SIX SIGMA IMPROVE

Transcription

1 SIX SIGMA IMPROVE 1. For a simplex-lattice design the following formula or equation determines: A. The canonical formula for linear coefficients B. The portion of each polynomial in the experimental model C. The canonical coefficients for a cubic model D. The number of design points Correct Answer: D Justification: The last answer is the correct one. The formula is used to determine the number of design points in a simplex-lattice experiment. 2. Which answer correctly describes the experimental design below? A. Graeco-Latin Square B. Latin Square C. Randomized Complete Block D. Youden Square Correct Answer: A 1 Powered by POeT Solvers Limited.

2 Justification: The Latin Square design has each treatment appearing once and only once in each row and column. The Randomized Complete Block design place treatments randomly. The Youden Square design is an incomplete Latin Square. The design shown is a Graeco-Latin Square (also called Graeco-Roman). 3. An experiment was conducted on five different extruders of polymer, with readings from 4 die positions, marked A, B, C, and D. Each die position is unique for each extruder. There were 4 replications per die position. Each extruder had its own die, and the 4 positions were marked for testing. This is a type of: A. 5 4 factorial experiment B. Nested experiment C. Completely randomized experiment D. Fractional factorial experiment Correct Answer: B Justification: This design is not completely randomized and thus does not have all trials fully randomized (such as the die positions). It is not a true fractional factorial experiment. Since the die positions are not randomized during the experiment. This is a nested experiment. 4. A hyper-graeco-latin (4 4) design is constructed as follows: Carburetor Type Car I II III IV 1 AαMϕ BβNχ CγOψ DδPΩ 2 BδNΩ AγMψ DβP CαOϕ 3 CβOχ DαPϕ AδMΩ BγNψ 4 DγPψ CδOΩ BαNϕ AβM 2 Powered by POeT Solvers Limited.

3 Drivers Tires A, B, C, D M, N, O, P Days α,β,γ,δ Speeds ϕ,χ,ψ,ω Assume that car mileage is the output factor. If the above design were converted to a full factorial design, how many tests would be required for a full factorial? A. 256 B C D Correct Answer: D Justification: There are 6 factors at 4 levels. The total number of required tests would be: 4 6 = The following is an example of what type of response surface? A. Rising ridge B. Maximum or minimum C. Stationary ridge D. Minimax Correct Answer: A 3 Powered by POeT Solvers Limited.

4 Justification: The drawing is a two dimension example of a rising ridge response surface. 6. A fractional factorial design for 5 factors (A, B, C, D and E) at 2 levels (+, -) with 8 runs has been designed. In this design, the D and E factors were overlaid into a standard 2 level, 3 factor design. The design matrix has which effects confounded? Test A B C D E I. ABC is confounded with E II. AB is confounded with D III. AC is confounded with E IV. BC is confounded with D A. I and II only B. I and IV only C. II and III only D. II and IV only Justification: The overlaying of factors D and E resulted in the confounding of the AB interaction with D, and the confounding of AC with E. 4 Powered by POeT Solvers Limited.

5 7. When considering EVOP as a statistical tool: A. A change in the means indicates that we are using the wrong model B. An external estimate of the experiment error is necessary C. EVOP may be extended beyond the two level factorial case D. We are limited to one response variable at a time Justification: Answers A and B are filler. Refer to the EVOP diagram below: The above drawing depicts EVOP for two input variables and one response variable. However, EVOP may be extended to three or more input variables. More than one response may also be measured for EVOP trials. 8. Data from mixture experiments are gathered and analyzed through canonical polynomials. These polynomials are primarily defined as canonical because: A. The sum of the proportions must equal one B. The polynomials are different from regular regression equations C. The number of terms in the polynomial is (q+m-1)! / m!(q-1)! D. The terms in the polynomials have simple interpretations Correct Answer: A 5 Powered by POeT Solvers Limited.

6 Justification: All of the answers A, B, C, and D are true for canonical mixture polynomials. The term canonical is used to describe relationships that are correlated. The equations are correlated because the various proportions must sum to one. Thus, answer A is the best choice. A change in one polynomial affects the other; there is a lack of independence. 9. The term collinear refers to: A. Two linear variables B. A linear interaction C. Variables being a linear combination of one another D. Linear correlation Justification: Variables that are linear combinations of one another are collinear. This creates high correlation among the variables making analysis very suspect. 10. Experimental design can be effectively used to: I. Choose between alternatives II. Select key factors affecting a response III. Reduce variability of a process IV. Control uncontrollable noise factors A. I only B. II and III only C. I, II, and III only D. I, II, III, and IV Justification: Designed experimentation can affect the first three items well. It will not control uncontrollable noise factors. 6 Powered by POeT Solvers Limited.

7 11. When performing one experiment with five repetitions, what are the six experiments called? A. Randomization B. Replications C. Planned grouping D. Sequential Correct Answer: B Justification: Repeated trials or replications are often conducted to estimate the pure trial experimental error so that lack of fit may be evaluated. Randomization frees an experiment from the environment and other biases. Sequential experiments are conducted one after another, not all at the same time. Adjustments may be made in the experimentation based upon knowledge obtained. Almost any DOE contains planned grouping. 12. A L8 (2 7 ) design matrix is shown below. What statements are true of this experimental design? Column Number Run O O X O X X O Number Note: O means ok to use column X means use, but involved with interactions from other columns I. Use seven factors if no interactions are present II. Use with four factors, which will be confounded with 2-factor interactions 7 Powered by POeT Solvers Limited.

8 III. IV. Column 3 is suitable for use in a four-factor experiment The design will be saturated at seven factors A. I only B. II and III only C. I, II, and IV only D. I, II, III, and IV Justification: This is a fractional factorial design with 7 factors at 2 levels. Taguchi placed some restrictions on this design matrix. One precaution is to use seven factors only if no interactions are present. The design will be saturated since all of the information will go into the main effects. Another consideration is that four factor designs will have confounding with 2-factor interactions. Column 3 is not suitable for use for a main effect. Column 3 will be designated for an interaction term. 13. A Latin square design is noted for its straight forward analysis of interaction effects. This statement is: A. True in every case B. True sometimes, depending on the size of the square C. False in every case D. False except for Graeco-Latin squares Justification: Both Latin and Graeco Latin square designs are fractional factorials which will not allow an analysis of interaction effects. The interactions are confounded with the results of the main effects. 14. Plackett and Burman designs are used for screening experiments. There are geometric and non-geometric designs. It has been stated that runs of 12, 20, 24, 28, and 36 runs are non-geometric designs. This is because: A. The runs are in multiples of Powered by POeT Solvers Limited.

9 B. The non-geometric design has a 2-factor interactions confounded with main effects C. The geometric design runs are in powers of 2 D. A PB design of 12 runs can have 11 factors covered Justification: Answers B and D are true statements but don t answer the question. Answer A is a condition for all Plackett and Burman designs. The ability to distinguish a non-geometric design is that they are not in powers of The iterative approach to DOE refers to: A. The use of sequential experimentation B. Assuring the stability of the process during experimentation C. Assuring the capability of the measurement system D. Appropriate estimates of experimental error Correct Answer: A Justification: The iterative approach to DOE is the recognition that sequential experimentation will often yield more satisfactory results that one big experiment. Answers B, C, and D refer to traditional experimental assumptions, that must not be taken for granted (they should be checked). 16. Highly fractional factorial designs are often used as: A. Simplex designs B. Orthogonal designs C. Screening experiments D. Mixture experiments Justification: In screening experiments, highly fractional factorial designs are used to look for factor main effects only. They are called screening because they try to eliminate seemingly unimportant factors. 9 Powered by POeT Solvers Limited.

10 17. In a full factorial experimental design, factors A and B are both tested at 4 levels. How many experiments are conducted? A. 8 B. 9 C. 12 D. 16 Correct Answer: D Justification: This question requires knowledge of experimental design and an answer review. In a two factor test at four levels, the number of experiments is 4 2 = A randomized block experimental design is most like a: A. Higher order experiment B. Steepest ascent/descent experiment C. Taguchi robustness design D. A Latin or Graeco- Latin design Correct Answer: D Justification: Latin and Graeco-Latin designs are block designs. The other answers don t fit the question. 19. When comparing a Box-Behnken design with central composite designs, which of the following statements are FALSE? I. Box-Behnken designs require fewer runs for 3 factors than CC designs II. Box-Behnken designs require fewer runs for 2 and 5 factors than CC designs III. Box-Behnken designs require fewer factor levels than all CC designs A. I and II only B. I and III only C. II and III only D. I, II and III 10 Powered by POeT Solvers Limited.

11 Justification: Note that a negative question response is requested. Item I is a correct statement. Item II is not correct for two reasons: (1) The Box-Behnken doesn t exist for 2 factors and (2) versions of CC designs have fewer runs at 5 levels. Item III isn t correct because the CCF design also requires three factor levels the same as Box- Behnken. 20. How many of the following are considered response surface methodology designs? I. CCC II. CCCF III. CCI IV. Box-Behnken A. I and IV only B. I, II and III only C. I, III and IV only D. I, II, III, IV Correct Answer: D Justification: Items I, II and III are varieties of central composite designs. They and the Box-Behnken are all response surface methodology designs. 21. A lack of statistical knowledge on the experimenter s part could result in several items going wrong including: I. Confounding of undesired effects and interactions II. Experimental results corrupted by measurement error III. Inappropriate ranges of control variables IV. Misidentified control factors causing distorted results A. I only 11 Powered by POeT Solvers Limited.

12 B. II and III only C. I, II, and IV only D. I, II, III, and IV Correct Answer: D Justification: Unfortunately, all four items can lead to a bad experiment. Coleman and Montgomery (1993) list six items on the experimenter s part that can lead to bad results. The two missing items are: misunderstanding of the nature of interactions, and lack of appreciation of different levels of error. 22. For a mixture experiment, the design is expressed as {4, 5}. This implies: A. 5 trials of 4 components B. 4 proportions, 5 components C. 4 components, 6 proportions D. 4 sided cube, 5 points on the cube face Justification: The {4, 5} design implies 4 components and 6 proportions for the mixture. Note that the number of proportions equals m + 1, to include both 0 and Box-Wilson central composite designs (CCC and CCI) are rotatable designs. This implies: A. The points of the exterior star design can be moved around easily B. Star points are +/1 unit away from the center of the design space C. There is a consistent and stable variance about any star point D. The star points are units away from the center Justification: Answers B and D are fabricated distractors. Answer A is almost correct, but not quite so. They are rotatable designs because the variance is the same at all points that are the same distance from the design center. The variance will remain unchanged when the design is rotated around the center Powered by POeT Solvers Limited.

13 24. The market value of a house is to be determined by 2 input factors. The input factors are the square feet of living space and the number of bedrooms. If the input factors are highly correlated with each other, this could indicate that: I. A multicollinearity condition exists II. The variables are linear combinations of each other III. This is an intercorrelation of factors IV. One of the factors is redundant A. I only B. I and III only C. II, III, and IV only D. I, II and III and IV only Correct Answer: D Justification: All 4 answers are correct. A multicollinearity condition exists per definition. The variables will be linear combinations of each other, with intercorrelation. Because of the correlation, one of the variables provides the same information and is redundant. 25. A 3 3 Latin Square would have how many error degrees of freedom? A. Two B. Three C. Four D. Five Correct Answer: A Justification: For the 9 tests there will be two degrees of freedom for the error term. Source of variation Degrees of freedom Df Treatments p = 2 Rows p = 2 Columns p = 2 Error (p 2) (p 1) (3 2) (3 1) = 1 (2) = 2 total p p = Powered by POeT Solvers Limited.

14 26. Plackett and Burman designs are used for screening experiments. They are 2 level designs with run multiples of 4 instead of powers of 2. Certain designs with runs of 12, 20, 24, 28, and 36 are considered non-geometric, which means that: A. Each interaction effect is confounded with exactly one main effect B. They cannot be represented as cubes C. These are very economical designs D. They are used for screening experiments Correct Answer: B Justification: This question pertains to the issue of what makes a Plackett and Burman (PB) design non-geometric. The Plackett and Burman designs are used for screening experiments and are economical, so answers C and D are not unusual. PB geometric designs have each interaction effect confounded with exactly one main effect. Thus, answer B remains as correct. They cannot be represented as cubes. 27. Given the Simplex-Lattice matrix below, what would the proper form of the design variables: q and m? X1 X2 X A. {6, 3} B. {3, 2} C. {3, 4} D. {2, 3} Correct Answer: B 14 Powered by POeT Solvers Limited.

15 Justification: For the design matrix, the form should be {q, m}. q is the number of component or factors in the blend. The m stands for the proportions at 0.5 or 1.0. The number of equally spaced levels will be m+1, to make the levels at 0, 0.5, A designed experiment is to be conducted with four factors at three levels. The factors and levels will be randomized and as uniform as possible. This design is termed: A. A one-way ANOVA design B. A completely randomized design C. A two-way ANOVA design D. A Latin square Correct Answer: B Justification: The one-way ANOVA and two-way ANOVA are methods of analyzing designs when one or two factors are to be tested. A Latin square is a more restricted design form. The completely randomized design is the correct answer. 29. Most modern computer programs will perform an analysis of experimental residuals. What other techniques can be employed? I. Control Charts II. Histograms III. Normal probability plots IV. Dot plots A. I and II only B. II, III and IV only C. II and IV only D. I, II, III and IV Correct Answer: B Justification: Control charts aren t applicable for this situation. Normal probability and dot plots are widely used. Histograms can be used in some cases Powered by POeT Solvers Limited.

16 30. A four factor, three level experiment must be conducted. What are the fewest number of trials possible if all interactions are ignored? A. 9 B. 18 C. 27 D. 81 Correct Answer: A Justification: A full factorial design requires (3) 4 or 81 experiments. A one-third fractional factorial design (properly chosen) can have main effects independent of two factor interactions, and at least 3 independent 3 factor interactions. A one-ninth fractional factorial experiment can analyze main effects only (but they are confounded with 2 factor interactions). 31. A fractional factorial experiment is to be conducted. The main effects will not be confounded with the two factor interactions. But two factor interactions may be confounded with other two factor interactions. The design resolution is: A. Resolution II B. Resolution III C. Resolution IV D. Resolution V Justification: This is a resolution IV design. See the CSSBB Primer definitions on VIII Taguchi describes noise as a nuisance factor that is difficult, impossible, or expensive to control. Types of noise include: I. Outer noise II. Inner noise III. Within product noise IV. Between product noise 16 Powered by POeT Solvers Limited.

17 A. I and II only B. II and III only C. I, II, and IV only D. I, II, III, and IV only Justification: Taguchi describes 3 types of noise: outer noise, inner noise, and between product noise. Outer noise is variation in operating environments and human errors. Inner noise is the aging of the machine, deterioration, and tolerances. Between product noise is manufacturing imperfection. There is no description for within product noise. 33. To state that a model in an experimental design is fixed indicates that: A. The levels used for each factor are the only ones of interest B. The levels were chosen from a fixed population C. The equipment from which the data are collected must not be moved D. The factors under consideration are qualitative Correct Answer: A Justification: Answers B, C and D are all filler answers. In fact, if you selected C as your choice, seriously consider taking the CSSBB exam at a later date. Experimental design levels are established (or fixed) based on the best advice of people knowledgeable of the process. A balance design is then considered only at those levels. Based upon analysis, factors may then be adjusted to other fixed levels for subsequent experimentation. The objective is to achieve optimum performance. 34. Residuals are estimates of experimental error obtained by subtracting the predicted responses from the observed responses. The residuals should be checked for behavior. This can be accomplished by which of the following methods? A. Applying a statistical test such as a t test B. Using a normal probability plot C. Using a box-and-whiskers box chart D. Comparing the Xs to the Ys 17 Powered by POeT Solvers Limited.

18 Correct Answer: B Justification: Answers A and C are not generally used to check residuals. Answer D is definitely not the correct choice. A normal probability plot of the residuals can be used to check the normality of the residuals. In addition, histograms and dot plots are commonly used. 35. The following Latin Square design of gas mileage by 5 drivers (A, B, C, D, & E) with 5 different carburetors. The proposed Latin Square design lacks what requirement? Carburetor Type Car I II III IV V 1 A B C D E 2 B A D E A 3 C D A A B 4 D E A B C 5 E A B C D A. The car versus carburetor interaction B. A balanced model involving all factors C. The car and driver interaction D. The inner matrix of Greek letters Correct Answer: B Justification: No interactions among factors are possible with Latin square designs. The inner matrix of letters does not have to be Greek. A Latin Square must have an equal number of runs or tests on all factors. Notice that the Drivers do not have an equal number tested Powered by POeT Solvers Limited.

19 36. As the new experimenter for Six Sigma projects, you have allocated budget funds for preliminary trial runs. The reason(s) for this would be: I. Some practice trials are needed, since this has not been done before II. The plant manager wants evidence that experimentation will work III. Planning is critical for success IV. The financial manager wants evidence of possible success A. I only B. II and III only C. I, II, and IV only D. I, II, III, and IV Correct Answer: A Justification: Some of the item options have a grain of truth to them. However, the best answer is that most experiments are new to plant operating personnel. Some practice may be needed. As an additional observation, sufficient funds should be available to do the following: trial runs, actual runs, and verification runs. 37. A simplex design approach is being used to determine the steepest ascent path for a design that involves three independent variables. An initial experiment would require how many runs? A. 3 B. 4 C. 5 D. 6 Correct Answer: B Justification: Whether using a straight or modified simplex, under the conditions of the question, one more run, than the number of independent factors, will be required. Therefore, = Which of the following is the best description of randomization? 19 Powered by POeT Solvers Limited.

20 A. A means of assuring parallel experimentation B. A technique used to increase the validity of an experiment C. The repetition of an observation or measurement D. The relationship between two or more variables Correct Answer: B Justification: This is basically a definition question and requires familiarity with experimental design terms. Answer A is filler. Answer C is a definition or replication or repeated trials in an experiment. Answer D could represent correlation analysis or a simple two factor experimental design. Answer B is the best choice. Randomization enhances the precision and validity or an experiment by freeing the experiment from biases and the environment. 39. In a mixture experiment, the independent factors are blended into the end product. All of the following are proper mixtures of three components EXCEPT for: A. 0.33, 0.33, 0.33 B. 1.0, 0, 0 C. 0.50, 0, 0.50 D. 0.25, 0.25, 0.25 Correct Answer: D Justification: Note that a negative response is requested. The blending of the factors is in proportions from 0 to 1.0. The total must equal For the analysis of response surfaces, one special design is a cube with eight points, supplemented with a 2 3 factorial. The points are on each axis. These axis points are at a radius equal to the vertex. There are 15 points (including the center point). This design is termed: A. Central Composite design B. Box-Behnken design C. Response surface method D. EVOP 20 Powered by POeT Solvers Limited.

21 Correct Answer: A Justification: The type of response surface is what we want to know, so answer C is not correct. EVOP does not fit the question description. A Box-Behnken design does not contain an embedded factorial matrix, mentioned in the question. The central composite design consists of cube with a factorial design of points inside it. 41. If confounding occurs in a three factor experiment (A, B and C) conducted at two levels, one would expect that factor A would be confounded with: A. Factor B B. Factor C C. The BC interaction D. Either the AB or AC interaction Justification: Surely no experimenter would be stupid enough to confound one main effect with another main effect (Answers A and B are eliminated). For ½ fractional experiments, the main effect of interest (A in this case) is usually confounded with the interaction of the other two factors. 42. Many experimental design authors suggest the use of control runs. These control runs can include tests at the standard process set points. The conduct of a test with the center points as set points would most clearly imply or suggest: A. Use of a central composite design B. Use of a simplex-lattice design C. Use of a response surface method D. Use of a full factorial design Correct Answer: A Justification: A simplex-lattice design involves a mixture design. A response surface method is looking at the contours of the response. The full factorial design is a possible application but is not the most likely answer. A central composite design includes the center points of the operating process. If the factors are set at the limits of the existing set points, then the center points are the existing set points Powered by POeT Solvers Limited.

22 43. The term level in experimental design refers to: A. The complexity of the design B. The specific settings of input factors C. The number of output responses D. The number of independent trials or tests Correct Answer: B Justification: The term level most often refers to the different settings of an input factor. The other answer choices are meant to be distractors. 44. Randomized block designs are best suited for: A. Screening objectives B. Comparative objectives C. Response surface objectives D. Regression model objectives Correct Answer: B Justification: Randomized block designs are ideal for comparative experimental testing of 2 or more factors. Full or fractional factorial designs (including Plackett-Burman) are best for screening objectives. Response surface objectives require central composite or Box-Behnken designs. 45. The linear graphs which accompany Taguchi designs have as their objectives: I. Providing a compact design layout II. Providing a visualization of the design options III. Depicting where main factors can be assigned IV. Depicting where interactions may be evaluated A. II only B. I, II and III only C. II, III and IV only 22 Powered by POeT Solvers Limited.

23 D. I, II, III, IV Justification: The best inclusive answer choice is item II. However, items III and IV are major components of II and are certainly true statements. Item I is a debatable choice and should be eliminated in the question writer s opinion. 46. Experimental design plans usually call for testing a number of factors and keeping all other conditions as nearly constant as possible. Taguchi Methods call for similar techniques, but with a twist. Noise conditions are changed a bit to determine robustness. Where are the noise factors placed? A. Control array B. Inner array C. Outer array D. Quadratic array Justification: There are no arrays termed control or quadratic. The inner array consists of the controllable factors, while the outer array consists of the noise factors. The noise factors are themselves tweaked to simulate different conditions. 47. In examining the residuals of an experiment, one would expect to see all of the following results, EXCEPT? A. Some residuals higher than predicted B. Some residuals lower than expected C. Some residuals exhibiting correlation D. A consistent amount of error across the test range Justification: Except for answer C, the other answers are correct. Residuals should be normally and independently distributed with a mean of 0 and a constant variance. There should not be a correlation of residuals Powered by POeT Solvers Limited.

24 48. If an experimental design objective is to model a response as a mathematical function of a few continuous factors, then the design objective can be described as: A. An optimal fitting of a regression model B. A screening objective C. A response surface objective D. A comparative objective Correct Answer: A Justification: For experiments, a comparative objective is to determine if a factor is significant. A screening objective is to sort out the lesser factors. A response surface objective is to find the shape of the response geometry. The optimal fitting of a regression model fits the factors to a response model. 49. The following experimental design model presented below is described as a second-order model. The model has these characteristics: I. Curvature is present in the model II. An interaction of factors is shown III. Error is present in the model A. I only B. II and III only C. I and III only D. I, II and III Correct Answer: D Justification: All of the above items are present in the design model. 50. A Latin square design is an experimental design which: A. Cannot be used when estimation of the interaction effects is desired B. Affords a good estimate of interaction effects C. May not permit all treatments in every block 24 Powered by POeT Solvers Limited.

25 D. May require the need to estimate the parameters during the experimentation Correct Answer: A Justification: Answer D is filler. Answer B and C are incorrect statements. A Latin square design is essentially a fractional factorial experiment which requires less experimentation to determine main treatment results. However, like other fractional factorials, the interaction effects are confounded with main effects and cannot be estimated. One of the assumptions in a Latin Square experiment is that there are no row, column or factor interactions. 51. An experiment was conducted to determine the effectiveness of a new and improved feed for hogs. The exact amount (x) of feed was measured and the change in weight of the hogs become the response variable. If it was determined that the initial weight of the hogs was correlated to the weight gained, then the initial weight of the test hog could be termed: A. Covariate B. Collinear C. Confounding D. Interacting effect Correct Answer: A Justification: Two variables are collinear if they are totally correlated. It should be obvious that there is some correlation of weight gain to initial weight. But this is not the best answer choice. The initial weight of the hogs could be termed a covariant, since it is related to weight gain. The heavier the initial weight of hogs, the more weight they gain. 52. The repeated trials in a designed experiment allow for: A. First order modeling B. Determination of experimental error C. Nested experimentation D. The resolution of main effects Correct Answer: B 25 Powered by POeT Solvers Limited.

26 Justification: Repeated trials allow for determination of experimental error. 53. Any experimental equation that shows two factors multiplied by each other can indicate: I. A slope II. A twist III. A curve IV. An interaction A. I and II only B. II and III only C. I and III only D. II, III and IV only Correct Answer: D Justification: Multiplied factors represent interactions, which graphically become curves or twists in the response surface. 54. A Taguchi L9 design consists of: I. 9 design runs II. 3 factor levels III. 4 input factors A. I only B. I and II only C. II and III only D. I, II and III Correct Answer: D Justification: All of the answers are correct Powered by POeT Solvers Limited.

27 55. In a full factorial experiment with 4 factors at 3 levels each, how many trials are required? A. 24 B. 12 C. 64 D. 81 Correct Answer: D Justification: For a full factorial, the number of trials required is equal to the number of levels raised to the number of factors. For this problem, 3 raised to the 4 th power is 81 trials. 56. An experiment is being run with 8 factors. Two of the factors are temperature and pressure. The levels for temperature are 25, 50 and 75. The levels for pressure are 14, 28, 42 and 56. How many degrees of freedom are required for this experiment to determine the effect of the interaction between temperature and pressure? A. 1 B. 2 C. 4 D. 6 Correct Answer: D Justification: When experimenting, 1 degree of freedom is required to compute the overall mean, and n-1 degrees of freedom are required for each factor, where n is the number of levels for the factor. The degrees of freedom required for interactions are the product of the interactions for the factors involved in the interactions. For this problem, temperature has 3 levels and pressure has 4 levels. The interaction requires (3 1) (4 1) = 6 degrees of freedom. 57. Taguchi methodology seeks to reduce the loss to society by: I. Reducing variation in the process 27 Powered by POeT Solvers Limited.

28 II. III. IV. Reducing variation in the product Utilizing Shingo techniques Improving the product development process for reduced variation A. I only B. II and III only C. I, II and IV only D. I, II, III and IV Justification: All of the above items are suitable Taguchi methods except for item III. Shingo techniques are the basis of Lean Manufacturing. Variation reduction is the key to better quality. A better product development process will provide a robust design. It has been stated that 80% of the manufacturing costs are determined by product design decisions. 58. The following design equation: y = b 0 + b 1 x 1 + b 2 x 2 + Σ I. Is a quadratic equation II. Is a first order equation III. Accounts for no curvature IV. Has an interaction A. I only B. II and III only C. I and III only D. I, II, III, and IV Correct Answer: B Justification: The equation does not have any factors raised to the second power or beyond. Therefore, it has no interactions. Thus, it is a first order equation. The lack of second order factors also indicates a lack of curvature in the design data Powered by POeT Solvers Limited.

29 59. A 3 2 experiment means that we are considering: A. Two levels of three factors B. Two dependent variables and three independent variables C. Two go/no-go variables and three continuous variables D. Three levels of two factors Correct Answer: D Justification: As a mnemonic device (memory aid) the author uses this: levels are low, while factors fly. There are three levels of two factors or two factors at three levels. A total of nine experiments would be conducted. 60. Which of the following design runs are possible for a three factor simplex-lattice design? I , 0, 1 II. 1, 0, 0 III. 0.5, 0.5, 0.5 IV , 0.667, 0 A. I and II only B. I and III only C. II and IV only D. II, III and IV only Justification: The three mixture components must add to 1.0 (100%). Therefore, only items II and IV are possibilities. 61. Good planning and execution of an experimental design is essential for success. Which of the following steps is out of sequence? 1. Select an experimental design 29 Powered by POeT Solvers Limited.

30 2. Set objectives 3. Select process variables 4. Execute the design 5. Verify the data 6. Analyze and interpret the results 7. Present the results A. Select an experimental design B. Set objectives C. Verify the data D. Select process variables Correct Answer: A Justification: The NIST (2001) Engineering Statistics Handbook shows that the selection of an experimental design will be step 3. That is the step that is out of sequence. 62. From the following experiment yield plot, what can we ascertain was being tested? A. A two component full factorial design B. A two component fractional factorial design C. A two component mixture design 30 Powered by POeT Solvers Limited.

31 D. A two component steepest ascent design Justification: Note that the scaling for the two components (as a proportion) totals 1.0 in all cases. The plot represents the results of a two component mixture experiment. 63. An incomplete block design may be especially suitable when: A. There is missing data B. There is need for fractional replication C. It may not be possible to apply all treatments in every block D. There is need to estimate the parameters during the experimentation Justification: Answers B and D are incorrect statements. An experiment is designed to collect all necessary data. The design should not be altered based on whether some data was missing. Thus, answer A is inappropriate. In block designs, some combination of factors and levels (treatments) may not be possible or desirable. These block designs may be balanced or partially balanced. Consider an experiment to be conducted over four days (blocks) evaluating four competing formulas (treatments). All formulas must be processed through a furnace which can only accommodate three tests per day. The following balanced incomplete block design could be used: BLOCKS TREATMENTS (DAYS) A B C D 1 X X X 2 X X X 3 X X X 4 X X X 31 Powered by POeT Solvers Limited.

32 64. EVOP should be used: A. When there is a manufacturing problem B. When a process is not in statistical control C. When an experimenter first begins working on a new product D. When a process is producing satisfactory material Correct Answer: D Justification: Most manufacturing problems should not be addressed by EVOP. EVOP is used at the end of experimentation when the process essentially has statistical control. EVOP trials are conducted in the near vicinity of an already satisfactory process. 65. Which of the following is NOT true in regards to blocking? I. A block is a dummy factor which doesn t interact with real factors II. A blocking factor has 2 levels III. A block is a subdivision of the experiment IV. Blocks are used to compensate when production processes restrict randomization of runs A. I only B. II only C. I, II and III only D. II and IV only Correct Answer: B Justification: Blocking is used to compensate when production processes restrict randomization of runs. For example, assume an experimental factor is temperature, and is set at 3 levels. If it is very difficult to move the temperature between the 3 levels, the experiment could be blocked into 3 groups, low temperature, medium temperature and high temperature. Each block of trials would be run together. To compensate for not running the trials in random order, the block is a dummy variable. A dummy variable can 32 Powered by POeT Solvers Limited.

33 have as many levels as desired. A block can be a subdivision of an experiment. The question is seeking an incorrect choice, which is item II. 66. In the Taguchi design methodology, what are noise factors? A. Factors that strongly influence the mean response B. Factors that impact tolerance design C. Factors that maximize parameter design D. Factors that influence variation in the output Correct Answer: D Justification: Taguchi referred to signal factors as those factors that strongly influence the output response and noise factors as those factors that influence variation in the output response. 67. Central composite designs are one of the classes of response surface designs. They are popular because: I. Sequential runs of linear or curvature effects (if needed) can be made II. They provide much information from a minimum of runs III. They require only one set of runs for superior results IV. They are quite flexible over different experimental regions A. I only B. II and III only C. I, II, and IV only D. I, II, III, and IV Justification: According to Verseput (2001) the only item not meeting the properties of the central composite design would be item III. No one claims to have a design that produces superior results with only one run. All of the other items constitute desirable properties of a central composite design Powered by POeT Solvers Limited.

34 68. If five or more factors are under consideration and the experimenter s objective is to construct a design response surface, what is the appropriate first action step? A. Screen the list down to 2 4 factors B. Select a fractional factorial design C. Select an appropriate Box-Behnken design D. Choose a form of central composite design Correct Answer: A Justification: Ultimately the experimenter wants to conduct a Box-Behnken or central composite design. However, there are presently too many factors. First, a screening design must be conducted. 69. An experiment is to be conducted; you have requested that a statistics professor develop a design for you. From a practical viewpoint, you should review the design because: I. The professor may have limited plant knowledge II. There may be undesirable combinations of variable control levels III. The design may cause a violation of known physical laws A. I only B. I and II only C. II and III only D. I, II and III Correct Answer: D Justification: The professor can provide the design but you and the plant personnel will be conducting the experiment. Montgomery & Coleman (1993) provide a list of items that the statistician may be lacking. These items include: 1) Unwarranted assumptions of the process, 2) Undesirable combinations of the factors, 3) Violation of known laws of physics, 34 Powered by POeT Solvers Limited.

35 4) Too large or small design sizes, 5) Inappropriate confounding, 6) Imprecise measurement, 7) Unacceptable prediction error, and 8) Undesirable run order. 70. When selecting and scaling the process input variables for an experiment, what is NOT a desirable approach? A. Include as many important factors as possible B. Set factor levels at practical or possible levels C. Combine process measurement responses when possible D. Be bold, but not foolish, in selecting high and low factor levels Justification: Note that a negative answer response is requested. Answer C is not a good idea. If two or more measurement responses are combined, then the important factor (between them) may remain hidden. The other options (A, B and D) are valid, prudent actions. 71. An experimental design using a Latin Square of 3 factors and 5 levels will be able to determine which of the following? A. Main treatment effects and interactions B. Interactions only C. Column and row effects D. Main treatment effects Correct Answer: D Justification: A Latin Square design is a fractional factorial experiment. There are not expected to be any interactions, since they cannot be measured. Only the main effects will be determined Powered by POeT Solvers Limited.

36 72. The main objection to designed experimentation in an industrial environment is: A. Obtaining more information for less cost than can be obtained by traditional experimentation B. Getting excessive scrap as a result of choosing factor levels that are too extreme C. Verifying that one factor at a time is a most economical way to proceed D. Obtaining data and then deciding what to do with it Correct Answer: B Justification: Note that the key words are main objection, not objective. Answers C and D are filler. Answer A is the objective of designed experimentation. One main objection to designed experimentation is the chance of getting excessive scrap because of extreme factor levels. Other objections are: the chance of getting scrap from combinations that are a necessary part of the design, machine delays to take samples and ignorance of the whole experimental process (see the CSSBB Section VIII, cover quote by Nelson). 73. Which of the following is a correct statement? A. Variables are confounded if they are difficult to study B. Two or more variables are confounded if their effects cannot be separated given the experimental data C. Variables are confounded if they form a linear combination D. Two or more variables are confounded if they produce the same effects Correct Answer: B Justification: Variables are confounded when the effects of two or more factors are not separable. 74. A basic L4 Taguchi design is the same as: A. A two factor, two level, full factorial B. A two factor, two level, ½ fractional factorial C. A three factor, two level, full factorial 36 Powered by POeT Solvers Limited.

37 D. A test of a single variable at 4 levels Correct Answer: A Justification: This is a knowledge based question. The closest answer is choice A. In application, the L4 is regarded as a two factor, two level design with full treatment of the interaction. It has the same arrangement, however, as a design that would be used as a three factor, two level, ½ fractional factorial experiment. 75. Evolutionary Operation (EVOP) is being considered at your plant. You present these arguments for its use: I. EVOP is a conservative strategy for improvement II. Product runs will be conducted with very little scrap III. For any one series of tests only a few variables are changed IV. The runs and analysis can be conducted by production operators A. I only B. II and III only C. I, II, and IV only D. I, II, III, and IV Correct Answer: D Justification: EVOP is the sum of all of the above according to Box, Hunter, and Hunter. 76. If a sample space contains several unknown minimax areas, then what can happen using steepest ascent methodology? A. Many tests may be required B. The yield contours must be ignored C. The design area around point p must be expanded D. A wrong answer can result Correct Answer: D 37 Powered by POeT Solvers Limited.

38 Justification: If the initial experiment did not detect the possibility of several maximum peaks (or valleys) then there is a distinct possibility that a lower than optimum result can occur. 77. A Box-Behnken experimental design is an independent quadratic design. The endpoints of the design are not used for testing. The Box-Behnken design possesses which of the following features? I. It requires 3 levels for each factor II. It is a rotatable design III. It always requires fewer runs than other central composite designs A. I and II only B. II and III only C. I and III only D. I, II and III Correct Answer: A Justification: The Box-Behnken designs require 3 levels for each factor and are rotatable designs. They do not always require fewer runs than other central composite designs. Central composite designs require fewer treatments when the factors are equal to or greater than Which of the following DOE definitions is NOT correct? A. A block is defined as a group of treatments and levels that indicates the total number of experiments required B. Replication is defined as the additional experiments needed to increase the accuracy of a measurement C. A factor is defined as one of the variables whose influence is being studied in the experiment D. Treatments can be defined as the levels assigned to each factor during an experimental run Correct Answer: B 38 Powered by POeT Solvers Limited.

39 Justification: This question requires knowledge of experimental design. A negative response is requested. All answers are correct with the exception of B. It is true that taking the average of repeated measurements in metrology will often yield a truer actual reading (according to the central limit theorem). However, replication in experimental design is used to estimate the pure trial-to-trial experimental error so that further analysis of the experimental results can be made. 79. For a full factorial CCC design for four factors, what is the α value? A B C D Justification: This question requires a calculation. For a full factorial design, the formula is: Where, k = the number of factors. α = [2 k ] 1/4 α = [2 4 ] 1/4 α = [16] 1/4 = For five factors, answer D would be the closest selection. For three factors, answer B is correct. 80. In the following Simplex-Lattice design, what is the proportion of component X3 at the indicated test location? 39 Powered by POeT Solvers Limited.

40 A B C D Correct Answer: D Justification: The location is the middle of the Simplex-Lattice design with ingredients set at for each component, X 1, X 2 and X Sensitivity in experimentation is: A. Getting the true result B. Extreme care in data analysis C. Using the best measuring device D. Ability to distinguish significant treatment differences in the response variable Correct Answer: D Justification: Answer A is the goal of experimentation. Answers B and C reduce the error of experimentation. Sensitivity is the ability to distinguish differences in the response (output) variable or variables. 82. Experiments can have many different objectives. Which of the following would be included in the options? I. Comparative objective II. Screening objective III. Optimized mixture proportions objective 40 Powered by POeT Solvers Limited.

41 IV. Response surface determination A. I, II and III only B. II and III only C. I, III and IV only D. I, II, III and IV Correct Answer: D Justification: All of the items (I IV) are valid goals. They can all be legitimate design objectives. 83. Taguchi methods use a linear graph to help interpret the corresponding orthogonal array. For instance, for a L4 array, a linear graph with factors 1 and 2 at the endpoints, and factor 3 at the midpoint indicates: A. Factor 3 is the interaction of factors 1 and 2 B. That factor 4 is missing, since it is a L4 C. The main factors (1 and 3) are interactions D. Factor 2 will be the experiment result Correct Answer: A Justification: In the interpretation of the linear graph, the endpoints of the graph indicate the main effects, while the midpoint indicates the resulting interaction term. An interaction term is possible if the specified column in the design matrix is used. 84. Taguchi designs have as objectives which of the following alternatives? I. Reduce the quality loss to society II. Use a development strategy to intentionally reduce variation III. Identify and develop a parameter that will improve a performance characteristic IV. Identify a less expensive design material or method that provides equivalent or better performance 41 Powered by POeT Solvers Limited.