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applied statistics and probability for engineers

Questions and Answers of Applied Statistics And Probability For Engineers

=+45. In an experiment to assess the effects of curing time (factor A) and type of mix (factor B) on the compressive strength of concrete cylinders, three
=+b. Using 5 .01, test to see whether either factor or their interaction is significant. Describe your conclusions from these tests.
=+44. The following data was used to investigate whether the compressive strength of concrete depends on the type of capping material used or on type of curing method used. The numbers in the matrix
=+d. If the objective of the study is to maximize percent protection, what setting of each factor do you recommend?
=+c. Create an effects plot for the important effects identified in part (b).
=+b. Suppose that additional experimentation shows that only those effects whose magnitudes exceed 15 are important. Which factors or interactions have a significant effect on percent protection?
=+a. Calculate estimates of the various effects.
=+43. Exercise 39 described a half-fraction of a factorial experiment in which the Nitsch’s trace elements factor was aliased with the highest-order interaction term. The response variable,
=+d. Create a normal probability plot for the effects determined in part (b) and identify any effects that appear to be important.
=+solutions. These factors were pH (2 versus 4), temperature (25°C and 85°C), neutralizing agents[15% (W/W) MgO and 25% (W/W) CaCO3], Fe/Ni ratio (6 versus 18), and stirring speed (200 and 500
=+42. Lateritic nickel ore deposits are an important source of nickel. Atmospheric acid leaching (AL)has grown in popularity as a method to extract nickel from such deposits. In the AL process, a
=+f. If the objective of the study is to minimize the variation in plating thickness, what setting of each factor do you recommend?
=+e. From the results in part (d), which factors have a significant effect on plating thickness variation?
=+d. Assuming that the AB interaction is negligible, use this information to obtain an estimate of SSE and perform hypothesis tests for both main effects. (Use 5 .05.)
=+c. Calculate estimates of the effects for this experiment.
=+b. Determine the alias structure of this design.
=+a. Find k and p for this 2k2p design.
=+for lead seal .4572 .5588 twall Wall thickness of package .030 .050 The design matrix for the study was Run s wlead hlead rport twall 1 L L L L L 2 L L L H H 3 L L H L H 4 L L H H L 5 L H L L H 6 L
=+s Half the distance between neighboring leads .025 .35 wlead Horizontal width of lead .010 .020 hlead Distance from package base to center of lead .127 .381 rport Radius of port in package
=+Technique for Stress Analysis of Glass-to-Metal Lead Seals,” J. of Electronic Packaging, 1994: 98–104):Low High level level Factor Description (L, in.) (H, in.)
=+40. Metal “leads” that protrude from electronic components often have their bases sealed with glass to protect against moisture ingress. Fractures in the glass can be caused by bending or
=+c. Suppose that it is reasonable to assume that all interactions consisting of three or more factors are negligible. In this case, will any of the estimates of the remaining effects be aliased
=+b. Determine the alias structure of the design.
=+a. What are k and p for this 2k2p design?
=+Microbiol., 2012: 126–134). The variables studied were temperature (at 65°C and 75°C), pH (at 7 and 8), tryptone (at 5 and 10 g/L), yeast extract (at 5 and 10 g/L), and Nitsch’s trace
=+39. A fractional factorial experiment with 16 test runs was conducted to determine the effects of several factors on the antioxidant capacity in carotenoid extracts of the bacterium Thermus
=+b. Write down the alias structure for this design.
=+a. How many experimental runs (assuming no replications) must be conducted?
=+37. Using the design generators I 5 ABCD and I 5 ACE, verify all the entries in the alias structure of the 2522 design of Example 10.14.38. A quarter-fraction of a 27 experiment (factors A, B, . .
=+b. By multiplying the appropriate columns in the design matrix from part (a), show that AB and CD contrasts are identical.
=+a. Fill in the columns of the design matrix for this fractional factorial design.
=+35. Fill in all the columns in the design matrix for the 2522 design of Example 10.12.36. A 2421 design is specified by setting D 5 ABC.
=+c. What fraction of the runs of a full 27 design are used by this experiment?
=+b. How many experimental runs are required(assuming no replications)?
=+a. How many factors are being studied?
=+d. Develop a model equation for predicting arsenic removal percentage from the factors identified in part (b)34. In a 2723 fractional factorial design,
=+c. Which settings (high or low) of the factors in part (b) lead to maximizing the percentage of arsenic extracted?
=+b. Create a probability plot of the effects. Three effects in particular should appear to be important; what are they?
=+Factor Description Units Low level High level(21) (11)A Time s 30 120 B Currcnt amp .6 3.0 C EC area cm2 57 91.2 D Volume L 1 3 E Arsenic mg/L .23 1.18 Test run Removal(%)Test run Removal(%)Test
=+determine which factors affect the percent of arsenic removed from contaminated water by electrocoagulation (EC) (“Prediction of Arsenic Removal by Electrocoagulation: Model Development by
=+33. An unreplicated 25 experiment was performed to
=+d. Write a model for predicting iron extraction percentage from the factors identified in part (b).
=+c. Which settings (high or low) of the factors in part (b) lead to maximizing the percentage of iron extracted?
=+b. Create a probability plot of the effects. Which effects appear to be important?
=+Hydrometallurgy, 1997: 181–197). The factors and their levels are displayed in the following table:Low High level level Factor Description Units (21) (11)A H2SO4 M .10 .25 B Thiourea g/l 0.0 5.0
=+ experiment was conducted to assess the effects of four factors on the percentage of iron removed from kaolin samples (“Factorial Experiments in the Development of a Kaolin Bleaching Process
=+32. Impurities in the form of iron oxides lower the economic value and usefulness of industrial minerals, such as kaolins, to ceramic and paper-processing industries. A 24
=+d. Determine a model equation relating combustion time to the effects identified in part (b).e. Repeat parts (a)–(d) for the response variable coke burnoff.
=+c. Which settings (high or low) of the factors in part (b) lead to maximizing combustion time?Which settings lead to minimizing combustion time?
=+b. Create a probability plot of the effects in part (a).Which effects appear to be important?
=+a. For the response variable combustion time, calculate all main effects and interaction effects for this experiment.
=+design with no replications:Molar Com- Coke Partial Flow concen- bustion burn Run pressure rate tration time off 1 –1 –1 –1 10.6 5.73 2 1 –1 –1 11.2 5.70 3 –1 1 –1 24.4 3.05 4 1 1
=+Situ Combustion Experiments,” Trans. of the Institution of Chemical Engineers, 1991: 237–244). Two response variables, combustion time (in hours) and coke burnoff (in grams/hour), were studied
=+31. Combustion experiments of medium crude oil were conducted to determine which of three factors(oxygen partial pressure, oxygen flow rate, and oxygen molar concentration) affect various aspects
=+d. Determine a model equation relating time needed to reach 500-mm slump flow to the effects identified in part (b).
=+c. Which settings (high or low) of the factors in part (b) lead to maximizing the response variable? Which settings lead to minimizing the value of the response variable?
=+b. Create a probability plot of the effects from part (a).Which effects appear to be important?
=+a. Calculate all main effects and interaction effects.
=+(s) required for the SCC mixture to reach 500-mm slump flow.Run Slump S/A Coarse Time 1 21 21 21 1.71 2 21 21 1 3.19 3 21 1 21 1.75 4 21 1 1 3.06 5 1 21 21 .88 6 1 21 1 2.44 7 1 1 21 1.34 8 1 1 1
=+aggregate ratio by volume (B), and relative content of coarse aggregate (C)—on characteristics of the resulting SCC mixtures. The following table gives the coded factor levels along with values
=+also maintains high stability to prevent segregation.The authors of “Effect of SCC Mixture Composition on Thixotropy and Formwork Pressure” (J. Mater. Civ. Engr., 2012: 876–888) conducted a
=+30. Self-consolidating concrete (SCC) is a highly flowable product that can easily fill heavily congested reinforcement areas. Despite its low viscosity, SCC
=+d. Which settings (high or low) of the factors in part (b) lead to maximizing color quality?
=+c. Create main effects and interaction effects plots for the factors identified in part (b).
=+b. Construct an ANOVA table and use it as a basis for deciding which factors appear to affect color quality (Use 5 .01).
=+a. Calculate all main effects and two-factor interaction effects.
=+and Essays, 2012: 477–489). In the following table, higher values of the response variable (based on chromaticity measurements) are associated with higher color quality:Color Quality Storage
=+29. As with many dried products, sun-dried tomatoes can exhibit an undesirable discoloration during the drying and storage process. A replicated 23 experiment was conducted in an effort to
=+28. The article “Effect of Cutting Conditions on Tool Performance in CBN Hard Turning” (J. of Manuf.Processes, 2005: 10–16) reported the accompanying data, from a 23 design, on cutting speed
=+were used, with two replicate observations made at each combination of factor levels.Test run Response values(1) 200.0, 204.2 a 215.5, 219.5 b 272.7, 276.9 ab 299.5, 302.7 c 166.6, 172.6 ac 186.4,
=+27. The following data resulted from a study of the dependence of welding current on three factors:welding voltage (A), wire feed speed (B), and tipto-workpiece distance (C). Two levels of each
=+e. Using the important effects identified in part (b), write a model for predicting strength of a composite.
=+d. Which settings (high or low) of the factors in part (b) lead to maximizing the strength of a composite?
=+c. Draw the main effects and interaction effects plots for the factors identified in part (b).
=+b. Create the ANOVA table for the experiment.Which factors appear to have an effect on strength? (Use 5 .05.)
=+a. Calculate the main effects and the two-factor interaction effect for this experiment.
=+J. of Materials Science Letters, 1996: 1343–1345).The factors studied were the ratio of PP to LLDPE and the amount of red mud particles (in parts per hundred parts of resin). The levels at which
=+26. Polyolefin blends and composites can often improve the strength of existing polymers. In a study to determine which blends lead to increased material strength, composites of isotactic
=+25. Fill in the remaining columns of contrasts for the 24 design in Example 10.6.
=+b. Reversing the order of the factors, repeat the calculation in part (a) for the CB interaction.c. Show that the formulas in parts (a) and (b) are equivalent.
=+a. Using the definition that the BC interaction is one-half the difference between the main effect for B with C at its high level and the main effect for B at its low level, write the formula for
=+24. Write the design matrix (in Yates standard order) for a complete 23 experiment. Denote the response measurements associated with the runs as y1, y2, . . . , y8.
=+b. Test to see whether any interaction effects are significant at 5 .01.c. Test to see whether any main effects are significant at 5 .01.
=+Pressure 17.2 34.4 103.4 17.2 34.4 103.4 17.2 34.4 103.4 420-D 73 157 332 52 125 281 37 95 276 80 155 332 51 118 264 31 106 281 630-D 35 91 288 16 72 169 30 91 213 43 98 271 12 78 173 41 100 211
=+combination (“Analysis of Fabrics Used in Passive Restraint Systems—Airbags,” J. of the Textile Institute, 1996: 554–571).Temperature 8 50 75
=+is influenced by various factors is important for increasing effectiveness. In one study, the effects of three factors were studied: temperature(A), fabric denier (B), and air pressure (C). Two
=+23. One property of automobile air bags that contributes to their ability to absorb energy is the permeability of the woven material used to construct the air bags. Understanding how permeability
=+levels. The resulting mean squares were MSA 5 2,207.329, MSB 5 47.255, MSC 5 491.783, MSD 5 .44, MS(AB) 5 15.303, MS(AC) 5 275.446, MS(AD) 5 .470, MS(BC) 5 2.141, MS(BD) 5 .273, MS(CD) 5 .247,
=+22. A four-factor factorial design was used to investigate the effect of fabric (A), type of exposure (B), level of exposure (C), and fabric direction (D) on the extent of color change as measured
=+b. Use the appropriate F ratios to show that none of the two-factor interactions is significant at 5 .05.c. Which main effects are significant at 5 .05?
=+a. Construct an ANOVA table for this experiment, including all main effects and twofactor interactions (as did the authors of the cited article).
=+nickel in the alloyed layer is affected by carbon monoxide powder paste thickness (A, at three levels), scanning speed (B, at three levels), and laser power (C, at three levels). One observation
=+ The authors of “Parametrical Optimization of Laser Surface Alloyed NiTi Shape Memory Alloy with Co and Nb by the Taguchi Method”(J. of Engr. Manuf., 2012: 969–979) conducted a study to see
=+21. Recently, nickel titanium (NiTi) shape memory alloy (SMA) has become widely used in medical devices. This is attributable largely to the alloy’s shape memory effect (material returns to its
=+a. Fill in the missing entries in the table.b. Identify significant effects using 5 .01.
=+20. The deposition of thick protective coatings on substrates can be facilitated by laser cladding, in which an alloy powder is melted on the substrate surface. Experiments were conducted to
=+vb. Test to see whether any interaction effects are significant at 5 .05.c. Test to see whether any main effects are significant at 5 .05.
=+19. An experiment was conducted to investigate how the length of steel bars is affected by the time of day (A), heat treatment applied (B), and machine used (C).The three times were 8:00 a.m.,
=+b. Is there any single factor that appears to have no effect on thrust force? If so, how would you go about choosing the level of this factor that would minimize thrust force?
=+a. Construct an ANOVA table for this experiment, and identify significant effects using 5 .01.

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