lecture 7: decision making - university of victoriamech350/lectures/mech350-lecture-7.pdf · the...

1

MECH 350Engineering Design I

University of VictoriaDept. of Mechanical Engineering

Lecture 7: Decision Making

© N. Dechev, University of Victoria

2

CONSIDERING MULTIPLE DESIGN OBJECTIVESBASIC RANKINGTABLES AND SCALES FOR DESIGN OBJECTIVESWEIGHTING FACTORSTHE DECISION TABLE

Outline:


Detailed Design-Detailed Analysis-Simulate & Optimize-Detail Specifications-Drawings, GD&T

3

Decision Making within the “General” Design Process


Identify Need-Talk with Client-Project Goals-Information Gathering

Conceptualization-Brainstorming-Drawing/Visualization-Functional Decomp.-Morphologic Chart

Preliminary Design & Planning-Prelim. Specifications-Prelim. Analysis-Decision Making-Gantt Charts & CPM

Report/Deliver-Oral Presentation-Client Feedback-Formal Design Report

Prototyping-Prototype Fabrication-Concept Verification

Testing/Evaluation-Evaluate Performance-Are Objectives Met?-Iterate Process Steps 2 - 7 as needed

Problem Definition-Problem Statement-Information Gathering-Design Objectives(quantifiable/measurable)

4

An important aspect of ‘design’ is the decision making process, where we must choose between alternatives.

Choosing between design alternatives may be complex, when there are many ‘Design Objectives’ (quantifiable measures of performance) to consider.

Decision Making


5

Possible Methods:Try all the possible alternatives!Take a Poll.Ranked ListsOther...

There are various ‘techniques and tools’ available, to help make a decision between design alternatives:

RankingsTablesWeighting factors Consider question “What could happen if...?”

Decision Making


6

Consider the following Ranking Table:

The table shows four different Design Options/Concepts, where each is design is evaluated against three Design Objectives (Criteria)

Note: The textbook defines “Criteria” as a concise phrase, which describes a Design Objective into one-to-two key words.

According to this table, what is the best approach?

Decision Making: Basic Ranking Table


7

Consider the following Ranking Table:

The table shows three different Design Concepts/Options, where each is evaluated against four Design Objectives (Criteria).

According to this table, what is the best approach?



Questions:What is the magnitude of difference between the ranks?Do the criteria have equal importance?

8

When the choice is unclear, you may:- dig deeper and gather more information- consider the ‘consequences of wrong decisions’- further ‘sub-divide’ the Design Objectives (Criteria).

However, this is still ‘rather unstructured’ decision making.

We need a more ‘concise and structured’ method...



9

Lets consider a “Structured Method” to make a decision based on the information from Table 9.2.

We can rewrite Table 9.2 as follows:

Decision Making:Structured Method Using Scales and Tables


Design Objective Units Design Option A Design Option B Design Option C

Cost $Damage Cont. cmRecyclability $Drivability qualitative

Totals:Table 7.1(a) Blank Concept Summary Table

10

For your table, make sure to list Design Objectives in shortened form, which are clearly distinguishable from one another.

Ensure you define a set of “Metrics” for your Design Objectives. Metrics are usually the “Units of Measure” or “Units of Score” for the Design Objectives.

The purpose is to create a “numeric method” to be able to compare various Design Options.

The comparison of Design Options (i.e. A, B or C, etc...) is done by summing the Metric values for each Design Option, to figure out the “Total Score” for each Design Option.



11

Using the existing example, consider some hypothetical Metric values that have been determined as follows:



Design Objective Units Design Option A Design Option B Design Option C

Cost $ 1000 1800 1400Damage Cont. mm 2 25 12Recyclability $ 150 40 90Drivability qualitative Adequate Poor Excellent

Totals:

PROBLEM! This doesn’t work, since the Metrics don’t add up!You cannot add: $ + km = ???Also, what do the metrics mean? Are the numeric values Excellent, Good, Fair, or Poor?

Table 7.1(b) Complete Concept Summary Table

12

Since each Design Objective has different units of measurement and likely has a different measurement range, direct addition is not possible.

Therefore, it is essential to “map” all the various metric values onto a common Evaluation Scale, to be able to process the information.

These Evaluation Scales will convert the original Metrics into a set of Scaled Metrics that can be added together to get a total Score for each Design Option under consideration.


Decision Making: Evaluation Scales

13

Qualitative Evaluation Scales: We can use a qualitative statement to describe the particular criteria, as being excellent, great, good, adequate, poor, etc... We can create a qualitative evaluation scale, by mapping “Metric Values” to “Qualitative Ranks” as follows:


Cost Criteria Metric Value: Qualitative Rank< $1000 Excellent

$1000 - $1100 Great$1100 - $1500 Good$1500 - $2000 Adequate

> $2000 PoorTable 7.2: Qualitative Evaluation Scale: $ to Rank


14

Numeric Evaluation Scales:In order to perform numeric analysis, it is more useful to use numeric evaluation scales.We can use a quantitative ‘numeric score’ to describe the particular criteria, as being: 10 = excellent, 9 = great, 7 = good, 5 = adequate, 0 = poor, or some other variation. We can create a Numeric Evaluation Scale, by mapping “Metric Values” to “Numeric Scores” as follows:


Cost Criteria Metric Value: Numeric Score< $1000 10

$1000 - $1100 9$1100 - $1500 7$1500 - $2000 5

> $2000 0Table 7.3: Numeric Evaluation Scale: $ to Numeric Score


15

For example, consider the following “Numeric Evaluation Scales, for the four Design Objectives (Criteria) of Table 9.2 as follows:


Cost ($) Num.Score< $1000 10

$1000 - $1100 9$1100 - $1500 7$1500 - $2000 5

> $2000 0


Damage Control (mm) Num.Score< 3 10

3 - 5 85 - 20 6

20 - 60 4> 60 0

Recyclability ($) Num.Score

< $50 10

$50 - $100 8

$100 - $200 4

> $ 200 0

Drivability Num.Score

Excellent 10

Good 7

Adequate 5

Poor 0

Table 7.4: Damage measured as “mm” of indentation on bumper

Table 7.5: Recyclability measured as “$” to Recycle (i.e. high cost is bad)

Table 7.6: Drivability measured qualitatively, and mapped to score.

Table 7.3: Cost measured as “$” for total cost to Manufacture

16

Now, by applying these Evaluation Scales to Table 9.2, we obtain:


Decision Making: Criteria-based Tables and Scales

Design Objective Evaluation Scale Design Option A Design Option B Design Option C

Cost Table 7.3 9 5 7Damage Cont. Table 7.4 10 4 6Recyclability Table 7.5 4 10 8Drivability Table 7.6 5 0 10

Totals: 27 19 31

Great! Now we can “Add the Numeric Scores” in a meaningful way!Based on the values above, it would seem “Option C” has the highest total score. Hence we would choose Design Option C.

Table 7.7 Complete Concept Selection(Decision) Table

17

Relative Importance of Design Objectives:

In the previous examples, we have considered all Design Objectives to have ‘equal importance’ or ‘equal weight’.

However, this is generally not the case, as some Design Objectives are more important that others. So how do we decide on relative weight?

Subjective valuesClient and Designer inputSystematic Methods

Decision Making: Weighting Factors


18

Systematic Weighting Method: Pairwise Comparison

How it works:Evaluate each pair of Design Objectives (Criteria), with respect to one-another.Starting at the top left, compare cost-damage, then cost-recyclability, then cost-drivability. (Note: cost-cost is N.A.)Where cost is “more important” place a 1. Where cost is “less important”, place a zero.Compute the Row Total for each row.Divide the Row Total by total comparisons, to get the Weight.



19

Notes on: Pairwise Comparison Method

For small numbers of Design Objectives, N, where N = 4 to 10, this approach works well.

In this example, N = 4, hence the number of comparisons required is:PC = N*(N-1)/2 = 6, hence, there are 6 pairwise comparisons.



20

Limitations of the Pairwise Comparison Method:Digital comparison may be too coarse. i.e. some criteria may be unintentionally ruled out.



21

When there are many Design Objectives, it becomes more difficult to assign weights. It is even difficult to use systematic methods such as the pairwise comparison method.

For Example: Power Transmission Between two Parallel Shafts

The Design Objectives may be:

How do we weight these?

We need 105 comparisons!(Since N = 15)


Life ExpectancyLubrication Requirement

Install and ReplaceSize

Separation Distance FlexibleMisalignment

Large Separation DistanceNoise

Shock ProtectionOperating Temperature

Speed FlexibilityHigh Speed Capability

Slippage/CreepBearing Loads

High Torque Capability


22

In order to ‘weight’ a large number of Design Objectives, it is much more effective to arrange them into hierarchical groups. For example:


Decision Making: Hierarchical Weighting Factors

23

Within this hierarchy, we have two types of boxes:- Box with original Design Objective (in bold)- Category box, comprised of groups of Design Objective boxes and possible sub-category boxes.

In this example, the hierarchy is shown as 4 levels: 1, 2, 3 and 4.



24

To use this hierarchy for computing weighting factors, we use a two-stage approach:

(1) Perform a ‘pairwise comparison’ (or other weighting method of your choice) for each group and determine a value, ‘k’ representing the weight of each category/D.O. box within that group. Note: The total value for k for that group must sum to a value of 1.

(2) Establish the relative weight ‘w’ for each category/D.O. box. Where the relative weight w is the relative importance of that category/D.O. within its own group (i.e. k), multiplied by the relative weight (w) of the category in the next highest level from which it comes.



25

Example: Power Transmission Between to Parallel Shafts



26

Example: Power Transmission Between two Parallel Shafts

We can summarize these weights in our table as:


Design Objective: Relative WeightLife Expectancy 0.0400

Lubrication Requirement 0.0500Install and Replace 0.0100

Size 0.0250Separation Distance Flexible 0.0300

Misalignment 0.0225Large Separation Distance 0.0225

Noise 0.0600Shock Protection 0.2400

Operating Temperature 0.0875Speed Flexibility 0.0488

High Speed Capability 0.1138Slippage/Creep 0.1250Bearing Loads 0.0500

High Torque Capability 0.0750


Table 7.8: Relative Weight Table for Design Objectives

27

Finally, we need to Make a Decision!The is done by “combining” the Evaluation Scale Scores with all the Weighted Design Objectives into a single “Decision Table” (see below).Example: Power Transmission Between two Parallel Shafts


Making the Decision! The Decision Table

Design OptionsDesign Concept A Design Concept B Design Concept C

Design Objective: Rel.Weight Num. Scale Value Weighted Value Num. Scale Value Weighted Value Num. Scale Value Weighted ValueLife Expectancy 0.0400


Size 0.0250Separation Distance

Flexible0.0300

Misalignment 0.0225Large Separation

Distance0.0225

Noise 0.0600Shock Protection 0.2400


High Speed Capability 0.1138Slippage/Creep 0.1250Bearing Loads 0.0500

High Torque Capability 0.0750Total: Total: Total:

Table 7.9: Blank “Weighted Concept Decision Table”

28

Recall, each Design Objective will have its own Evaluation Scale to Score Metrics. As an example, the Evaluation Scales for 4 of the 15 Design Objectives may be:


Life Expect. (cycles) Num. Score< 1,000,000 0

1 mil - 25 mil 325 mil - 100 mil 6100 mil - 200 mil 8

> 200,000,000 10

Size (mm) Num. Score< 50 10

50 - 75 975 - 125 6

125 - 200 4> 200 0

Noise (dB) Num. Score

< 45 10

45 - 60 8

60 - 85 4

> 85 0

Bearing Loads (N) Num. Score

> 5,000 10

5,000 - 4,000 7

4,000 - 1,000 5

< 1,000 0

Size measured as “mm” of width, where smaller is good

Noise measured as “dB” of sound, where low is good Loads measured as “Newtons”, where high loads are good.

Making the Decision! Sample Evaluation Scales

Life Expectancy measured as “cycles”, where high is good

29

Finally, we need to Make a Decision!A partially complete table is shown: (Adapted from Table 9.6 in Text):


Making the Decision! The Decision Table

Design OptionsDesign Concept A Design Concept B Design Concept C

Design Objective: Rel.Weight Numeric Score Weighted Value Numeric Score Weighted Value Numeric Score Weighted ValueLife Expectancy 0.0400 10 0.4 8 0.32 5 0.2


Size 0.0250 9 0.225 9 0.225 6 0.15Separation Distance

Flexible0.0300

Misalignment 0.0225Large Separation

Distance0.0225

Noise 0.0600 4 0.24 10 0.6 8 0.48Shock Protection 0.2400


High Speed Capability 0.1138Slippage/Creep 0.1250Bearing Loads 0.0500 7 0.35 10 0.5 0 0

High Torque Capability 0.0750 7 0.525 5 0.375 5 0.375Total: 1.74 Total: 2.02 Total: 1.205

We can total the “Weighted Numeric Values” for each Design Concept. Based on the totals, it would seem “Concept B” has the highest score. Hence we would choose Design Concept B.

Table 7.10: Partially Completed “Weighted Concept Decision Table”

Decision Making: Advanced Weighting Methods

30

Consider using ‘Analytical Hierarchy Process’ described in Section 9.3 in text. (Note, Analytical Hierarch Process is beyond the scope of this course. Treat it as optional information)


lecture 7: decision making - university of victoriamech350/lectures/mech350-lecture-7.pdf · the...

Documents