Module - 5. Robust Design Strategies

Transcription

1 Module - 5 Robust Strategies Variation in performance occurs mainly due to control factor and noise factors (uncontrollable). While DOE can identify the influential control factors which can indeed be adjusted to improve the consistency in performance, for many system, the uncontrollable factors cause most of the variation. In such situations, Taguchi, in his ROBUST DESIGN strategy, proposes to minimize the influence of uncontrollable factors by adjusting the levels of the controllable factors. In this approach, the desired design is sought not by selecting the best performance under ideal condition, instead by looking for a design that produce consistent performance having been exposed to the influence of the uncontrollable factors. Topics and objectives: * Understand the necessity of multiple runs. * Follow the experimental strategy for robust product/process. * Include noise factors using outer array design. * Develop criteria for analyzing multiple results: - MSD - S/N Ratios 5. Ambitious Business Goals Make product robust (rugged, insensitive) such that they work, all the time, the way that they are supposed to. Try to achieve: - Consistent performance - Robust design - Performance that is unaffected by influence of uncontrollable factors. Why does the performance vary? - Noise factors How do we minimize the influence of noise factors? - not by controlling them, but by adjusting The Controllable Factors What is the design strategy: - Robust design strategy - Outer array design with noise factors

2 Module 5: Robust Strategies Page 5 - Why do we need to repeat experiments(trials) When performance varies, we need to test more samples to get a representative performance reading. How to Repeat? Just repeat or repeat with a purpose? What is the purpose? Our purpose is to reduce variation of performance around the target. What causes variations? Variation in performance is caused by factors we cannot control, do not want to control or are not aware of their influence. Such factors are called "Noise Factors". What do we want to do about the influence of the noise factors? Contrary to the traditional approach to determine the causes of variation and try to control them, in ROBUST DESIGN strategy, the approach is to reduce the influence of the noise factors by simply controlling the controllable factors. What can you do to reduce the influence of the noise factors? experiments with controllable factors as usual. Identify the applicable noise factors for the subject project and determine their combinations by using the appropriate orthogonal array. Repeat the trial conditions by exposing them to the influence of the noise factors. # OF FA CT OR S Control Factors Noise Factors R&D Adv.Engg &Dev. Test&Valid. Manufg. Prod. Robust Strategy - Identify noise factors - Control them during tests in laboratory environment and work with at least two levels. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

3 Module 5: Robust Strategies Page Combine the noise factors using the orthogonal array (outer array) to produce a number of noise conditions. - Repeat samples in the same trial conditions exposing each to the noise conditions. Consider that we have three -level noise factors in the experiment with the cake baking process. Noise Factors: Oven type (N) Humidity (N ) Room temperature (N 3 ) These 3 noise factors, at -level each, can be combined to produce 8 conditions. Or Alternatively we can use Taguchi L4 OA to produce 4 conditions. Objectives: determine the optimum condition by selecting the controllable factor levels such that variations due to uncontrollable factors is minimized. " Reduce variability without actually removing the cause of variation " Approach: Run multiple experiments ( or more samples/trial). 5. Mechanics of the Outer Array s Outer Array design incorporates both control and noise factors. control factors and inner array define the trial conditions, while the noise factors being assigned to outer array define the conditions to which the trial conditions are exposed to while performing the experiments. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

4 Module 5: Robust Strategies Page 5-4 Experiment With Noise Factors Tr# 3 * 8 Noise Factors Humidity3 Temperature Control factors Oven type L 8 Inner Array Outer Array 3 4 R e s u l t s R R R R R R R R R R R R 73 R R R R L 4 Symbolic Result Notations: The design requires (8 x 4 =) 3 samples tested and the results arranged as shown above. For example, R73 represents the result obtained by testing trial number 7 under the noise condition 3 i.e. Oven at level, Temperature at level and Humidity at level. (Subscripts of all results, R, are not shown) Advantages: Information about noise factors, interaction between control and noise factors, number repetitions, noise conditions, etc. Disadvantages: Higher level of disciplines, costlier, etc. Order of Sophistication in Experiment (From most desirable to least desirable). Formal treatment of noise factors by outer array design. Repeating experiments with "RANDOM NOISE" 3. Run multiple samples per trial (Simply repeat) 4. Run one sample per trial (Poor man's experiment) R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

5 Module 5: Robust Strategies Page Benefits of Outer Array designs * Optimum condition determined using outer array is least sensitive to the variation of noise factors. (robust design) * Number repetition and the conditions of the noise factor levels are discretely determined by the size of the outer array. * Influence of noise factor can be easily calculated in the same manner as control factors (main effect of noise factors). * Interaction between control factors and noise factors can also be determined if desired. Example 5: Robust Bearing Study s Factors and Their Levels 4 factors at -levels each 3 interactions and 3 noise factors at -levels each Inner Array(L-8) With Control Factors Col# Factor Description Level- Level- Collar Rotor Shaft To Bearing Interaction x N/A 4 Finger To Drive Interaction x4 N/A 6 Interaction x4 N/A 7 Rotor Chuck Outer Array(L-4) And The Noise Factors Col# Factor Dec. Level- Level- Temperature 70 F 50 F Pressure Fuel Type Type A Type B R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

6 Module 5: Robust Strategies Page 5-6 General Guidelines for Repeating Experiments * Whenever experimenting with actual hardware, run multiple samples per trial. * When results under the same trial condition do not repeat, repeat samples. * Experiments with analytical simulation need not be repeated. * When possible, identify noise factors and include outer array in your design. - If outer array isn't possible, run experiments under random noise conditions. * Determine number of repetitions arbitrarily based on expected variability and cast of extra sample. Note: Noise condition is considered random when the noise factors are identified and the experiments are carried out at their varying noise levels. 5.4 Analysis of Repeated Results Trl# A B C R R R3 R4 AVG Comparison of Multiple Data => Average => Average 9 This two set would look the same if we only compared the averages. Nature of distribution of data represented by Standard Deviation, Scatter, etc. will be required to accurately compare the two data sets. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

7 Module 5: Robust Strategies Page 5-7 Observations: - Need a single quantity to compare each trial condition - Average alone does not tell the whole story - Require a quantity that includes both average and standard deviation Conclusion: - Need to devise a new yardstick of measurements which will be simple, yet include all the desirable characteristics. MSD And S/N Ratio Mean Squared Deviation (MSD) Reducing variation around the target is the objective of taguchi experiments. MSD measures variation around the target and is also a function of Average and Standard Deviation. Avg. Target _ y Y Y o Lower (Y avg. - Y 0 ) And STD. Deviation are satisfied by minimizing MSD. MSD = A measure of Deviation of result from the target. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

8 Module 5: Robust Strategies Page 5-8 generally speaking MSD = (Y i - Y o ) /n Where Y o = Target Value. It can be shown that MSD = (STD. DEV.) + (Y avg. - Y o ) Which means that MSD can be minimized by lowering standard deviation and /or reducing the distance of the average to the target. 5.5 Definition of MSD for the Three QC s MSD is a quantity of which we always seek a smaller value. to maintain this characteristic common for all three QC., the definitions of MSD are modified slightly for the other two QC's. accordingly. Nominal: Smaller: Bigger: MSD = [(Y - Y o ) +.(Y - Y o ) + (Y 3 - Y o ) +..]/n MSD = [( Y +.Y +Y 3 +..)]/n MSD = [( / Y + / Y + Y )] / n Recommended Yardstick for Analysis For convenience of handling a wide range of results and to increase its linear behavior, MSD is transformed to S/N. when results are made to influence the performance in a linear manner, the estimate of performance (Yopt), which uses a linear predictor model, becomes more capable of performance more accurately. S/N = - 0 LOG 0 (MSD) S/N is called the Signal to Noise ratio of the result. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

9 Module 5: Robust Strategies Page 5-9 S/N ratio and MSD are defined such that, regardless of the quality characteristic, i.e. bigger, smaller or nominal, * Smaller value for MSD and * Larger value for S/N ratio is desired Example 6: Cam Lifter Study An experiment with three -level factors (A, B and C) and 3 samples per trial yielded the following results (QC = Smaller is Better) Expt. A B C R R R3 S/N Avg Sample calculation of S/N: st. ROW: MSD = ( )/3 = S/N = -0 LOG0(MSD) = nd. ROW: MSD = ( )/3 = etc. S/N = -0 LOG0(MSD) = -.8 If we were to compare results of trials 3 and 4 to determine which one is better, we can now easily do that by comparing the S/N ratios. Based on averages, condition results of trials 3 & 4 are equal. Based on S/N ratios, condition 3 is better, since comparing -4. > -4.4 ( -4. is bigger than -4.4 ) The Main Effects Col# Factors Level- Level- (L-L) Spring Rate Cam Profile Wt of Push Rod R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

10 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page Plot of Factor Average Effects - T A A B B C C Optimum Condition : A B C Note that optimum condition is selected based on the higher values of S/N. while performing S/N analysis, higher values will always be selected regardless of quality characteristic (in this case, smaller the better). Estimate of Performance at the Optimum Condition (QC: smaller is better) Factor description level description Level# Contribution Spring rate Current design.605 Cam profile Type Wt. Of push rod Lighter Contribution from all factors (total) Current grand average of performance Expected result at optimum condition Example 7: Engine Idle Stability Study Three Factors at 3-levels each Three Repetitions ( normal operating noise) Factors and their Levels Col. # Factors level- level- level-3 Indexing -30 deg o deg +50 deg Overlap area -30% 0 % +30 % 3 Spark advance 0 deg 30 deg 40 deg 4 Unused/upgraded M/U Characteristic: Smaller is better (as selected for analysis) R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

11 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page 5 - L9(3 4 ) COL==> COND TRIAL RESULTS Trial# R() R() R(3) S/N Ratios Main Effects (Qualitek-4 Software Output) Col#/ Factors Level Level Level 3 Level 4 (L-L) Indexing Overlap Area Spark Advance Quality Characteristic: The Smaller The Better Data Type : S/N Ratio A N O V A Table Data Type: S/N Ratio Col.#/Factor F S V F S' P(%) Indexing Overlap Spark Adv Other/Error Total: % R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

12 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page 5 - Optimum Table ( Estimated Performance At Optimum Condition) Col #/ Factors Level Desc. Level# Contribution Indexing O Deg.947 Overlap Area -30% Spark Advance 30 Deg.0484 Total Contribution From All Factors Current Grand Average Of Performance Expected Result At Optimum Condition The expected result (-5.874) shown above represents the S/N ratio of the results of multiple samples tested at the Optimum Condition. To get an estimate of the performance expressed in the measured units, the S/N must be transformed back as follows: MSD = 0 - [(S/N)/0] (Since S/N is now known) = 0 - [(-5.874)/0] = But MSD = [ Y + Y + Y Yn ]/n (For Smaller is better) = [ Yexpected] / ( assuming same result for all samples) Or Y expected = [ MSD ] / = ].50 = 9.66 (in terms of the original units) 5.6 Experiment design and Analysis Strategies The experiment you design will follow one of this paths illustrated in the following diagram depending on the complexities of your experiment. No matter your control factor design (INNER ARRAY), you should always attempt to identify and formally treat the noise factors by using ROBUST DESIGN principles outlined earlier. An of course, regardless of your design, run your experimental conditions in RANDOM ORDER when possible. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

13 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page Experiment Tips Experiment designs with all factors at one level are likely to be accomplished with standard orthogonal arrays. These are simpler kinds of designs and do not require any modifications. On the other hand, if factors are of mixed levels, and there are interactions included in the experiment, modifications of the array will be necessary. Of course, no matter how your inner array design is, presence of noise factors in your system requires consideration of formal treatment of the noise effects by use of the appropriate outer array. When possible, and if variation is a concern, each trial condition should be repeated multiple times. EXPERIMENT DESIGN ROADMAP s Using Standard Arrays Mixed Level & Interaction s Assigns Factors Arbitrarily Modify Columns and Assign Interacting Factors Properly Consider Noise Factors Determine Repetitions Run Experiments in Random Order R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

14 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page 5-4 Experiment Tips Experiment Requirements # -L 3-L fact Fact ors ors 4-L Fact ors Interacti ons Practices Orthogonal array and column assignments (Solutions are not necessarily unique) L-4, factors assigned to columns arbitrarily AxB L-4, factors A in col.,b in col. and interaction AxB in col L-8, factors cols.,, 4 & 6. Remaining columns left empty L-8, 4-L factor in col., -L factors in cols. 4, 5, 6 & L-8, 3-L factor in col., -L factors in cols. 4, 5, 6 & 7 as appropriate L-8, 3-L factor in col., -L factors in cols. 4, 5, 6 & 7 as appropriate AxB L-8, factor A in col., B in col. and interaction AxB in col. 3. Other -level factors in the remaining column AxB L-8, Factors A in col., B in col. and C in col. BxC AxB, BxC and CxA AxB, AxC and AxD AxB CxD Present but ignored. 4. Interactions AxB in col. 3 and BxC in col. 6 L-8, Factors A in col., B in col. and C in col. 4. Interactions AxB in col. 3, BxC in col. 6, and CxA in col. 5. L-8, Factors A in col., B in col., C in col. 4 and Din col. 7. Interactions AxB in col. 3 and AxC in col. 5 and AxD in col. 6 L-6, factor A in col., B in col. and int. AxB in col. 3. Factors C in col. 4, D in col. 8 and int. CxD in col.. L-, assign factors to columns arbitrarily L-6, assign factors to columns arbitrarily L-9, factors assigned arbitrarily L-9, Dummy treat columns for -level factors. Similarly hundreds of such common experiment designs can be conceived and proposed for everyday use by experimenters. A large set of such designs are available in the web site: R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

15 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page 5-5 REVIEW QUESTIONS 5-: experiments to suit the following experimental study objectives. Determine the appropriate INNER and OUTER arrays. a. Four -level factors and three -level noise factors. b. Five -level factors and three 3-level noise factors. c. Ten -level factors and five -level noise factors. 5-: Check the answers that most closely match yours, in the following situations. a. Why do we need to consider running multiple samples for each trial condition? Ans: To [ ] obtain better representative performance [ ] reduce trials [ ] reduce experimental error. b. While repeating experiments, what was the objective/purpose Taguchi wanted to satisfy? Ans: [ ] study more factors [ ] learn about noise factors [ ] design robustness. 5-3: Answer the following questions as they relate to projects you are involved in. a. What are noise factors? Give an example of noise factors related to a project you know of. What does robust design mean as applied to your project. b. Can averages be used to compare two data sets? Discuss the limitations. c. Why is MSD preferred as a better representative of a data set over the average? d. What are the advantages of transforming MSD to S/N ratio. e. If set A: has MSD = 5 and set B: has MSD = 6, Would S/N for set B: be higher than set A: 5-4: An L-6 OA was used to design an experiment to study fifteen -level factors. What is the degree of freedom of an error factor when: a.) Each trial condition is tested once. b.) Each trial condition is repeated 3 times and standard analysis is carried out. c.) Each trial condition is repeated 5 times and the S/N ratio of the result is used for analysis. 5-5: What does zero error term (f e = 0, S e = 0) mean? Check all appropriate boxes. a. ( ) It indicates a poorly run experiment. b. ( ) It represents a very well run experiment. c. ( ) It does not mean that there is no experimental error. It simply means that the information concerning error sum of squares can not be specifically determined. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

16 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page : What are noise factors? Check all appropriate boxes. a. ( ) Factors which influence the performance but cannot be controlled in field application/production. b. ( ) Factors that are difficult to control. c. ( ) Control factors which are not included in the experiment. d. ( ) Factors which have strong influence on the outcome. e. ( ) Environmental factors like temperature, humidity, etc., only. 5-7: A group of process engineers involved in a soldering process optimization study selected the following factors for investigation: 3 4-level factors -level factor 3 noise factors to be evaluated at -levels each For evaluation of performance, each soldered sample was to be evaluated by 4 separate criterion (solder overflow, flexibility, resistance and shape). Determine the following for the experiment: a.) OA for inner array b.) OA for outer array c.) Total number of samples required d.) Number of trial conditions e.) Number of repetitions f.) Total number of observations/evaluations g.) Evaluations per result 5-8: Compare S/N ratios of the following two sets of data and determine which set is more desirable. Consider the Target/nominal value =. SET :, 9,, 0 AND 9. SET : 0,, 8, 4 AND 6. Ans: Comparing the S/N ratios, Since > set is the desired set. (Please Show All Calculations) 5-9: In an experiment, the estimate of performance at optimum condition is expressed as S/N =.5. If the quality characteristic is "Bigger is Better", Determine the expected performance in terms of the measured value. R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

17 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page : [Concept: Outer array for Noise factors ] i) What is the smallest size of the outer array? Ans. ii) Which orthogonal array will you use to formally include five -level noise factors? Ans. iii) For an experiment designed using an L-6 inner array and L-9 outer array, how many samples will you need to complete the experiment? Ans. iv) An experiment was designed to study seven -level factors and three -level noise factors as shown below. Using descriptions of the control factors and the noise factors, determine the following items: (a) Describe the condition(levels) of the noise for the second sample in trial #. Ans. Toll Holder Coolant Operator (b) Calculate the average effect of Tool Holder type A. Ans. Noise Factors Level Level X: Operator Average Above average Y: Coolant Oil Water Base Z: Tool Holder Type A Type B Outer Array X Control Factors Noise Factors (X, Y, and Z) Y Z 3 4 L-8 A B C D E F G Trial\Col# Results Inner Array R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach

18 Module 5: Robust Strategies of Experiments Using Taguchi Approach Page [Concept: Analysis Using S/N Ratio ] Determine the performance at the optimum condition in terms of S/N ratio of the results when the quality characteristic is smaller is better. Trial\Column A B C Results S/N trial : MSD = ( ) / 4 = 3.5 S/N = - 0 Log (MSD) = - 0 Log(3.5) = trial : MSD = ( ) / 4 = S/N = trial 3: MSD = ( ) / 4 = S/N = -3.3 trial 4: MSD = ( ) / 4 = S/N = -9.6 _ Grand Average T = ( )/4 = A = ( )/ = A = ( )/ = -.4 B = ( )/ = -4.5 B = ( )/ = C = ( )/ = -.07 C = ( )/ = Optimum Condition : A B C Yopt = ( ) + ( ) + ( ) = = R. Roy/Nutek, Inc. All Rights Reserved of Experiments Using Taguchi Approach