.56

1.66

860

10.6

DF

12

2.07

3.57

1.67

870

10.7

GC

13

2.08

3.58

1.68

880

10.8

KH

14

2.09

3.59

1.69

890

10.9

LH

15

2.10

3.60

1.70

900

11.0

LT

16

2.11

3.61

1.71

910

101.1

LJ

17

2.12

3.62

1.72

920

11.2

RP

18

2.13

3.63

1.73

930

11.3

MR

19

2.14

3.64

1.74

940

11.4

RC

20

2.15

3.65

1.75

950

11.5

RW

21

2.16

3.66

1.76

960

11.6

KS

22

2.17

3.67

1.77

970

11.7

SF

23

2.18

3.68

1.78

980

11.8

TS

24

2.19

3.69

1.79

990

11.9

JT

25

2.20

3.70

1.80

1000

12.0

MW

