1、 Design of Experiments (DOE) The subject matter contained herein is covered by a copyright owned by: FORD MOTOR COMPANY CORPORATE QUALITY DEVELOPMENT CENTER DEARBORN, MI Copyright 2001 Ford Motor Company This document contains information that may be proprietary. The contents of this document may no
2、t be duplicated by any means without the written permission of Ford Motor Company. All rights reserved 2001 Ford Motor Company Version: June 2001 i Table of Contents Introduction . 1 Agenda 1 Purpose of the Course . 3 Goal . 3 Objectives 3 Design of Experiments (DOE) History . 5 DOE and the STA Engi
3、neer 5 Definition of DOE . 5 Uses of DOE 6 Planning 7 Steps for Experimental Design 7 DOE Plan Analysis 9 Common Failures 9 Influences on Control Factors 9 Evaluation Procedures 10 Steps of the DOE . 11 Checklist for DOE 13 Questions to Ask the Supplier about the Plan . 15 Adding up (Pool) Standard
4、Deviations 16 Steps for Simple Analysis 17 Factorial Experiments . 18 Basic Concept . 18 Interaction Effects 20 Fractional Factorials 21 Use of the Results . 22 A Practical Aid for Experimenters 错误错误!未定义书签。未定义书签。 Participant Guide Design of Experiments (DOE) ii Version: June 2001 2001 Ford Motor Com
5、pany Significance of Factor Effects 23 Activity: Typical Three-factor two-level experiment 24 Fractional Factorial Design 25 DOE Methods . 26 Classical Versus Taguchi Methods 26 Taguchis Loss Function 27 Optimal cost of quality . 28 Taguchi Method . 29 Taguchi Cake-Baking Example . 30 Tips from Tagu
6、chi 31 Signal-to-Noise Ratio . 32 Controlling Noise . 33 Inner and Outer Arrays 34 Signal to Noise for Maximum or Minimum . 35 Confirming the Experiment 36 Evolutionary Operation (EvOp) 37 ANOVA Methods . 38 Assumptions for Applying ANOVA . 38 Analysis of Variance 39 Calculations for ANOVA Table . 4
7、0 Case Studies 41 Case Study 1 The Mismatched Muffler . 42 Case Study 2 . 43 Summary 44 Additional Resources 错误错误!未定义书签。未定义书签。 Subject Matter Expert (SME) . 错误错误!未定义书签。未定义书签。 Additional Training . 错误错误!未定义书签。未定义书签。 References 错误错误!未定义书签。未定义书签。 2001 Ford Motor Company Version: June 2001 iii Review of
8、 Answers to Pre-Test and Post-Test 错误错误!未定义书签。未定义书签。 Introduction Welcome to the Design of Experiments (DOE) course, part of the Corporate Quality Development Center curriculum. This is one of the courses in the Quality Tools module, which is designed to provide STA Engineers with practical knowledg
9、e of the tools required to successfully accomplish their jobs. Agenda Introduction Design of Experiment (DOE) History Planning DOE Plan Analysis Factorial Experiments DOE Methods Case Studies Summary Additional Resources Design of Experiments (DOE) 2001 Ford Motor Company Purpose This course focuses
10、 on reviewing a DOE as a task of the STA Engineer rather than on conducting a DOE. The learner will use real-life experiences, samples, and case studies as a basis for learning key content. This is critical due to the mix of experiences in the class. The sharing of experiences will help all members
11、of the audience learn. The identification of common failure modes and strategic questions will be integrated throughout the course. Linkages with other quality tools will also be made where appropriate throughout the course and summarized in the conclusion. Design of Experiments (DOE) 2001 Ford Moto
12、r Company Goal To provide STA Engineers with sufficient knowledge of DOE, in order to determine if the Supplier has appropriate knowledge and ability to set up, perform, implement, and analyze the DOE correctly. Design of Experiments (DOE) 2001 Ford Motor Company Objectives 1 Upon completion of the
13、training, the participant will be able to: Define the role of the STA Engineer in relation to DOE and process improvement Define the purpose of DOE and application types (Classical versus Taguchi) Identify criteria for conducting a DOE Recognize appropriate and inappropriate outcomes and processes o
14、f a Supplier DOE (case studies) Design of Experiments (DOE) 2001 Ford Motor Company Objectives 2 Upon completion of the training, the participant will be able to: Identify common failures that an STA Engineer may encounter while reviewing a DOE Explain the relationship between DOE and the rest of th
15、e quality tools Identify additional resources available to assist with the conduct or analysis of a DOE Purpose of the Course This course presents statistical concepts needed to design, conduct, analyze, and interpret multi-factor experiments, which are used in factor screening, characterizing and o
16、ptimizing of processes. Goal The goal of this course is to provide STA Engineers with the knowledge to review a Suppliers DOE to determine if it has been set up, performed, implemented and analyzed correctly. Objectives Upon completion of this course, the participant will be able to: Define the role
17、 of the STA Engineer in relation to DOE and process improvement Define the purpose of DOE and application types (Classical and Taguchi) Identify criteria for conducting a DOE Explain the basic steps of conducting a DOE Recognize appropriate and inappropriate outcomes and processes of a Supplier DOE
18、(case studies) Identify common failures that an STA Engineer may encounter while reviewing a DOE Identify strategic questions that should be asked when reviewing a DOE Explain the relationship between DOE and the rest of the quality tools Identify additional resources available to assist with the co
19、nduct or analysis of a DOE Design of Experiments (DOE) 2001 Ford Motor Company DOE and the STA Engineer Make sound judgments when dealing with Suppliers Recognize if the Supplier has ability to recognize and perform setup Recognize if the Supplier can analyze the DOE system correctly Design of Exper
20、iments (DOE) 2001 Ford Motor Company Definition of DOE Design of Experiments is a total plan of action aimed at obtaining knowledge about a given process to improve it or to solve a problem. The objective of a designed experiment is to obtain more information with less expenditure of resources than
21、can be obtained by traditional techniques. Design of Experiments (DOE) 2001 Ford Motor Company History of DOE Design of Experiments was discovered by R.A. Fisher in England in 1920s. He used the technique to study the effect on the outcome of multiple variables simultaneously. Fisher wanted to find
22、out how much rain, water, fertilizer, sunshine, etc. were needed to produce the best crop. Design of Experiments (DOE) History The history of DOE goes back to the 1920s, when it was used in agriculture. Today it is a widely expected engineering tool used at Ford and by its Suppliers. DOE and the STA
23、 Engineer The role of an STA Engineer is to understand DOE in order to make sound judgments when dealing with Suppliers. The STA Engineer will need to recognize if a Supplier has the ability to set up, perform, implement, and analyze the improvement process correctly. Definition of DOE DOE is a tota
24、l plan of action aimed at obtaining knowledge about a given process to improve it or to solve a problem. The objective of a designed experiment is to obtain more information with less expenditure of resources than can be obtained by traditional (one factor at a time) techniques. DOE was pioneered by
25、 R.A. Fisher, an agricultural scientist, in England in the 1920s. He used the technique to study the effect on the outcome of multiple variables simultaneously. Fisher wanted to find out how much rain, water, fertilizer, sunshine, etc. were needed to produce the best crop. 2“ 4“ 6“ 8“ PESTICIDE B1 B
26、2 FERTILIZER A1 A2 Uses of DOE Design of Experiments can play a key role in understanding and improving the reliability of Fords vehicles. Experimentation can be used to: Model degradation of function in vehicle systems Identify factors that significantly improve system life or degradation rate Mode
27、l multivariate functional relationships that can be used for optimization studies DOE at Ford will: Reduce imperfections in parts Reduce costs Reduce guess work Reduce lost time Improve customer relations Improve relations with Suppliers Improve productivity Classical DOE provides a predictive equat
28、ion. Taguchi DOE quickly solves problems. Planning Steps for Experimental Design 1. State the problem(s): Use quality measures to clearly indicate the level of quality or loss. This may come from the Global 8D analysis. The problem statement should address the following: a. What data exists that cha
29、racterizes the problem as it occurs b. How the problem is observed c. When the problem occurs d. How severe the problem is e. Where the problem occurs 2. State the objective of the experiment: This statement should address the scope of the experiment and should be based on: a. The problem statement
30、b. Competitive benchmark information concerning the problem c. Customer information concerning the problem Start Date _ End Date _ 3. Select the quality characteristics and measurement systems: The characteristics (responses, dependent variables, or output variables) should be related to customer ne
31、eds and expectations. The chart below captures the response, the type, and the anticipated range that helps to determine the method of measurement Response Type Anticipated Range Measurement Method/Accuracy Steps for Experimental Design, continued 4. Select the factors that may influence the selecte
32、d quality characteristics: Process flow diagrams, cause/effect diagrams, specifications, statistical process control chart results are some sources for this information and may be captured in a chart similar to the one below. Factor Type Controllable or Noise Range of Interest Levels Anticipated Int
33、eractions with How Measured 1. 2. 3. 4. 5. Determine the number of resources to be used in the experiment: Consider the desired number, the cost per resource, time per experimental trial and the maximum allowable number of resources. 6. Determine which design types and analysis strategies are approp
34、riate: Discuss advantages and disadvantages of each. 7. Select the best design type and analysis strategy to suit the needs. 8. Determine if all the runs can be randomized and which factors are most difficult to randomize. 9. Conduct the experiment and record the data: Monitor both the events for ac
35、curacy. 10. Analyze the data, draw conclusions, make predictions, and do confirmatory tests. 11. Assess results, make decisions, and document results: Evaluate new state of quality and compare with level prior to improvement effort. DOE Plan Analysis When analyzing the plan, it is important to under
36、stand the common failures and influences of control factors in order to verify that the plan has accounted for these factors. Common Failures The common failures that occur when conducting a DOE are: Data is collected when there is only one variable. Supplier often leaves out the interaction. Suppli
37、er has not identified recent changes in the process. Influences on Control Factors Temperature Different operators Humidity Location of plant Environmental factors Lack of consistency Different sample size Evaluation Procedures Define precisely the procedures for running the experiment, indicating w
38、hich factors can be easily changed from one run to the next. Get information regarding past data and repeatability. Determine desirability and opportunities for running the experiment in stages. List relationship between the independent variable and response variable. Steps of the DOE Tasks Task Aid
39、s Who State problem(s) Quality Function Deployment, test failures, warranty items, scrap items, Pareto Analysis Product and/or process experts State objective(s) Customer requirements, competitive benchmarks Select quality characteristic(s) determine control and noise factors Fishbone diagram, flowc
40、harts, SPC charts Select levels Specification limits, operational limits Select orthogonal array(s) OA selection tables D-1, D-2; blank OAs Assign factors interaction tables; OA modification rules DOE expert Conduct tests Computer software, trial data sheets, randomization plan, part serialization p
41、lan, material logistics plan Product, process, and DOE experts Analyze and interpret data Observation method, column effects method, ANOVA, computer software, plotting, ranking (magnitude L = loss in dollars T = target value (normal aim) K = cost coefficient Y = actual quality value Although the equ
42、ation cannot be proven, it emphasizes the point that a consistent product minimizes the total loss. Merely attempting to produce a product within specifications doesnt prevent loss. Taguchi further defines quality as the loss inflicted on society after the shipment of a product. Example: The specifi
43、cations for a product are 6 and 14, with a target of 10. If 20% of the product is produced at exactly 8, 20% on target and 60% at exactly 11, what is the loss function? Solution: L = .2K(8-10)2 + .6K(11-10) 2 L = .8K + .6 L = 1.4K Target L Traditional Concept Taguchi Concept Optimal cost of quality
44、Historical View Current View Taguchi Method Taguchis main contribution is his concept of robustness. When developing a design, or a process, two types of factors are considered: Controllable factors (or Design factors) Inner Array Noise factors (or Environmental factors) Outer Array Controllable fac
45、tors are can be set and maintained. Noise factors are impossible, difficult, or too expensive to control. Taguchi uses the statistic called Signal to Noise Ratio (S/N). The primary purpose is to maximize performance while minimizing variation. There are three types of S/N ratios: Maximizing the resp
46、onse: 2 10n y 1 n 1 log10S Minimizing the response: 2 10n y n 1 log10S Target response (y at optimum value and minimize S2) n 1 S y log10S 2 10n Taguchi Cake-Baking Example Factor Description Level 1Level 2 Egg2 Eggs3 Eggs Milk2 Cups3 Cups Butter1 Stick1.5 Sticks Flour1 Extra Scoop2 Extra Scoops Sug
47、ar1 Spoon2 Spoons Type of Oven 1. Gas 2. Electric Baking Time 1. +5 min. 2. -5 min. Humidity 1. 80% 2. 60% 1111 1222 2123 1214 123Columns R1R2R3R47654321 1111111 2222111 2211221 1122221 2121212 1212212 1221122 2112122 1 2 3 4 5 6 7 8 Column Number Experiment Number Tips from Taguchi The goal of engi
48、neering experiments is to economically improve real-world products and processes, not scientific knowledge. Use a consistent method thats versatile enough to work almost any time (orthogonal arrays). Use a system to adapt the method to the problem, not vice versa (linear graphs). Study lots of varia
49、bles, including the noise variables that the design doesnt control. Study a limited number of interactions, selected by engineering knowledge and experience. Choose parameters that minimize variation, and also move the design toward the target. Predict the results. Run a confirming experiment to check real-worl
