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organization theory and design
Questions and Answers of
Organization Theory and Design
Hierarchical models. Several times we have used the hierarchy principle in selecting a model; that is, we have included nonsignificant lower order terms in a model because they were factors involved
Often the fitted regression model from a 2k factorial design is used to make predictions at points of interest in the design space. Assume that the model contains all main effects and two-factor
An article in the Journal of Hazardous Materials(“Feasibility of Using Natural Fishbone Apatite as a Substitute for Hydroxyapatite in Remediating Aqueous Heavy Metals,”Vol. 69, Issue 2, 1999, pp.
Continuation of Problem 6.44. The experiment in Problem 6.44 actually included six center points. The responses at these conditions were 35, 35, 35, 36, 36, and 34.Is there any indication of
A paper in the Journal of Chemical Technology and Biotechnology (“Response Surface Optimization of the Critical Media Components for the Production of Surfactin,” 1997, Vol. 68, pp. 263–270)
An article in Quality and Reliability Engineering International(2010, Vol. 26, pp. 223–233) presents a 25 factorial design. The experiment is shown in Table P6.12.(a) Analyze the data from this
The book by Davies (Design and Analysis of Industrial Experiments) describes an experiment to study the yield of isatin. The factors studied and their levels are as follows:Factor Low (−) High
Continuation of Problem 6.40. Suppose that the experimenter had also run four center points along with the 16 runs in Problem 6.40. The resistivity measurements at the center points are 8.15, 7.63,
Resistivity on a silicon wafer is influenced by several factors. The results of a 24 factorial experiment performed during a critical processing step are shown in Table P6.10.(a) Estimate the factor
An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A = tool angle(12, 15∘), B = cutting
A missing value in a 2k factorial. It is not unusual to find that one of the observations in a 2k design is missing due to faulty measuring equipment, a spoiled test, or some other reason. If the
Consider the single replicate of the 24 design in Example 6.2. Suppose that we ran five points at the center(0, 0, 0, 0) and observed the responses 93, 95, 91, 89, and 96. Test for curvature in this
Continuation of Problem 6.35. Use the regression models for molecular weight and viscosity to answer the following questions.(a) Construct a response surface contour plot for molecular weight. In
An experiment was conducted on a chemical process that produces a polymer. The four factors studied were temperature(A), catalyst concentration (B), time (C), and pressure(D). Two responses,
The scrumptious brownie experiment. The author is an engineer by training and a firm believer in learning by doing.I have taught experimental design for many years to a wide variety of audiences and
Continuation of Problem 6.32. Use the regression model in part (c) of Problem 6.32 to generate a response surface contour plot of yield. Discuss the practical value of this response surface plot.
In a process development study on yield, four factors were studied, each at two levels: time (A), concentration (B), pressure (C), and temperature (D). A single replicate of a 24 design was run, and
Continuation of Problem 6.30. Suppose that the experimenter had run four center points in addition to the 32 trials in the original experiment. The yields obtained at the center point runs were 68,
An experiment was run in a semiconductor fabrication plant in an effort to increase yield. Five factors, each at two levels, were studied. The factors (and levels) were A = aperture setting (small,
Consider the single replicate of the 24 design in Example 6.2. Suppose that we had arbitrarily decided to analyze the data assuming that all three- and four-factor interactions were negligible.
A company markets its products by direct mail. An experiment was conducted to study the effects of three factors on the customer response rate for a particular product.The three factors are A = type
Reconsider the experiment described in Problem 6.24.Suppose that four center points are available and that the UEC response at these four runs is 0.98, 0.95, 0.93, and 0.96, respectively.Reanalyze
Semiconductor manufacturing processes have long and complex assembly flows, so matrix marks and automated 2d-matrix readers are used at several process steps throughout factories. Unreadable matrix
I am always interested in improving my golf scores.Since a typical golfer uses the putter for about 35–45 percent of his or her strokes, it seems reasonable that improving one’s putting is a
Consider a variation of the bottle filling experiment from Example 5.3. Suppose that only two levels of carbonation are used so that the experiment is a 23 factorial design with two replicates. The
The effect estimates from a 24 factorial experiment are listed here. Are any of the effects significant? ABCD =−2.5251, BCD = 4.4054, ACD = −0.4932, ABD = −5.0842, ABC = −5.7696, CD = 4.6707,
The effect estimates from a 24 factorial design are as follows: ABCD = −1.5138, ABC = −1.2661, ABD =−0.9852, ACD = −0.7566, BCD = −0.4842, CD = −0.0795, BD = −0.0793, AD = 0.5988, BC =
An experimenter has run a single replicate of a 24 design. The following effect estimates have been calculated:A = 76.95 AB = −51.32 ABC = −2.82 B = −67.52 AC = 11.69 ABD = −6.50 C = −7.84
Continuation of Problem 6.19. One of the variables in the experiment described in Problem 6.19, heat treatment method (C), is a categorical variable. Assume that the remaining factors are
A nickel–titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure.Atest
Continuation of Problem 6.17. How would your answer to Problem 6.17 change if arsenic flow rate was more difficult to control in the process than the deposition time?
Continuation of Problem 6.16. Use the regression model in part (c) of Problem 6.16 to generate a response surface contour plot for epitaxial layer thickness. Suppose it is critically important to
An article in the AT&T Technical Journal (March/April 1986,Vol. 65, pp. 39–50) describes the application of two-level factorial designs to integrated circuit manufacturing. A basic processing step
Calculate approximate 95 percent confidence limits for the factor effects in Problem 6.14. Do the results of this analysis agree with the analysis of variance performed in Problem 6.14?
In Problem 6.13, the engineer was also interested in potential fatigue differences resulting from the two types of bottles. As a measure of the amount of effort required, he measured the elevation of
An industrial engineer employed by a beverage bottler is interested in the effects of two different types of 32-ounce bottles on the time to deliver 12-bottle cases of the product.The two bottle
A bacteriologist is interested in the effects of two different culture media and two different times on the growth of a particular virus. He or she performs six replicates of a 22 design, making the
An experiment was performed to improve the yield of a chemical process. Four factors were selected, and two replicates of a completely randomized experiment were run.The results are shown in the
Reconsider the experiment described in Problem 6.5.Suppose that the experimenter only performed the eight trials from replicate I. In addition, he ran four center points and obtained the following
A router is used to cut locating notches on a printed circuit board. The vibration level at the surface of the board as it is cut is considered to be a major source of dimensional variation in the
Plot the factor effects from Problem 6.5 on a graph relative to an appropriately scaled t distribution. Does this graphical display adequately identify the important factors? Compare the conclusions
Find the standard error of the factor effects and approximate 95 percent confidence limits for the factor effects in Problem 6.5. Do the results of this analysis agree with the conclusions from the
Reconsider part (c) of Problem 6.5. Use the regression model to generate response surface and contour plots of the tool life response. Interpret these plots. Do they provide insight regarding the
An engineer is interested in the effects of cutting speed(A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three
A 23 factorial is replicated three times. The ANOVA indicates that all main effects are significant but two of the interactions are not significant. The interaction terms are dropped from the model.
A 23 factorial is replicated twice. The ANOVA indicates that all main effects are significant but the interactions are not significant. The interaction terms are dropped from the model. The number of
A 23 factorial is replicated twice. The number of pure error or residual degrees of freedom are(a) 4 (b) 12 (c) 15(d) 2 (e) 8 (f) none of the above
In a 24 factorial design, the number of degrees of freedom for the model, assuming the complete factorial model, is(a) 7 (b) 5 (c) 6(d) 11 (e) 12 (f) none of the above
Consider the following incomplete ANOVA table:Source SS DF MS F A 50.00 1 50.00 ?B 80.00 2 40.00 ?AB 30.00 2 15.00 ?Blocks 10.00 1 ?Error ? ? ?Total 185.00 11(a) The pure error estimate of the
Consider the following incomplete ANOVA table:Source SS DF MS F A 50.00 1 50.00 ?B 80.00 2 40.00 ?AB 30.00 2 15.00 ?Error ? 12 ?Total 172.00 17 In addition to the ANOVA table you know that the
Consider the following ANOVA for a two-factor factorial experiment:Source DF SS MS F P A 2 8.0000 4.00000 2.00 0.216 B 1 8.3333 8.33333 4.17 0.087 Interaction 2 10.6667 5.33333 2.67 0.148 Error 6
Continuation of Problem 5.48. Suppose that Laura did actually conduct the experiment in Problem 5.48 as a randomized complete block design. Assume that the block sum of squares is 60.00. Reconstruct
In Problem 4.58 you met physics PhD student Laura Van Ertia who had conducted a single-factor experiment in her pursuit of the unified theory. She is at it again, and this time she has moved on to a
Reconsider the lens polishing experiment in Problem 5.46. Suppose that this experiment had been conducted as a randomized complete block design. The sum of squares for blocks is 4.00. Reconstruct the
The C. F. Eye Care company manufactures lenses for transplantation into the eye following cataract surgery. An engineering group has conducted an experiment involving two factors to determine their
Reconsider the keyboard experiment in Problem 5.35.Suppose that this experiment had been conducted in three blocks, with each replicate a block. Assume that the observations in the data table are
Reconsider the bone anchor experiment in Problem 5.34. Suppose that this experiment had been conducted in two blocks, with each replicate a block. Assume that the observations in the data table are
Reconsider the three-factor factorial experiment in Problem 5.24. Suppose that this experiment had been conducted in three blocks, with each replicate a block. Assume that the observations in the
Reconsider the three-factor factorial experiment in Problem 5.23. Suppose that this experiment had been conducted in two blocks, with each replicate a block. Assume that the observations in the data
Reconsider the experiment in Problem 5.13. Suppose that this experiment had been conducted in two blocks, with each replicate a block. Assume that the observations in the data table are given in
Reconsider the experiment in Problem 5.11. Suppose that this experiment had been conducted in three blocks, with each replicate a block. Assume that the observations in the data table are given in
Reconsider the experiment in Problem 5.9. Suppose that this experiment had been conducted in three blocks, with each replicate a block. Assume that the observations in the data table are given in
An article in Quality Progress (May 2011, pp. 42–48)describes the use of factorial experiments to improve a silver powder production process. This product is used in conductive pastes to
An experiment was performed to investigate the keyboard feel on a computer (crisp or mushy) and the size of the keys (small, medium, or large). The response variable is typing speed. Three replicates
Bone anchors are used by orthopedic surgeons in repairing torn rotator cuffs (a common shoulder tendon injury among baseball players). The bone anchor is a threaded insert that is screwed into a hole
A manufacturer of laundry products is investigating the performance of a newly formulated stain remover. The new formulation is compared to the original formulation with respect to its ability to
I have recently purchased new golf clubs, which I believe will significantly improve my game. Below are the scores of three rounds of golf played at three different golf courses with the old and the
An experiment was conducted to study the life (in hours) of two different brands of batteries in three different devices (radio, camera, and portable DVD player). A completely randomized two-factor
An article in the IEEE Transactions on Electron Devices (Nov. 1986, pp. 1754) describes a study on polysilicon doping. The experiment shown below is a variation of their study. The response variable
An article in the Journal of Testing and Evaluation(Vol. 16, no. 2, pp. 508–515) investigated the effects of cyclic loading and environmental conditions on fatigue crack growth at a constant 22 MPa
Consider the data in Problem 5.13. Analyze the data, assuming that replicates are blocks.
Consider the data in Problem 5.12. Analyze the data, assuming that replicates are blocks.
The yield of a chemical process is being studied. The two factors of interest are temperature and pressure. Three levels of each factor are selected; however, only nine runs can be made in one day.
In Problem 5.8, suppose that we wish to reject the null hypothesis with a high probability if the difference in the true mean yield at any two pressures is as great as 0.5. If a reasonable prior
The quality control department of a fabric finishing plant is studying the effect of several factors on the dyeing of cotton–synthetic cloth used to manufacture men’s shirts.Three operators,
The percentage of hardwood concentration in rawpulp, the vat pressure, and the cooking time of the pulp are being investigated for their effects on the strength of paper. Three levels of hardwood
Consider the three-factor modelNotice that there is only one replicate. Assuming all the factors are fixed, write down theANOVAtable, including the expected mean squares. What would you use as the
Consider the following data from a two-factor factorial experiment. Analyze the data and draw conclusions. Perform a test for nonadditivity. Use ???? = 0.05.Column Factor Row Factor 1 2 3 4 1 36 39
Derive the expected mean squares for a two-factor analysis of variance with one observation per cell, assuming that both factors are fixed.
An experiment was conducted to determine whether either firing temperature or furnace position affects the baked density of a carbon anode. The data are shown below:Temperature (∘C)Position 800 825
Use Tukey’s test to determine which levels of the pressure factor are significantly different for the data in Problem 5.8.
Consider the experiment in Problem 5.8. Fit an appropriate model to the response data. Use this model to provide guidance concerning operating conditions for the process.
An experiment is conducted to study the influence of operating temperature and three types of faceplate glass in the light output of an oscilloscope tube. The following data are collected:Temperature
A mechanical engineer is studying the thrust force developed by a drill press. He suspects that the drilling speed and the feed rate of the material are the most important factors.He selects four
The factors that influence the breaking strength of a synthetic fiber are being studied. Four production machines and three operators are chosen and a factorial experiment is run using fiber from the
Johnson and Leone (Statistics and Experimental Design in Engineering and the Physical Sciences, Wiley, 1977) describe an experiment to investigate warping of copper plates. The two factors studied
An article in Industrial Quality Control (1956, pp. 5–8)describes an experiment to investigate the effect of the type of glass and the type of phosphor on the brightness of a television tube. The
For the data in Problem 5.9, compute a 95 percent confidence interval estimate of the mean difference in response for feed rates of 0.20 and 0.25 in∕min.
An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. He selects three feed rates and four depths of cut. He then conducts a factorial
The yield of a chemical process is being studied. The two most important variables are thought to be pressure and temperature. Three levels of each factor are selected, and a factorial experiment
The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment.Two-way ANOVA: y versus A, B Source DF SS MS F P A 1 ? 0.0002 ? ?B ? 180.378 ? ?
The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment.Two-way ANOVA: y versus, A, B Source DF SS MS F P A 1 0.322 ? ? ?B ? 80.554
Consider the following incomplete ANOVA table:Source SS DF MS F A ? 1 50.00 ?B 80.00 ? 40.00 ?AB 30.00 2 15.00 ?Error ? 12 ?Total 172.00 17(a) Complete the ANOVA calculations.(b) Provide an
A biomedical researcher has conducted a two-factor factorial experiment as part of the research to develop a new product. She performed the statistical analysis using a computer software package. A
If an interaction effect in a factorial experiment is significant, the main effects of the factors involved in that interaction are difficult to interpret individually.(a) True(b) False
A factorial experiment may be conducted as a RCBD by running each replicate of the experiment in a unique block.(a) True(b) False
An interaction effect in the model from a factorial experiment involving quantitative factors is a way of incorporating curvature into the response surface model representation of the results.(a)
Consider the direct mail marketing experiment in Problem 4.13. Suppose that this experiment had been run as a completely randomized design, ignoring potential regional differences, but that exactly
Physics graduate student Laura Van Ertia has conducted a complete randomized design with a single factor, hoping to solve the mystery of the unified theory and complete her dissertation. The results
Suppose that a single-factor experiment with five levels of the factor has been conducted. There are three replicates and the experiment has been conducted as a complete randomized design. If the
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