Lecture 7: Decision Making

Transcription

1 MECH 350 Engineering Design I University of Victoria Dept. of Mechanical Engineering Lecture 7: Decision Making 1 Outline: CONSIDERING MULTIPLE DESIGN OBJECTIVES BASIC RANKING TABLES AND SCALES FOR DESIGN OBJECTIVES WEIGHTING FACTORS THE DECISION TABLE 2

2 Decision Making within the General Design Process Identify Need -Talk with Client -Project Goals -Information Gathering Problem Definition -Problem Statement -Information Gathering -Design Objectives (quantifiable/measurable) Conceptualization -Brainstorming -Drawing/Visualization -Functional Decomp. -Morphologic Chart Preliminary Design & Planning -Prelim. Specifications -Prelim. Analysis -Decision Making -Gantt Charts & CPM Detailed Design -Detailed Analysis -Simulate & Optimize -Detail Specifications -Drawings, GD&T Prototyping -Prototype Fabrication -Concept Verification Testing/Evaluation -Evaluate Performance -Are Objectives Met? -Iterate Process Steps 2-7 as needed Report/Deliver -Oral Presentation -Client Feedback -Formal Design Report 3 Decision Making 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. 4

3 Decision Making Possible Methods: Try all the possible alternatives! Take a Poll. Ranked Lists Other... There are various techniques and tools available, to help make a decision between design alternatives: Rankings Tables Weighting factors Consider question What could happen if...? 5 Decision Making: Basic Ranking Table 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? 6

4 Decision Making: Basic Ranking Table 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? 7 Decision Making: Basic Ranking Table 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... 8

5 Decision Making: Structured Method Using Scales and Tables 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: Design Objective Units Design Option A Design Option B Design Option C Cost $ Damage Cont. cm Recyclability $ Drivability Totals: qualitative Table 7.1(a) Blank Concept Summary Table 9 Decision Making: Structured Method Using Scales and Tables 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. 10

6 Decision Making: Structured Method Using Scales and Tables 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 $ Damage Cont. mm Recyclability $ Drivability qualitative Adequate Poor Excellent Totals: Table 7.1(b) Complete Concept Summary Table 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? 11 Decision Making: Evaluation Scales 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. 12

7 Decision Making: Evaluation Scales 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 $ $1100 Great $ $1500 Good $ $2000 Adequate > $2000 Poor Table 7.2: Qualitative Evaluation Scale: $ to Rank 13 Decision Making: Evaluation Scales 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 < $ $ $ $ $ $ $ > $ Table 7.3: Numeric Evaluation Scale: $ to Numeric Score 14

8 Decision Making: Evaluation Scales For example, consider the following Numeric Evaluation Scales, for the four Design Objectives (Criteria) of Table 9.2 as follows: Cost ($) Num.Score < $ $ $ $ $ $ $ > $ Table 7.3: Cost measured as $ for total cost to Manufacture Recyclability ($) Num.Score < $50 10 $50 - $100 8 $100 - $200 4 > $ Table 7.5: Recyclability measured as $ to Recycle (i.e. high cost is bad) Damage Control (mm) Num.Score < > 60 0 Table 7.4: Damage measured as mm of indentation on bumper Drivability Num.Score Excellent 10 Good 7 Adequate 5 Poor 0 Table 7.6: Drivability measured qualitatively, and mapped to score. 15 Decision Making: Criteria-based Tables and Scales Now, by applying these Evaluation Scales to Table 9.2, we obtain: Design Objective Evaluation Scale Design Option A Design Option B Design Option C Cost Table Damage Cont. Table Recyclability Table Drivability Table Totals: Table 7.7 Complete Concept Selection(Decision) Table 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. 16

9 Decision Making: Weighting Factors 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 values Client and Designer input Systematic Methods 17 Decision Making: Weighting Factors 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 costrecyclability, 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. 18

10 Decision Making: Weighting Factors 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. 19 Decision Making: Weighting Factors Limitations of the Pairwise Comparison Method: Digital comparison may be too coarse. i.e. some criteria may be unintentionally ruled out. 20

11 Decision Making: Weighting Factors 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 Expectancy Lubrication Requirement Install and Replace Size Separation Distance Flexible Misalignment Large Separation Distance Noise Shock Protection Operating Temperature Speed Flexibility High Speed Capability Slippage/Creep Bearing Loads High Torque Capability 21 Decision Making: Hierarchical Weighting Factors In order to weight a large number of Design Objectives, it is much more effective to arrange them into hierarchical groups. For example: 22

12 Decision Making: Hierarchical Weighting Factors 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 Decision Making: Hierarchical Weighting Factors To use this hierarchy for computing weighting factors, we use a twostage 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. 24

13 Decision Making: Hierarchical Weighting Factors Example: Power Transmission Between to Parallel Shafts 25 Decision Making: Hierarchical Weighting Factors Example: Power Transmission Between two Parallel Shafts We can summarize these weights in our table as: Design Objective: Relative Weight Life Expectancy Lubrication Requirement Install and Replace Size Separation Distance Flexible Misalignment Large Separation Distance Noise Shock Protection Operating Temperature Speed Flexibility High Speed Capability Slippage/Creep Bearing Loads High Torque Capability Table 7.8: Relative Weight Table for Design Objectives 26

14 Making the Decision! The Decision Table 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 Design Options Design 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 Value Life Expectancy Lubrication Requirement Install and Replace Size Separation Distance Misalignment Flexible Large Separation Distance Noise Shock Protection Operating Temperature Speed Flexibility High Speed Capability Slippage/Creep Bearing Loads High Torque Capability Total: Total: Total: Table 7.9: Blank Weighted Concept Decision Table 27 Making the Decision! Sample Evaluation Scales 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, mil - 25 mil 3 25 mil mil mil mil 8 > 200,000, Life Expectancy measured as cycles, where high is good Size (mm) Num. Score < > Size measured as mm of width, where smaller is good Noise (db) Num. Score < > 85 0 Noise measured as db of sound, where low is good Bearing Loads (N) Num. Score > 5, ,000-4, ,000-1,000 5 < 1,000 0 Loads measured as Newtons, where high loads are good. 28

15 Making the Decision! The Decision Table Finally, we need to Make a Decision! A partially complete table is shown: (Adapted from Table 9.6 in Text): Design Options Design Concept A Design Concept B Design Concept C Design Objective: Rel.Weight Numeric Score Weighted Value Numeric Score Weighted Value Numeric Score Weighted Value Life Expectancy Lubrication Requirement Install and Replace Size Separation Distance Misalignment Flexible Large Separation Distance Noise Shock Protection Operating Temperature Speed Flexibility High Speed Capability Slippage/Creep Bearing Loads High Torque Capability Table 7.10: Partially Completed Weighted Concept Decision Table Total: 1.74 Total: 2.02 Total: 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. 29 Decision Making: Advanced Weighting Methods 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) 30