Principles of Problem
Solving
PPS-13: Define the
Stated Problem
(Adapted
from MPS 8,
Pre-class assignment
- Read sections What is It?, Why Do It?,
New Concepts, How to
Do It, and Learning
Objectives
- Take the Define
the Stated Problem Pretest
- Be able to describe the step Define the Stated Problem and how
it fits into the Six Step Problem Solving Method
What is It?
As stated
in PPS-11, this is the step when you dissect the words of the problem
description to extract the important information – the problem, what is known,
and the constraints before you can begin.
It is the
second step in the Six Step Method of Engage, Define, Explore, Plan, Do It, and
Look Back.
Note that
the problem that you extract from the problem statement may not be the “Real
Problem”. For example, you may be facing
the problem of getting a production line back up and running after a machine
breakdown. The “Real Problem” may be a
lack of preventive maintenance, but you need to first address the stated
problem of resuming production.
New Concepts
Given,
Known, Constraint, Problem Ownership, Real Problem
Why Do It
Again, we
are learning the techniques used by expert problem solvers. Defining the problem is like setting a clear
measurable goal. We’ll be able to tell if
we have solved the problem if it is clearly defined.
How to Do It
Two tasks
in problem definition are determining Problem Ownership and Dissection of the
problem statement.
Problem Ownership
Before
diving into a problem, you should check to see if you have ownership. The problem owner has the authority,
resources, and power to define the goal and implement the solution. People affected by the problem and/or its
solution are called stakeholders. In
engineering practice, you will often face problems for which you do not have
ownership, but may be given some responsibility. In that case, you are faced with developing
cooperative problem definitions and solutions.
In this
unit, we will be mostly concerned with the sort of technical problems you will see
in engineering problems courses. Since
you are assigned the problem by the instructor through a textbook, you probably
don’t have complete ownership. You
interpret the problem statement, rather than define the problem, but you are
responsible for the solution.
Problem Dissection
In PPS-10
it says that in this stage you will:
- Systematically classify
information
- Organize the information in a
way that will be useful
- Extract the words relevant to
the problem
- Be thorough in reviewing the
problem statement
- Begin to translate the words
into pictures
- Recognize that some information
may be inferred rather than explicit
We will
take care of the first five of those by dissecting the words and pictures of
the problem statement into components, and placing those individual organs into
appropriate bins. As we place those
parts in the bins, we remove those words from the original problem statement.
The Bins
are –
Goal/Unknown Given/Known Constraints Situation
You will
notice that these bins are typical categories seen in the standard format for
solutions used in many courses.
Consider an
example problem from Callister
A piece of copper originally 305 mm (12in.) long is
pulled in tension with a stress of 276 MPa (40,000 psi). If the deformation is entirely elastic, what
will be the resultant elongation?
Let’s put
this information into our bins and cross out the information as we use it.
A piece of copper originally 305 mm (12in.)
long is pulled in tension with a stress of 276 MPa (40,000 psi). If the deformation is entirely elastic,
what will be the resultant elongation?
|
Goal/Unknown |
Given/Known |
Constraints |
Situation |
|
What will
be the resultant elongation? |
·
Material is copper ·
Stress is 276 MPa ·
Original length is 305 mm |
·
Deformation is entirely elastic |
Pulled in
Tension |
We
- tried to use the wording of the
problem statement as much as possible
- used up all of the problem
statement
- started to picture the
situation.
We did not
- start or even discuss a
solution
- translate the information into
engineering symbols and pictures
- try to make the stated problem
“just like” an example problem in the text.
You may not
bin this information exactly the same as I did.
You may think that “Deformation is
entirely elastic” could also be a Given/Known. It probably could, but looked more like a
constraint to me.
What about implied information?
In this case the instructor probably wants the numerical answer in
decimal form with no more that 3 significant figures, wants you to do it
yourself rather than copy it our of the solution manual, wants no round off
error in the first two decimal places, and wants to see a step by step solution
rather than a single number. The stress
is probably the normal rather than shear stress and elastic means linear
elastic.
Important
inferred statements should be listed in their own bin as Assumptions.
Learning Objectives
Given a
problem statement, you should be able to:
- Identify the Goal/Unknowns
- Identify Given/Knowns
- Identify the Constraints
- Identify Inferred Knowns and
Constraints
Pretest
Awareness:
How
aware are you of what you do when you define the stated problem? _________
On a scale of 1-10,
where
1 is Unaware, I just do it,
5 is Aware of some
10 is Very aware: I can describe the details of how
I do it
Skill:
How
skilled are you in doing this activity? _________
On a scale of 1-10,
where
1 is poor, 3 is fair,
5 is good, 7 is very good, and 10 is excellent?
In-Class
Exercise 1 (5 min.): (instructor hands out
problem statement with bins shown.)
- Individually sort the
information in a problem statement by the instructor into the defined
bins.
- Compare your list with one or
two people near you, note differences, and try to resolve those
differences.
PPS-13 Define the Stated Problem
Assignment 1 Individual
For the
problem statement assigned,
- Sort all the information into
bins of Goal/Unknown, Given/Known, Constraints, Situation
- List Inferred Knowns and
Constraints as Assumptions
|
Goal/Unknown |
Given/Known |
Constraints |
Situation |
|
|
|
|
|
Assumptions
Evaluation:
1. Considered All information
Excellent (10) - all
of information in problem statement was binned
Mediocre (5) - some
of information in problem statement was not binned
Weak (0) - significant information was not binned
2. Appropriate
Binning
Excellent (10) – all
information was in appropriate (or reasonable) categories
Mediocre (5) - some information
was not in appropriate categories
Weak (0) – most
information was incorrectly binned
3. Avoiding
the Jump to Solution
Excellent (10) – information was not translated to
engineering symbols, wording of information was similar to problem statement
Mediocre (5) - significant “interpretation” of the
wording, use of engineering symbols and equations
Weak (0) – solution scheme suggested, words
translated to symbols and equations.