Product and Process Improvement Through The Use of Taguchi Method (TM)

Transcription

1 Product and Process Improvement Through The Use of Taguchi Method (TM) Presented By Jafri Mohd. Rohani Department of Manufacturing and Industrial Engineering, Faculty of Mechanical Engineering Universiti Teknologi Malaysia April, 00

2 Objectives On completion of this module, the student will be able to : Describe Taguchi OA Experimental Design Define what is meant by factors & levels, and explain the notation used for Taguchi OA experimental design Explain main effects & interactions Set-up and analyze Taguchi OA experiment using Simple plots for mean and S/N

3 Module Content Key basic concept Quality Loss Function Experimental Designs Orthogonal Arrays & Linear Graph Analysis of Means & S/N Ratio Examples of Experimental Design Case Study

4 The key basic concept of Taguchi Approach: Why current mind-set needs to be changed? Goalpost mentality to stay within a customer s specification limits Doesn t encourage manufacturers to produce goods that are on target because the products that are close to the upper and lower specification limits are equal status to those with the desired target value Taguchi s approach is to produce goods with the least possible variation, with the goal of on target 00 % of the time, lead to more satisfied customers

5 What poor quality really means to society? Each time a poor-quality product is shipped, there is a loss imparted to society. Developed Quality Loss Function(QLF) Model The resulting graph of QLF model is parabola, with zero loss when the quality characteristics is equal to the target value Taguchi s approach is to strive for zero loss

6 How to produce high-quality goods? Taguchi approach emphasizes building quality into the design of products and their processes A product s designer needs to select those parameters that define the product and reduce variability in the performance The process of selecting a product s important parameters is called parameter design

7 Brief history of TM Japanese engineer who developed an interest in statistics and experimental design methods in the 950 s Methods used extensively in Japanese industry since 950 with great success Used initially for improvement of production processes Used later for improvement of product design

8 Taguchi s 7 Principles. The quality of a product can be quantified by the loss it imparts to society - Society, as well as the end user, is affected by quality of a product - Eg. If a product uses more energy than necessary, the ownership/running costs are higher for the customer. Quality improvement and cost reduction are necessary to survive - High quality, low cost likely to be the market leader - low quality, high cost no chance of survival

9 Taguchi s 7 principles 3. Continuous quality improvement programme should be based on reducing product/process variation -Every product/process has a target performance -The bigger the average variation, the less likely the performance will be acceptable and reliable

10 Taguchi s 7 Principles 4. Financial loss due to variation is approximately proportional to the square deviation from target -Loss(RM) = k(dev. From target)^ - Loss occurs even within specifications 5. Final quality and product cost are determined largely by design -When product has high variability, it acts in an unpredictable and unreliable manner. Good design leads to product and/or processes that are robust in the face of causes of variation.

11 Taguchi s 7 Principles 6. Performance variations can often be reduced by exploiting non-linear effects that some design factors have on performance 7. Statistically planned experiments to find factor values that minimizes variation in performance - Other methods include: One-factor at a time method, full factorial, trial-and-error, orthogonal array.

12 Quality Loss Function (QLF) Quality is the losses a product imparts to society. These include losses caused by functional variation from target. Quality should be measured quantitatively by some loss function Taguchi s loss function has uses:. To evaluate specification. To evaluate the impact of engineering improvements

13 Taguchi Notation - m : mid-value : manufacturing target where performance minimizes L(y) - L(y): Loss function : Total loss (RM) associated with performance y -? 0 : customer allowance : The limits m ±? 0 describe the products functional range as viewed by the customer -? : Manufacturer s allowance : The limits m ±? describe the manufacturer s tolerance range - A 0 : Society Loss : The total cost to customer when the performance characteristics exceeds the customer s tolerance tolerance limit m ±? 0 - A : manufacturer s Loss : The cost (RM) to manufacturer for repairing or scrapping a non-conforming product

14 Taguchi s Quadratic Loss Function L (y) = K (y m) - y : The performance characteristics - K : The loss parameter - m : The performance target

15 Expected Loss Functions, E[L(y)] - Expected Loss, E[L(y)]: The mean loss over many instances of the product. E[L(y)] = E[ K (y m) ] = K[var(y) + (µ m) ] = K(Mean Squared Deviation, MSD) MSD = S(yi m) / n Where n represents sample of n items

16 House of Quality ( Hauser & Clausing, 988)

17 Example QLF Suppose it costs RM 50 to fix the product that exceeds the customer tolerance limits. The customer tolerance limits for the high are:.5 ± 0.0 m. 0 products selected randomly and yield the following height:.53,.49,.5,.49,.48,.5,.54,.53,.5,.5. Question:. What is the loss function, L(y). Find the average loss per product per unit, E[L(y)]

18 Evaluating Impact of Improving the process - Suppose that the cost of improved process by reducing variability is estimated to be RM 5.50 / unit. Annual production = 0,000 units. 8 units are selected randomly from improved process and yields the following:.5,.5,.49,.5,.5,.5,.48,.5 Question:. Is the new process cost efficient?. If so, what is the annual savings?

19 Process Investigation Process Operation > Data > Information > Knowledge How to generate or collect data: statistical design How to extract the information contained in the data: statistical data analysis

20 Types of Data Acquisition Passive : Routine Operating Data Statistically Design of Experiments

21 Taguchi Strategy For the Design Process Design Process (Products and Processes) System Design Parameter Design Tolerance Design

22 Design Process: System Design - A conceptual stage in which scientific and engineering knowledge is used to select the appropriate technology to achieve the desired function - Taguchi offers nothing new here, system design requires know how, experience, etc.

23 Design Process: Parameter Design A stage where functional quality can be improved without extra cost through statistical designed experiments. It is the acts of selecting the nominals of the system and to find the combination of nominals that is robust despite this component variability. Tolerances should be kept as wide as possible at the parameter design stage

24 Design Process: Tolerance Design - A stage in which functional variability can be further reduced if parameter design hasn t achieved sufficient improvement. Tolerance design includes tightening up tolerances, upgrading materials, specifying better processes etc. and therefore involves extra cost. - System design and tolerance design are expensive and only parameter design offers the opportunity for improved quality and reduced cost. - We need an experimental methods to find out how design factors affect functional variation.

25 What is an experimental method or design of experiments(doe)? - DOE is a test or a series of test in which purposeful changes are made to the input variables of a process or system that we may observe and identify the reasons for changes in the output response (Montgomery, 99)

26 Attacking The Issue Through DOE approach Practical Problem: Eg. Too many auto accidents Convert to Statistical Problem: How can we improve that auto accidents (Y) are reduced to less than 0. % of cars per year? Y = Auto Accidents = f (X, X,, X n )

27 Converting the issue Convert from statistical problem to statistical solution: What do we know about the problem? Y = Auto Accidents = f (X, X,, X n ) What are the Xs? (eg. Speed, DUI) What are the specifications limits for the Xs? Use brainstorming session

28 Solving the issue Convert from statistical solution to practical solution Change spec. limits on key variables (speed limit; DUI) Implement controls to maintain variables (speed traps, jail terms)

29 Focus of DOE: Y = f (X) To get results, should we focus our behavior on the Y or X? Y Dependent Output Effect Symptom Monitor X.X n Independent Input-Process Cause Problem Control

30 The problem solving methodology Process Map C&E Diagram & FMEA Multi-Vari Studies Experimentation Control Plans/SPC +30 inputs All X s st Hit List Screened List Found Critical X s Controlling Critical X s

31 Types of Experimental Methods. One-Factor-at-a time(ofat). Full Factorial Design 3. Trial-and-error 4. Taguchi Method

32 DOE Notation -Output Response : A measured result of interest Factor : A variable being explicitly manipulated in an experiment

33 . OFAT To investigate several factors is to fix them all and change only one factor at a time The experimental plan would consist of ( + n) trials where n is the number of factors being investigated Eg. Suppose we want to investigate the effects of two factors, A and B, on a product or process and that each factor has two possible values low and high represented by and respectively.

34 OFAT Example Trials Factor A Factor B Output Response

35 OFAT Example What is the effect of Factor A? Effect of Factor A = What is the effect of Factor B? Effect of Factor B =

36 Weaknesses of OFAT strategy. Doesn t consider all possible permutations of A and B and the information gathered is therefore incomplete. Eg. The combination A, B isn t considered.. Factors effects are based upon results of a single trial instead of all trials and the information gathered is unreliable. 3. Doesn t take account of possible interactions between factors. We don t know what might happen if these factors were changed, not individually, but together.

37 Interactions Between Factors An interaction is present when the combined effect of two or more factors is bigger or smaller than the sum of their individual effects. It means that the factors are affecting each other as well as the product or process performance. Eg. Suppose we want to make a cup of sweet tea, adding sugar and stirring are two factors that affect the result. Stirring alone has no effect, adding sugar alone has some effect. Doing both has a big effect. Variability is reduced since the tea is uniformly sweet.

38 Comparison of Full Factorial vs. Taguchi OA # of Factors # of Level Total Runs # of Factors Taguchi OA Total runs L L L L L6 6

39 -Level Orthogonal Arrays(OA) and Linear Graph Each Factor is Varied Over Two Levels Also referred to as fractional factorial designs since they are the subsets from full factorials, and therefore, reduce the amount of experimental time and cost Useful designs for identifying key factors

40 L4 Orthogonal Array(OA) This designed is used for:. Evaluating two factors and their interaction, or. Evaluating three factors assuming there are no interaction

41 Linear Graph For L4 Taguchi uses linear graph with OA s to deal with interaction. These graphs show the assignment of factors to the column of OA and help us visualize interaction between factors. For two factors, use column 3 to represents the interaction between factors (column & )

42 L8 OA This design is used to evaluate 3 7 factors

43 Linear Graph for L8

44 Linear Graph for L8 Explaination The numbers refer to the seven column of L8 OA Columns represented by nodes (,,4) are purely for single factors Columns represented by lines between nodes (3,5 and 6) are where the -factor interaction effects between factors at the nodes will appear

45 L8 OA Example For example, the interaction between factors in column and will influence column 3. If that interaction is thought likely to be significant, then, no factor is assigned to column 3. Since the effect of the factor would be confused with that of the interaction. Column/node 7 is where the three-factor interaction effect between the factors at column, and 4 will appear. Fifth, sixth, and seventh single factors can be included when the twofactor interactions are not likely to be significant The L8 OA can be used for three factors with three significant interactions or seven factors with no significant interactions.

46 Rules for selecting Standard OA for -Level No of factors OA to be used L4 L8 L L6

47 Rules for selecting Standard OA for 3-Level No of factors OA to be used L4 L8 L L6

48 No of factors OA to be used - 4 L9 5-7 L7

49 Inner Array Definition Sometimes referred as design factors and controllable factors The factors in which the experimenter can or wants to control The factors that the design parameters need to be optimized

50 Outer Array Definition Sometimes referred as uncontrollable factors or noise factors The factors in which for various reasons cannot or will not be controlled, but, whose influence should be known

51 Signal-to-Noise(S/N) Ratio: Target is Best Response at the target value with reduced variation S/N = 0 Log 0 [y /s ] Where y = sample mean s = sample standard deviation of the output response variable, y

52 Signal-to-Noise(S/N) Ratio: Smaller is Better Reduced value of original response with reduced variation. Target value of zero Eg. Wear rate, fuel consumption S/N = -0 Log 0 [(/n ) S y ] Where n = number of replicates

53 Signal-to-Noise(S/N) Ratio: Larger is Better Increased value of original response with reduced variation Eg. Weld strength S/N = -0 Log 0 [(/n ) S (/ y ) ] Where n = number of replicates

54 Case Study Suppose an engineer is interested in studying the following factors in order to reduce the wear on a slider pump. The following -level factors were considered: Slider Material (A), Weight (B), Surface Roughness (C), Clearance (D), and Side Material (E). Interactions A X B and A X C were thought likely. The wear was measured (in µm) at eight points on the slider of the pump, the wear at each point being considered to be of equal importance. These eight measurement points were assumed to reflect the effect of noise factors. The experiment was carried out using L8 OA. Carry out necessary analysis for optimization of the factor settings.

55 L8 OA Experimental Results E D A X C C A X B B A Tr ial

56 Case Study Step : Select an appropriate S / N Ratio Step : Calculate S/N and X-bar(mean) for each control factor combination (Analyse by rows)

57 Case Study Trial Mean (µm) S/N (db)

58 Analysis of Means Factor A Factor B Factor C Factor D Factor E Level Level

59 Analysis of S/N Ratio Factor A Factor B Factor C Factor D Factor E Level Level

60 Plot Response Graph for Mean

61 Plot Response Graph For S/N Ratio

62 Calculate interaction effects A -way interaction between factors with - level gives four combination Eg. A x B Interaction, the 4 combinations are: AB, AB, AB, AB AB (mean) = ( )/ = 9.88 µm AB (S/N) = ( )/ = -.5 db

63 A x B Interaction effects for Mean Factor A: Level Factor A: Level Factor B : Level 9.88 Factor B : Level

64 A x B Interaction effects for S/N Factor A : Level Factor A : Level Factor B : Level -.5 Factor B : Level

65 Exercise: Calculate interaction effects for A x C

66 Plot Interaction effects for mean and S/N

67 Predicted Performance Predicted Outcome = Overall average experimental results + Respected Significant factor Settings Where the respected significant factor setting = average for that factor at that level overall experimental results If the trials confirm the predicted outcome, the experiment succeeds. If not, possible interactions have to be considered and catered for in a new experiment.