KB7044 Engineering Management Data Analysis

Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 1
Assignment
July 2019

Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 2
Assignment
July 2019
KB7044 Engineering Management Data Analysis
Assignment
Learning Outcomes
On successful completion of this assignment, you will:
1. Know how to perform correlation and regression analyses on a set of given data
and interpret the results.
2. Perform straightforward statistical inferences.
3. Practice the principle of risk-based approach to data analysis through a
mathematically case study with analytical and numerical approaches.
4. Use the probabilistic-based method so derived to support decision making under
uncertainty.
5. Be able to carry out your own literature research prior to solving engineering
decision making problems (in the form of an independent learning project) and
present the result with an in depth discussion.
Introduction
The assignment forms the main part of the portfolio for the assessment of the module KB7044
which consists of elements of research linked to the teaching and learning of this module. You
are also expected to carry out research related to data analysis and decision making. You will
need to demonstrate competency in two approaches of data analysis/modelling techniques
to deal with variability and uncertainty through two given computation cases. In addition you
will carry out an independent learning project involving modelling of a problem with
uncertainty to support decision making.
Analytical Approach: Case 1
Company ABC designs and builds supporting structures for machinery. There have been a
number of complaints about yielding (i.e. the actual stress of the section exceeds the yield
stress of the material) of an important section of a given type of structure designed and built
by the company. There is also a cause for concern for failure of the structure which will have
a range of consequences from malfunctioning (reliability issues) to serious consequence
leading to loss of lives and damage to both public and private properties (safety and risk
issues). (Differences and similarities of reliability, quality and risk/safety are important and
interesting areas for researchers and practitioners).
The section of the structure in question can be modelled by a simple strut under direct
compression. There is no risk of buckling. The direct compressive stress is therefore:

where F is the applied force
A is the cross-sectional area of the section
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 3
Assignment
July 2019
As with most design practices, a safety factor approach is used in determining an acceptable
level of design stress. A safety factor (SF) ranging from 2 to 3 is normally recommended (code
of practice) as a single parameter to deal with uncertainty or possible fluctuations in load and
material properties. Hence the design stress σ d is simply given by:

On the basis of this perceived unsatisfactory performance (mainly to do with reliability), it was
felt that a review is required to examine the adequacy of using safety factor in the face of
uncertainty. You have been engaged as a consultant to investigate the problem and to look
into the feasibility of incorporating a reliability and risk based method to support decision
making under uncertainty within the company’s design practice. The findings are to be
compiled into a technical report. However, it should be noted that the current Safety Factor
used has not been disclosed due to commercial reason.
Tasks
Your first task is to investigate if there is a reasonable degree of correlation between
uncertainty and actual stress in the section. If there are reasons to believe that correlation
exists between certain factors then a regression analysis needs to be performed. A sample
consisting of 22 data items, which is shown in Table 1, is then collected.
Table 1: Data for Correlation & Regression Analysis

Task 1 Organise/sort the data to see if patterns can be observed. Perform correlation
and regression analysis on this set of data. Explain and interpret the results as
clearly as possible.
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 4
Assignment
July 2019
Task 2 Your second task is to look into variability in the yield stress of the material used.
According to the supplier of the material, the yield stress of the material is 130
MPa. A sample consisting of 10 specimens have been prepared and tested. The
results are shown in Table 2. Analyse the data by plotting histogram and/or x-y
plot.
Question: Is there sufficient evidence to accept the manufacturer’s claim that the mean
yield stress of the material is 130 MPa? What would you recommend? Do
you have reason to suspect “noise” from the data set?
Table 2: Yield Test Result from the Sample

You then feel that the vague classification of uncertainty into three arbitrary categories,
although this serves the first task adequately well, does not fit very well with a rigorous riskbased modelling framework. The feasibility of this framework is to be illustrated with a
“design case”. This proposed design case involves a given load, and the structure is to be
designed using a given material.
The next logical task is to set up an analytical framework to model the process using a riskbased approach which aims to estimate the load and the capability of the structure in an
attempt to obtain a rational and defensible solution. The concept of balancing load versus
capability of structure is illustrated in Figure 1.
Figure 1: The Concept behind Risk-Based Approach to Structural Design
The load and capability of the structure in question can now be derived. From equation (1):
FA
σ = , it can be seen that:

sectional area. Assuming that the variability of the
Load Capability
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 5
Assignment
July 2019
cross-sectional area is negligible, hence you need
only to model the variation of the yield stress.
After a series of extensive tests, it is found that the following data can be established with
confidence:

The two parameters can be modelled by two distributions which in our case can be assumed
to be near normal. It is convenient to define excess capacity (FEC) as the difference between
capacity of structure at yield point (FC) and Load (FL) so that we need to deal with one resultant
distribution:

Task 3 On the basis of this analytical framework, set up a spreadsheet to calculate the
numerical values of the probability that the excess capacity <= 0 (i.e. risk of structure
yielding) over a range of excess capacity (recommended range: 10 kN – 100 kN). A
sample spreadsheet is shown in Table 3.
You may also want to plot the sensitivity of the problem (over variation of one or
more parameters), the sensitivity of the decision problem over a range of yield
stress’s standard deviation is shown in Figure 2.
Task 4 The risk-based model can then be used to determine an acceptable level of failure
probability, and hence the optimum excess capacity (or margin) as contrast to the
safety factor approach. The main consideration is the trade-off between additional
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 6
Assignment
July 2019
material cost to provide a given level of excess capacity and the penalty cost
incurred by failed components. For this exercise, the following data applies:
Annual production rate, N = 100,000 pieces
Material cost
Cm = £9,000 per m2
Penalty cost = £200 per failed component, CP , plus replacement material cost
ka = 20,000 where ka is a coefficient used to compute additional material cost
1.1

In equation (10) areamargin is the additional area of a given component to provide a
given level of excess capacity.
The total cost is simply the sum of penalty cost and additional material cost.
Minimising this total cost therefore yields the optimum level of risk (purely from the
consideration of cost). The resultant computation can be summarised as shown in
Figure 3. It is also possible to calculate the variation of optimum risk level
corresponding to changes in yield stress deviations of 10 and 15 MPa, assuming the
former material cost is 10% higher (say) and the later 10% lower.
Table 3: The Sample Spreadsheet for Task 3

Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 7
Assignment
July 2019

Task 5 Comment on the appropriateness of current safety factor, using data from Table 1.
Recommend revised level of safety factor. Note: you can assume the current safety
factor(s) to be constant(s).
Task 6 Tasks 1 -4 relates to reliability (and quality) issues. Extend your investigation to
include failure of materials (i.e. beyond yielding to complete failure by compressive
stress). What would be acceptable failure probability? Given that the
Tensile/Compressive Stress of the material is 360 MPa with a standard deviation of
10 MPa.
Numerical Approach: Case 2
A short concrete strut carries a compressive load applied at an eccentricity e along one
of the principal axes of the section. The eccentrically applied force P causes both axial
(i.e. compressive) stress σ a and flexural (i.e. bending) σ f stress. These stresses, and
the resultant combined stresses are shown in equations (11) – (13), and Figures 4 and
5.
I
P e c
f
⋅ ⋅
σ = (11)
PA
σ a = (12)
A e
I
a
⋅
= (13)
where
P is the applied force
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 8
Assignment
July 2019
e is the eccentricity
c is the distance from neutral axis
I is the second moment of area of the section
A is the cross-sectional area of the section
a is point of zero stress
Yield stress of concrete 40 MPa in compression, 6 MPa in tension.
Figure 4: Eccentrically Applied Load P
Figure 5: Combined Stresses
Tasks
For the worked example you are to formulate a deterministic and a probabilistic
solution procedure for the example problem.
Task 7 Your first task is to solve the problem deterministically, employing
equations (11) – (13), using Excel spreadsheets or MathCAD. The members
of staff of the company are familiar with the deterministic solution
procedure and this should be used as a starting point for the worked
example before introducing the probabilistic solution procedure of
simulation.
a
σa = P/A σf = (Pec)/I
σf – σa σf + σa
P

P
M=Pe
l
w
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 9
Assignment
July 2019
You may use the following data:
e = 85 mm
l = 350 mm
w = 250 mm
c = 175 mm
12
I = wl 3
P = 1000 kN
What is the safety factor/margin against tensile failure?
Task 8 Your second task is to model the variables associated with the problem.
 Eccentricity, e, can be modelled using a Beta distribution having: α = 4 ,
β = 2 , A(min) = 60 mm, B(max) = 90 mm, as shown in Figure 6..
 Length of the section, l, can be modelled by a normal distribution having a
mean of 350 mm and a standard deviation of 20 mm.
 Width of the section, w, can be modelled by a normal distribution having a
mean of 250 mm and a standard deviation of 12 mm.
 The load, P, can be modelled by a triangle distribution having a mode value,
M, of 1000 kN, a low value, L, of 700 kN, and a high value, H, of 1200 kN, as
shown in Figure 4. The triangle distribution is used when one is unable to
model the parameter confidently with a precise distribution. In this case,
the designer can only give a low, high and mode values of the parameters.
 The value of c can be taken as L/2.
Figure 6: Beta Distribution of Eccentricity e.
You are to model the parameters with the given information. Random
sampling of the parameters for the simulation process is to be done on the
basis of above distributions.
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 10
Assignment
July 2019
Figure 7: Triangular Distribution of Load, P.

The axial stress, σ a .
The flexural (bending) stress, σ f .
The combined compressive stress, σ f + σ a .
The combined tensile stress, σ f – σ a .
The distance, a, of axis of zero stress.
The simulation should be performed with no less than 1,000 random
sampled data points for all the parameters.
The statistics and distributions of the output parameters are to be
presented in your report, together with samples of all intermediate
computations.
An example spreadsheet for the above task is shown in Figure 8.
Task 10 Your last task is to explore the effect of eccentricity has on the tensile
failure, and hence determine an optimum quality (as measured in terms of
variability) eccentricity on the basis of cost. A batch size of 10,000 is to be
assumed for the cost calculations.
The low safety margin against tensile failure is a reason for concern as the
concrete struts had already been fabricated. However, by using different
setup processes the characteristics of eccentricity, e, can be varied.
Essentially e can be modelled by Beta distributions between 60 and 90 mm
but with different α and β values (i.e. different skewness).
The additional setting up costs to achieve different characteristics of
eccentricity is shown in Table 4.
L M H
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 11
Assignment
July 2019
Figure 8: An Example Spreadsheet
Table 4: Setting up Costs for Various Characteristics of Eccentricity, e

Penalty cost involved in replacing a faulty strut is £1,380.
With the above information, it is possible to determine the optimum setting
for eccentricity value on the basis of minimum additional cost. A series of
simulations with different  and  values can be performed to determine the
values of tensile failure probability and total additional cost involved for each
combination of α and β values. The result of this exploration can be plotted
as shown in Figure 9.
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 12
Assignment
July 2019
Figure 9: Failure Probability versus Total Additional Cost
Independent Learning Project
This is essentially an open-ended project which allows you to research into a topic with a
critical literature review, formulate a workable quantitative model (analytical or/and
numerical), perform modelling of a problem with uncertainty, problem solving and
exploration of solution space and then present the results in relation to decision making.
The area of investigation is Engineering Cost Estimation. In many engineering projects, under
estimation of costs during the design stage is often a cause of financial loss. Hence, financial
risk analysis and assessment often involves engineering cost estimation. The usual “point
estimate” cost estimation often fails to address the likelihood of estimated cost exceed the
point estimated amount. Your report
Your data and model of problem can be formulated using a standard spreadsheet tool or a
specific risk modelling software tool. As a Level 7 (Master degree) assignment, this section
allows you to investigate a problem/issue to a certain depth and formulate a model in an
attempt to explore the problem/solution space in order to arrive at a defensible decision.
Assignment Report
For the portfolio report the following sections must be included (marks allocation to each
section is also shown):
1. Introduction 10%
2. Computations Case 1 20%
3. Computations Case 2 20%
4. Independent Learning Project 35%
5. Discussion, recommendations, further work and conclusion(s)
(including marks awarded to referencing and citations 15%
Length of Report – not exceeding 20 pages (excluding references and appendices).
Formulations and computations for Cases 1 and 2 will be guided during the lecture sessions
and you will be given opportunities to practice these during seminar sessions. You will be able
Failure Probability vs Costs
£0
£500,000
£1,000,000
£1,500,000
£2,000,000
£2,500,000
£3,000,000
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
Failure Probability, %
Costs, £
Add setup cost, £
Penalty, £
Total add cost, £
Mechanical & Construction Engineering Department
KB7044 Engineering Management Data Analysis Page 13
Assignment
July 2019
to discuss your topic for the independent learning project during the teaching sessions to
ensure you are supervised. In addition, I will be available to discuss and assist outside the
teaching sessions.
Deadline
Deadline of this assignment is Thursday 6th May 2020. Late submission without late
authorization will not be accepted. Submission requirements: submit through ELP upload
together with a hard copy submission to the Student Central.
Feedback
The University standard period of 21 days after the submission date will be applicable.
Academic Misconduct
Students should be aware that when submitting assessed work that the work (both the report
and the computer model) is their own and that it fully acknowledges the work and opinions
of others. For further clarification students should read Appendix 1 of the latest version of
the Assessment Regulations for Northumbria Awards. These can be found at the following
URL:
https://www.northumbria.ac.uk/about-us/university-services/academic-registry/qualityand-teaching-excellence/assessment/guidance-for-students/
Further Support
All references must be cited and listed in accordance to the Harvard standard, a copy of
citation reference “cite them right” can be found in the ELP site for this module.
Feedback and comments from the past year submitted work is also listed in the ELP course
assignment section.

The post KB7044 Engineering Management Data Analysis appeared first on My Assignment Online.