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organization theory and design

Questions and Answers of Organization Theory and Design

Explain the dierence between a sub-sample and a duplicate in relation to the experiment described in 1.
Explain the dierence between an experimental unit and a sub-sample or sub-unit in relation to the experiments described in 1.
A series of runs were performed to determine how the wash water tem-perature and the detergent concentration aect the bacterial count on the palms of subjects in a hand washing experiment.(a)
In an experiment that has at least one nested factor(a) the nested factor will always be a random effect.(b) the primary factor will always be a fixed effect.(c) one may identify the key factor by
It is usually easier or cheaper to change the levels of the whole-plot factor in a split-plot design.(a) True(b) False
If an experiment is conducted as a split plot but analyzed as a factorial the resulting error estimate will usually be too large for properly testing the subplot factor and could lead to misleading
In a split-plot design the subplot error is usually smaller than the whole-plot error.(a) True(b) False
A good reason to consider a split-plot design is a situation where some experimental units are larger than others.(a) True(b) False
In a split-plot design the interaction between the whole-plot factor and the subplot factor is always tested against the whole-plot error.(a) True(b) False
If there are three levels of the main factor and five levels of the nested factor there will be four degrees of freedom for the nested factor.(a) True(b) False
Both the ANOVA method and REML can be applied to a nested design.(a) True(b) False
The nested factor is always random.(a) True(b) False
There is always an interaction term in a nested design.(a) True(b) False
Reconsider the experiment in Problem 14.26. This is a rather large experiment, so suppose that the experimenter had used a 25−1 design instead. Set up the 25−1 design in a split-plot, using the
An article in Quality Engineering (“Quality Quandaries:Two-Level Factorials Run as Split-Plot Experiments,”Bisgaard et al., Vol. 8, No. 4, pp. 705–708, 1996) describes a 25 factorial experiment
Consider the experiment described in Example 14.4.Demonstrate how the order in which the treatment combinations are run would be determined if this experiment were run as (a) a split-split-plot, (b)
Suppose that in Problem 14.22 four technicians had been used. Assuming that all the factors are fixed, how many blocks should be run to obtain an adequate number of degrees of freedom on the test for
Rework Problem 14.22, assuming that the technicians are chosen at random. Use the restricted form of the mixed model.
Consider the split-split-plot design described in Example 14.4. Suppose that this experiment is conducted as described and that the data shown in Table P14.3 are obtained.Analyze the data and draw
Repeat Problem 14.20, assuming that the mixes are random and the application methods are fixed.
An experiment is designed to study pigment dispersion in paint. Four different mixes of a particular pigment are studied. The procedure consists of preparing a particular mix and then applying that
Steel is normalized by heating above the critical temperature, soaking, and then air cooling. This process increases the strength of the steel, refines the grain, and homogenizes the structure. An
Suppose that in Problem 14.16 the bar stock may be purchased in many sizes and that the three sizes actually used in the experiment were selected randomly. Obtain the expected mean squares for this
Rework Problem 14.16 using the unrestricted form of the mixed model. You may use a computer software package to do this. Comment on any differences between the restricted and unrestricted model
A structural engineer is studying the strength of aluminum alloy purchased from three vendors. Each vendor submits the alloy in standard-sized bars of 1.0, 1.5, or 2.0 inches.The processing of
Reanalyze the experiment in Problem 14.14 assuming the unrestricted form of the mixed model. You may use a computer software package to do this. Comment on any differences between the restricted and
Suppose that in Problem 14.13 a large number of power settings could have been used and that the two selected for the experiment were chosen randomly. Obtain the expected mean squares for this
A process engineer is testing the yield of a product manufactured on three machines. Each machine can be operated at two power settings. Furthermore, a machine has three stations on which the product
Variance components in the unbalanced two-stage nested design. Consider the model Yijk =++j) + k(ij) i = 1,2, ..., a j=1,2,...,b k = 1,2, where A and B are random factors. Show that E(MS) = 0 + c0 +
Unbalanced nested designs. Consider an unbalanced two-stage nested design with bj levels of B under the ith level of A and nij replicates in the ijth cell.Factor A 1 2 Factor B 1 2 1 2 3 6 −3 5 2 1
Verify the expected mean squares given in Table 14.1.
Repeat Problem 14.7 assuming the unrestricted form of the mixed model.You may use a computer software package to do this. Comment on any differences between the restricted and unrestricted model
Reanalyze the experiment in Problem 14.5 using the unrestricted form of the mixed model. Comment on any differences you observe between the restricted and the unrestricted model results. You may use
Consider the three-stage nested design shown in Figure 14.5 to investigate alloy hardness. Using the data that follow, analyze the design, assuming that alloy chemistry and heats are fixed factors
To simplify production scheduling, an industrial engineer is studying the possibility of assigning one time standard to a particular class of jobs, believing that differences between jobs are
A manufacturing engineer is studying the dimensional variability of a particular component that is produced on three machines. Each machine has two spindles, and four components are randomly selected
The surface finish of metal parts made on four machines is being studied. An experiment is conducted in which each machine is run by three different operators and two specimens from each operator are
A rocket propellant manufacturer is studying the burning rate of propellant from three production processes.Four batches of propellant are randomly selected from the output of each process, and three
In a two-factor factorial experiment with at least one random factor(a) the statistical test on the interaction effect is identical to the interaction effect test in the fixed effects case.(b) the
In a two-factor factorial experiment with at least one random factor(a) the statistical tests on main effects are identical to the corresponding main effects tests in the fixed effects case.(b) the
A negative point estimate of a variance component implies that the variance of that fixed effect is zero.(a) True(b) False
In a mixed model, the statistical tests on fixed factors are always exactly the same as they are in the fixed effects model.(a) True(b) False
Random factors are always categorical.(a) True(b) False
Both the ANOVA method and REML will produce the same point estimate of a variance component if the design is balanced.(a) True(b) False
The REML method is preferred as a technique for estimating variance components because it can also provide the standard error of the variance component leading to a confidence interval.(a) True(b)
The random factor is assumed to have a normal distribution with a mean of zero and a variance component that may be nonzero.(a) True(b) False
The levels of a random factor are sampled from a large population of possible levels.(a) True(b) False
Rework Problem 13.30 using REML. Compare all sets of CIs for the variance components.
Consider the experiment in Problem 13.1. Analyze the data using REML. Compare the CIs to those obtained in Problem 13.27.
Consider the experiment described in Problem 5.13.Estimate the variance components using the REML method.Compare the confidence intervals to the approximate CIs found in Problem 13.28.
Rework Problem 13.27 using the modified largesample method described in Section 13.6.2. Compare this confidence interval with the one obtained previously and discuss.
Rework Problem 13.25 using the modified largesample approach described in Section 13.6.2. Compare the two sets of confidence intervals obtained and discuss.
Consider the three-factor experiment in Problem 5.24 and assume that operators were selected at random. Find an approximate 95 percent confidence interval on the operator variance component.
Use the experiment described in Problem 5.13 and assume that both factors are random. Find an exact 95 percent confidence interval on ????2. Construct approximate 95 percent confidence intervals on
Consider the variance components in the random model from Problem 13.1.(a) Find an exact 95 percent confidence interval on ????2.(b) Find approximate 95 percent confidence intervals on the other
Consider the two-factor mixed model. Show that the standard error of the fixed factor mean (e.g., A) is[MSAB∕bn]1∕2.
Analyze the data in Problem 13.1, assuming that operators are fixed, using both the unrestricted and the restricted forms of the mixed models. Compare the results obtained from the two models.
Invoking the usual normality assumptions, find an expression for the probability that a negative estimate of a variance component will be obtained by the analysis of variance method. Using this
Show that the method of analysis of variance always produces unbiased point estimates of the variance components in any random or mixed model.
In the two-factor mixed model analysis of variance, show that Cov[(????????)ij, (????????)i′j] = −(1∕a)????2????????for i ≠ i′.
The three-factor factorial model for a single replicate is yijk = ???? + ????i + ????j + ????k + (????????)ij+(????????)jk + (????????)ik + (????????????)ijk + ????ijk If all the factors are random,
Consider the three-factor factorial model yijk = ???? + ????i + ????j + ????k + (????????)ij+(????????)jk + ????ijk⎧⎪⎨⎪⎩i = 1, 2, . . . , a j = 1, 2, . . . , b k = 1, 2, . . . , c Assuming
In Problem 5.24, assume that the three operators were selected at random. Analyze the data under these conditions and draw conclusions. Estimate the variance components.
Reconsider cases (c), (d), and (e) of Problem 13.17.Obtain the expected mean squares assuming the unrestricted model. You may use a computer package such as Minitab.Compare your results with those
Consider a four-factor factorial experiment where factor A is at a levels, factor B is at b levels, factor C is at c levels, factor D is at d levels, and there are n replicates. Write down the sums
Derive the expected mean squares shown in Table 13.10.
Consider the experiment in Example 13.5. Analyze the data for the case where A, B, and C are random.
Consider the three-factor factorial design in Example 13.4. Propose appropriate test statistics for all main effects and interactions. Repeat for the case where A and B are fixed and C is random.
By application of the expectation operator, develop the expected mean squares for the two-factor factorial, mixed model. Use the restricted model assumptions. Check your results with the expected
Rework Problem 13.8 using the REML method.
Rework Problem 13.7 using the REML method.
Rework Problem 13.6 using the REML method.
Rework Problem 13.5 using the REML method.
In Problem 5.13, suppose that there are only four machines of interest, but the operators were selected at random.(a) What type of model is appropriate?(b) Perform the analysis and estimate the model
Reanalyze the measurement system experiment in Problem 13.2, assuming that operators are a fixed factor. Estimate the appropriate model components using the ANOVA method.
Reanalyze the measurement systems experiment in Problem 13.1, assuming that operators are a fixed factor. Estimate the appropriate model components using the ANOVA method.
Suppose that in Problem 5.18 the furnace positions were randomly selected, resulting in a mixed model experiment.Reanalyze the data from this experiment under this new assumption. Estimate the
Reconsider the data in Problem 5.20. Suppose that both factors are random.(a) Analyze the data from this experiment.(b) Estimate the variance components using the ANOVA method.
Reconsider the data in Problem 5.13. Suppose that both factors, machines and operators are chosen at random.(a) Analyze the data from this experiment.(b) Find point estimates of the variance
An article by Hoof and Berman (“Statistical Analysis of Power Module Thermal Test Equipment Performance,”IEEE Transactions on Components, Hybrids, and Manufacturing Technology Vol. 11, pp.
An experiment was performed to investigate the capability of a measurement system. Ten parts were randomly selected, and two randomly selected operators measured each part three times. The tests were
The (3,2) simplex-lattice design is a rotatable design for fitting a second-order mixture model.(a) True(b) False
When axial check blends are added to a simplexlattice, these blends are as far as possible (Euclidean distance)from the other design points.(a) True(b) False
The simplex-lattice and simplex-centroid designs have most of the design points on the boundary of the experimental region.(a) True(b) False
In designing mixture experiments, a good rule of thumb is to assume that at least a second-order mixture model is likely to be adequate.(a) True(b) False
If the sign of all of the eigenvalues is the same, the response surface will have a global maximum.(a) True(b) False
The existence of a ridge system in the canonical variables can restrict the choice of optimal location.(a) True(b) False
The location of the stationary point corresponds to a global maximum or minimum of the surface.(a) True(b) False
Using a second-order model to estimate the underlying relationship is a common approach to approximating the surface.(a) True(b) False
The method of steepest ascent is a gradient procedure.(a) True(b) False
For a first-order model with three variables, the variance of the predicted response at the design center (in coded units) is ????2, if an unreplicated 23 design is used to collect the experimental
The coordinates of the points on the path of steepest ascent are proportional to the effect estimates from the first-order model.(a) True(b) False
If a first-order model with interaction is used, the path of steepest ascent is a straight line.(a) True(b) False
When conducting steepest ascent experiments, it may be a good idea to replicate runs at some or all of the points along the path.(a) True(b) False
A 22 factorial design with four center points has been used to fit the first-order model ̂y = 175 + 25x1 + 10x2 −8x3. The variance of the predicted response at any design point other than the
Consider the first-order model ̂y = 150 + 20x1 +12x2. If the experimenter used one coded unit in the x1 direction as the step size, the point x1 = 1.5, x2 = 1.0 is a point on the path of steepest
Any point on the path of steepest ascent is proportional to the unit vector of the first-order regression coefficients.(a) True(b) False
Suppose that you have fit the following model̂y = 20 + 10x1 − 4x2 + 12x3(a) The experimenter decides to choose x1 as the variable to define the step size for steepest ascent. Do you think that
It is stated in the text that the development of the path of steepest ascent makes use of the assumption that the model is truly first-order in nature. However, even if there is a modest amount of
Given the fitted response function̂y = 72.0 + 3.6x1 − 2.5x2 which is found to fit well in a localized region of (x1, x2).(a) Plot contours of constant response, y, in the (x1, x2)plane.(b)

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