Problem Solving Methods

Engineers Solve Problems

Problem solving is a powerful human activity. Computers are useful tools in problem solving,

but it is the human who actually solves the problem.

It is impossible to teach specific facts that will always lead to a solution. The ability to solve problem comes from doing it.

Many things must pull together to solve a problem.

Problem Solving Problem solving is a combination

of experience, knowledge, process, and art

Design process is a series of logical steps that when followed produce an optimal solution given time and resources as two constraints

Problem Solving; cont’

A problem is a situation, quantitative or otherwise, that confronts an individual or group of individuals, that requires resolution, and for which the individual sees no apparent path to the solution.

Problem Solving; cont’

Problem solving is a process, an activity whereby a best value is determined for an unknown, subject to a specific set of conditions. It is a means by which an individual uses previously acquired knowledge, skills and understanding to satisfy the demands of an unfamiliar situation.

What skills must be used when solving a problem?

Knowledge

Motivation

Experience

Communication Skills

Learning Skills

Group Skills

Problem Analysis A distinguishing characteristic of a

qualified engineer is the ability to solve technical problems; both art and science Science; knowledge of mathematics,

chemistry, physics, etc Art; proper judgment, experience,

common sense, and know-how; to know when and how rigorously science should be applied and whether the resulting answer reasonably satisfies the original problem is an art

Techniques for Error Free Problem Solving

Always draw a picture of the physical situation,if possible. State any assumptions made. Indicate all given properties on the diagram with their units. Convert units to a given unit system. Label unknown quantities with a question mark.

Skills used in Implementing Problem Solving Strategies

Analysis

Use logic to: Identify the system to be analyzed Identify the objective Identify relationships Divide the system into parts

Skills used in Implementing Problem Solving Strategies

Synthesis

Use creativity to: Develop ideas via brainstorming Evaluate the ideas by analysis when

enough ideas have been generated

Skills used in Implementing Problem Solving Strategies

Decision MakingUse logic to compare the various ideas and select the “best” one(s)

Generalization - Going from the specific to the broad use abstraction to:Aid in analysis, synthesis, and decision making

3.1 Types of Problems

Research Problems Knowledge Problems Troubleshooting Problems Mathematics Problems Resource Problems Social Problems Design Problems

Difficulties in Problem Solving

Most common difficulty: failure to use known information.

To avoid this problem: Write the problem in primitive form and

sketch an accurate picture of the setup (where applicable).

Transform the primitive statements to simpler language.

Translate verbal problems to more abstract mathematical statement(s) and figures, diagrams, charts, etc.

General Problem Solving Method

Define and understand problem1. Sketch the problem2. Gather information3. Generate and evaluate potential

solutions Use applicable theories and assumptions

4. Refine and implement solution5. Verify and test solution

Define and Understand

Understand what is being asked Describe input/output (I/O)

what are you given knowns

what are you trying to find unknowns

Sketch the problem

Gather Information

Collect necessary data List relevant equations/theories State all assumptions

CHECK YOUR WORK!!

Don’t stop at getting an answer!! Think about whether the answer makes

physical sense. you are the instructor and you have to turn in

final grades. In your haste, you calculate the average of Susie’s grades (100, 70, 90) to be 78 and give Susie a C...

Getting It Right

The problem solving process may be an iterative process. If at first you don’t succeed (i.e., the

algorithm test fails), try again… The more thorough you are at

each step of the problem solving process, the more likely you are to get it right the first time!!

Creative Problem Solving

The nine dots shown are arranged in equally spaced rows and columns. Connect all nine points with four straight lines without lifting the pencil from the paper and without retracing any line.

Individual Exercise (3 minutes)

Creative Problem Solving

Creative Problem Solving If you enjoy solving puzzles, you will enjoy

engineering Crick and Watson figured DNA when they

were young Engineers create from nature what did not

exist before In this creative process, the engineer

marshals skills in mathematics, materials, and other engineering discipline and from these resources create a new solution for a human need

Creative Problem Solving Engineering is not dull or stifling;

send people to moon, communication from battlefield, etc

Creative artists spent many years perfecting their skills

Engineers need patience, practice, and gaining problem-solving techniques by training

Self-Questions for Problem Solving

How important is the answer to a given problem?

Would a rough, preliminary estimate be satisfactory or high degree accuracy demanded?

How much time do you have and what resources are at your disposal? Data available or should be collected,

equipments and personnel, etc

Self-Questions for Problem Solving

What about the theory you intend to use? Can you use it now or must learn to use it? Is it state of the art?

Can you make assumptions that simplify without sacrificing needed accuracy?

Are other assumptions valid and applicable?

Optimize time and resources vs reliability

Engineering Method1. Recognize and understand the

problem (most difficult part)2. Accumulate data and verify

accuracy3. Select the appropriate theory or

principles4. Make necessary assumptions5. Solve the problem6. Verify and check results

Engineering Method Perfect solutions to real problems

do not exist. Simplify the problem to solve it; steady state, rigid body, adiabatic, isentropic, static etc

To solve a problem, use mathematical model; direct methods, trial-and-error, graphic methods, etc.

Standards of Problem Presentation

Engineers should have ability to present information with great clarity in a neat, careful manner

Poor engineering documents can be legal problems in courts

Follow standard forms such as shown in the textbooks

Building Effective Leadership Skills

Creating Your Own Leadership Legacy

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Background/Overview Effective leadership skills are needed more than

ever to stay ahead of the competition. Through the examples of five leadership legends,

you will hear ideas and strategies that you can incorporate into your personal leadership style to help drive winning results in your organization.

Historically, the training of actuaries has underserved the leadership component. Using effective leadership skills can help actuaries be more impactful, and better influence the businesses they support.

Historically, the training of actuaries has underserved the leadership component. Using effective leadership skills can help actuaries be more impactful, and better influence the businesses they support.

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The essence of leadership is service to others

On a basic level, as a leader, you exist to:– Inspire others to strive for excellence– Ensure the work environment is safe, challenging, and fair– Teach, mentor, provide guidance

True leaders put the welfare of the group ahead of their own self-interest

“Selfless” does not mean “hands-off” Great leaders enhance institutional capability by

driving the actions of others to achieve greatness

Leadership is all about helping others to succeed.Leadership is all about helping others to succeed.

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The perceived complexity of leadership arises from its seemingly overwhelming number of duties

Create and establish strategies Ensure effectiveness and efficiency Communicate openly and often Build solid relationships Act with integrity and fairness Provide counsel and direction Exert influence in the absence of

ownership Foster collaboration Motivate, coach and develop others Produce results, meet objectives and

exceed goalsHow can a leader avoid being overwhelmed by this complexity?How can a leader avoid being overwhelmed by this complexity?

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Focusing on a few key qualities and incorporating them into every action simplifies the act of leading others, and increases leadership effectiveness

There is no standardized approach to effective leadership

Your effectiveness as a leader is directly proportional to how well the key qualities you focus on align with your values and your personality

My five qualities of a great leader are:1. Maintains and demonstrates strong convictions2. Develops and communicates a clear, winning

vision3. Creates a high performance culture4. Convinces rather than controls5. Continually learns

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Maintain and Demonstrate Strong ConvictionsLeadership Profile: Joan of Arc

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Maintaining and demonstrating strong convictions gives leaders their credibility

Integrity Lead by example Personal accountability Strive for excellence

– “Play for your paycheck”– “Bring your ‘A’ game every day”– “Average is defined as the best of

the worst, or the worst of the best”

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Develop and Communicate a Clear, Winning VisionLeadership Profile: Martin Luther King, Jr.

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A clear, compelling, winning vision is the cornerstone of building organizational success Establish and articulate a clear vision of the future for

your business to inspire commitment from others: Should be “stretch,” but not “folly” Include measurable indicators of progress and success

Develop compelling long-term business strategies to achieve the vision: Built with a strong understanding of the external environment Takes into account perspectives and capabilities of your

organization and those with which it interacts Ensure broad strategies are translated into clear and

effective operating plans and tactical initiatives

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Create a High Performance CultureLeadership Profile: Herbert D. Kelleher, Southwest Airlines

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A High Performing Culture engages, challenges, and fully leverages employees, which promotes innovation and continuous improvement

Build your team to win! Assess, then stretch/challenge top players Seek to Redeploy, Rehabilitate, or, if needed, Remove underperformers Hire winners

Execute aggressive performance management as part of your overall talent management strategy

Set clear performance objectives and expectations Monitor and document performance; reward success, and hold people

accountable for poor performance Provide direct, helpful feedback Take corrective action when necessary

Pay for performance, pay for potential Drive a culture of open and fast communication to

support rapid response to changing business conditions Build inclusion, leverage diversity Continually raise the bar – don’t get complacent

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Convince Rather Than ControlLeadership Profile: William Wallace - “Braveheart”

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Any leader can get work done by barking orders…

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…But the enlightened leader convinces people to engage in the right behaviors, gains buy-in, and gives them choices while influencing them to perform at a high level

Clearly articulate your point of view and persuade employees to accept your proposal and/or recommendation

Project self-confidence without arrogance Develop effective and constructive

strategies for influencing important decisions, sometimes shifting the organization’s direction or way of looking at things

Use high-impact, efficient communication vehicles to get your points across

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Continuous LearningLeadership Profile: Jack Welch

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The Profession of Leadership requires continuous learning, just like Actuarial Regularly conduct an honest self-assessment Initiate efforts to develop skills that will enhance

performance in current role and/or accelerate readiness for future roles

Take full advantage of available learning and development programs, e.g., executive development programs, courses, professional certifications

Solicit feedback and guidance from mentors or coaches, then genuinely listen to feedback and apply learnings

Seek challenges that provide opportunities for on-the-job development of critical knowledge and skills

Ask questions to learn from others with different knowledge, experience or perspective

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Summary The essence of leadership is service to others Don’t be overwhelmed by the seemingly endless

number of tasks and obligations leadership requires

Rather, focus on a few core attributes as you practice the profession of leadership, like these:

1. Have strong convictions2. Develop and communicate a clear, winning vision3. Create a high performance culture4. Convince rather than control5. Be a continuous learner

What qualities of a great leader would you add to this list?What qualities of a great leader would you add to this list?

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Some Final Thoughts Your role as a leader is more

critical than ever

Identify a take-away to work on towards building more effective leadership skills

What will be your leadership legacy?

Open Discussion

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