FME461
Engineering Design II
Dr.Hussein Jama
Hussein.jama@uobi.ac.ke
Office 414
Lecture: Mon 8am -10am
Tutorial Tue 3pm - 5pm
6/28/2016
1
Statistical
Considerations
6/28/2016
2
Introduction





Engineering design considerations
This lecture is based on Shigley Ch 20
20 - 1 Random Variables
20 – 2 Mean, variance & Std Deviation
20 – 3 Probability distributions




Normal
Weibull
20 - 4 Probability of error
20 – 5 Linear Regression
6/28/2016
3
Engineering Design


is an iterative process that has as its
primary objective the synthesis of
machines in which the critical problems
are based upon material sciences and
engineering mechanics sciences.
This synthesis involves the creative
conception of mechanisms, and
optimization with respect to performance,
reliability and cost.
6/28/2016
4
Engineering design
•
Machine design does not encompass the entire
field of mechanical engineering. Design where
the critical problems involve the thermal/fluid
sciences fall under the broader category of
“mechanical engineering design.”
•
The primary objective of machine design is
synthesis, or creation, not analysis. Analysis is a
tool that serves as a means toward an end.
6/28/2016
5
Design Process
6/28/2016
6
Design steps
Often the first step in which a designer becomes
involved, and may not involve intense iteration.
In this phase, we deal with the entire machine:

•
Define function
•
Identify constraints involving cost, size, etc.
•
Develop alternative conceptions of mechanism/process
combinations that can satisfy the constraints
•
Perform supporting analyses (thermodynamic, heat
transfer, fluid mechanics, kinematics, force, stress, life,
cost, compatibility with special constraints)
•
Select the best mechanism
6/28/2016
•
Document the design
7
Design steps- prelim
Concept 1 Two longitudinal members, one trans-verse split-end
cross member, small transverse member in transmission tunnel,
rear transverse member similar to original, gauge reduction.
Concept 6 Two integrated, split transverse cross members, rear transverse
member similar to original, reduced sheet thickness in cross members.
6/28/2016
8
Intermediate step
Generally occurs after preliminary design, but the two phases may
overlap. Intermediate design always involves iterations. In this
phase, we deal with individual components of the machine:

•
Identify components
•
Define component functions
•
Identify constraints involving cost, size, etc.
•
Develop tentative conceptions of the components
mechanism/process combinations using good form synthesis
principles
•
Perform supporting analyses (including analyses at each critical
point in each component), FMEA, C& E
•
Select the best component designs
•
Document component designs; prepare a layout drawing
6/28/2016
9
Detail Design Phase
Subsequent to intermediate phase. In this phase,
we deal with individual components of the machine
and the machine as a whole:
•
Select manufacturing and assembly processes
•
Specify dimensions and tolerances
•
Prepare component detail drawings
•
Prepare assembly drawings
6/28/2016
10
Ass 2 - requirements

General consideration of similar machines








Availability
Cost
Designs
Weakness/strengths
Design , details in the appendix
Cost
Analysis
Drawings
6/28/2016
11
Statistics – engineering design

Engineering statistics is the study of how best
to…



6/28/2016
Collect engineering data
Summarize or describe engineering data
Draw formal inferences and practical conclusions
on the basis of engineering data all the while
recognizing the reality of variation
12
Use of statistics in engineering
1.
Design of experiments (DOE)

2.
3.
use statistical techniques to test and construct model of
engineering components and systems.
Quality control and process control
 use statistics as a tool to manage conformance to
specifications of manufacturing processes and their
products.
Time and method engineering

6/28/2016
use statistics to study repetitive operations in manufacturing in
order to set standards and find optimum (in some sense)
manufacturing procedures.
13
Collection of quantitative data
(Measurement)


If you can’t measure, you can’t do statistics…
or engineering for that matter!
Issues:



6/28/2016
Validity
Precision
Accuracy
14
Statistics

FME471
6/28/2016
15
Precision and Accuracy
Not Accurate
Not Precise
Precise, Not
Accurate
6/28/2016
Accurate, Not
Precise
Accurate and
Precise
16
Statistical thinking


Statistical methods are used to help us describe
and understand variability.
By variability, we mean that successive
observations of a system or phenomenon do not
produce exactly the same result.
Are these gears produced exactly the same size?
6/28/2016
NO!
17
Sources of variability
Method
Environment
Material
Man
Machine
6/28/2016
18
Example



An engineer is developing a rubber
compound for use in O-rings.
The engineer uses the standard rubber
compound to produce eight O-rings in a
development laboratory and measures the
tensile strength of each specimen.
The tensile strengths (MPa) of the eight Orings are
103,104,102, 105, 102, 106, 101, and 100.
6/28/2016
19
Variability

There is variability in the tensile strength
measurements.





The variability may even arise from the measurement
errors
Tensile Strength can be modeled as a random
variable.
Tests on the initial specimens show that the
average tensile strength is 102 MPa.
The engineer thinks that this may be too low for
the intended applications.
He decides to consider a modified formulation of
rubber in which a Teflon additive is included.
6/28/2016
20
Random sampling

Assume that X is a measurable quantity related
to a product (tensile strength of rubber). We
model X as a random variable


Occur frequently in engineering applications
Random sampling




Obtain samples from a population
All outcomes must be equally likely to be sampled
Replacement necessary for small populations
Meaningful statistics can be obtained from samples
R : x1 , x2 , x3 ,, xi ,, x N 
6/28/2016
21
Point estimation

The probability density function f(x) of the
random variable X is assumed to be known.

Generally it is taken as Gaussian distribution basing
on the central limit theorem.
f x  

  x   2
exp  
2
2

2 

1




Our purpose is to estimate certain parameters of
f(x), (mean, variance) from observation of the
samples.
6/28/2016
22
Sample mean

1
Sample mean: M 
N
N
x
i 1
i
N
1
2
2
 xi  M 
Sample variance: S 

N  1 i 1
M is a point estimator of 
S is a point estimator of 
6/28/2016
23
Normal Distribution

Mean and standard deviation to describe the
sample or population
6/28/2016
24
Example
6/28/2016
25
Solution
6/28/2016
26
Weibull distribution
6/28/2016
27
Example 2
6/28/2016
28
6/28/2016
29