The document discusses design of experiments (DOE) and Taguchi methods. It explains key concepts in Taguchi's approach such as quality robustness, quality loss function, and target specifications. Taguchi techniques use experimental design methods to identify important variables affecting a product or process and optimize the design. The document provides examples of full and fractional factorial experiments to study the effects of multiple factors and interactions. It emphasizes the importance of considering interactions between factors rather than just main effects.

1. Operations Management-II Dr. S.Venkataramanaiah Assistant Professor OM & QT Area IIM Indore, Pigdamber, Rau Indore- 453 331 Email : [email_address]

2. Design of Experiments (DOE) and Taguchi Methods

4. Taguchi’s View of Variation Traditional view is that quality within the LS and US is good and that the cost of quality outside this range is constant, where Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs. Tolerances are continuous, not yes/no Incremental Cost of Variability High Zero Lower Spec Target Spec Upper Spec Traditional View Incremental Cost of Variability High Zero Lower Spec Target Spec Upper Spec Taguchi’s View

9. Quality Loss Function and its distribution Low loss High loss Frequency Lower Target Upper Specification Loss (to producing organization, customer, and society) Quality Loss Function (a) Unacceptable Poor Fair Good Best Target-oriented quality yields more product in the “best” category Target-oriented quality brings products toward the target value Conformance-oriented quality keeps product within three standard deviations Distribution of specifications for product produced

20. DESIGN OF EXPERIMENTS (DOE)

30. EXAMPLE OF AN EXPERIMENT Studying the effect of two different hardening processes, oil quenching and salt water quenching on an aluminium alloy. OBJECTIVE: To determine the quenching solution that produces the maximum hardness. PROCEDURE: The experimenter decides to subject a number of alloy specimens to each quenching solution and measure the hardness of the specimens after quenching. The average hardness of the specimens treated in each quenching solution will be used to determine the best solution.

32. STATISTICAL DESIGN OF AN EXPERIMENT The process of planning the experiment so that appropriate data collected which shall be analyzed by statistical methods resulting in valid and objective conclusions. Two aspects of experimental problem: The design of the experiment The statistical analysis of the data

35. Blocking: Is a technique used to increase the precision of an experiment. A block is a portion of the experimental material that should be more homogeneous than the entire set of material. Blocking involves making comparisons among the conditions of interest in the experiment within each block. It is also a restriction on complete randomization. Three basic principles of design

45. FACTORIAL DESIGNS MAIN EFFECT : Change in response produced by a change in the level of the factor B A FIG. 1 FIG. 2 FIG 1 Avg. effect of A = [(40-20)+(52 –30)]/2 = 21 Avg. effect of B = [(52-40)+(30-20)]/2 = 11 B A L L H H . . . . 20 40 50 12 L L H H . . . . 20 40 30 52

46. INTERACTION EFFECT The difference in response between the levels of one factor is not the same at all levels of the other factors. At low level of ‘B’, the ‘A’ effect is : 50-20=30 At high level of ‘B’, the ‘A’ effect is : 12-40=-28 The avg. interaction effect ‘AB’ = (-28-30)/2 = -29 RESPONSE RESPONSE FACTOR A FACTOR A A1B1 A1B1 A1B2 A1B2 A2B2 A2B2 A2B1 A2B1 NO SIGNIFIANT INTERACTION SIGNIFIANT INTERACTION

47. INTERACTION EFFECT When interaction is maximum, then corresponding main effects have little practical meaning. However, the effect of A at different levels of factor B is significant Ex. Effect of A is : (50+12)/2-(20+40)/2= 1 may lead to a conclusion that A has no effect ( Is it correct?) Factor A has an effect and it depends on the level of factor B. Hence the knowledge about interaction between AB is more useful than main effects. The interaction effect of one factor (let A) with levels of other factors fixed to draw conclusions. Information on both can be studied by varying one at a time. The effect of changing factor A (B is fixed) is given by A + B - – A - B - B A L L H H . . . A - B - A + B - A + B + B A L L H H . . . . 20 40 50 12

50. H 0 : No significant difference If F 0 > F x,v1,v2 , reject H 0 abn-1 TOTAL MS E =SS E / ab(n-1) ab(n-1) SS E Error MS AB /MS E MS Ab =SS AB / (a-1)(b-1) (a-1)(b-1) SS AB AB MS B /MS E MS B =SS B /b-1 b-1 SS B B MS A /MS E MS A =SS A /a-1 a-1 SS A A F 0 Mean square Degrees of freedom Sum of squares Source of variation

51. TWO FACTOR EXPERIMENT : AN ILLUSTRATION Life Data (Hrs) for a battery Design T=3799 770 1291 1738 Ti 60 82 139 150 160 168 1501 342 104 96 583 120 174 576 110 138 3 45 58 115 106 126 159 1300 198 70 25 79 122 136 623 188 150 2 58 82 75 80 180 74 998 230 70 20 229 40 34 539 155 130 1 125 70 15 T j Temperature (A) Material Type (B)

53. ANOVA : Battery Life F 0.05, 4,27 = 2.73 F 0.05, 2,27 = 3.35 35 77646.97 Total 675.21 27 18230.75 Error 3.56 S 2403.44 4 9613.78 Interaction (AB) 7.91 S 5341.86 2 10683.72 Material Type (B) 28.97 S 19559.36 2 39118.72 Temperature (A) F O Mean Square Degrees of freedom Sum of Squares Source of variation

55. A SINGLE FACTORS EXPERIMENT (one-way ANOVA) FABRIC WEAR RESISTANCE DATA T… = 38.41 CF = T 2 /N SS TOTAL = SS FACTOR + SS E SS TOTAL = 1.93 2 + 2.38 2 +……+ 2.25 2 –(38.41) 2 /16 = 0.7639 SS FACTOR = (8.76 2 + 10.72 2 + 9.67 2 + 9.26 2 )/4 – CF = 0.5201 Col. Total 9.26 9.67 10.72 8.76 2.25 2.28 2.70 2.25 2.28 2.31 2.75 2.20 2.40 2.68 2.72 2.38 2.33 2.40 2.55 1.93 D C B A TYPE OF FABRIC

56. ANOVA : Fabric Wear Resistance F 0.05, 3,12 = 3.49 15 0.7639 Total 0.0203 12 0.2438 Within Fabrics (Error) 8.54 S 0.1734 3 0.5201 Between Fabrics F O MS df SS Source