Introduction To Engineering Statistics And Six Sigma 1st Edition Theodore T. Allen - Solutions

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For the platelet counts in the growth factor database (DB9), "normal"is often taken as being in the range from 150,000 to 400,000. How accurately should platelet counts be recorded to avoid interfering with clinical decisions?
How could the variable sex in the emphysema database (DB3) be quantified?
Into what phase-type would the question addressed in the gallbladder database (DB2) fall?
Give an example of a question from the bronchoconstriction database(DB14), the answer for which would fall into (a) the description stage,(b) the explanation stage, or (c) the prediction stage.
Give an example of a question from the prostate biopsy database (DB1), the answer for which would fall into (a) the description stage, (b) the explanation stage, or (c) the prediction stage.
Adapt the genetic algorithm in Chapter 19 to select n1, n2, c1, r, and c2 to minimize a weighted sum of the expected number of tests and the chance of errors for a t-testing procedure of the type shown in Figure 21.2. Assume thatσ0 is known to equal 1.0. (Hypothetically, this procedure might be
Which is correct and most complete according to the text?a. The concept of a method rollercoaster emphasizes individual expertise levels.b. Optimization has not yet been used to produce methods or strategies.c. The nature of six sigma projects places no restriction on relevant test beds.d. Six
Which is correct and most complete using the notation from the text?a. In general, g(x) corresponds to the primary KOV.b. Control charting likely results in improved recommendations for settings, xop.c. Regression models cannot be used to specify constraint sets.d. Formal optimization is generally
Which is correct and most complete according to the text?a. Six sigma emphasizes credit-sharing between statistical experts and engineers.b. The control phase is important primarily because it motivates management.c. Encouraging adoption of project settings is critical for achieving project ROI.d.
Which is correct and most complete according to the text?a. Documenting a project case study is generally a micro-level contribution.b. Future opportunities for survey based contributions are generally not possible.c. Models predicting the value of specific strategies are entirely lacking.d. The
Resolve the co-packers’s problem assuming σ1 = 0.4, σ2 = 0.20, and σ3 = 0.04.
Consider three resistors in series each with resistance uniformly distributed with mean 10 ohms and uniform limits a = 8.5 ohms and b = 11.5 ohms.Which is correct and most complete?a. The series resistance is not uniformly distributed.b. The mean or average series resistance is 29.0 ohms.c. The
Consider two resistors in series each with resistance uniformly distributed with mean 10 ohms and uniform limits a = 8.5 ohms and b = 11.5 ohms. Which is correct and most complete?a. Pr{series resistance is between 19.0 and 21.0 ohms is} > 0.95.b. The series resistance is not uniformly
Use the assumption, B2 = (1.25)2 I an Run A B C 1 -0.5 -1.0 -0.5 2 -0.5 0.5 -1.0 3 0.5 1.0 -0.5 45678 -1.0 0.0 0.0 0.5 -1.0 0.5 0.0 0.0 0.0 1.0 0.0 0.0 -0.5 -0.5 1.0 9 -0.5 1.0 0.5 10 0.5 0.5 1.0 11 05 05 -10
Which is correct and most complete?a. In planning experiments, one generally does not know the true model.b. Without added information, one must assume E[β2β2′] = 0.c. In general, x′Ax = Tr[A] xx′.d. All of the above are correct.e. All of the above are correct except (a) and (d).
Which is correct and most complete?a. The EIMSE is always equal to or larger than the integrated variance.b. The bias depends on assumptions about the coefficients not in the fitted model.c. Moment matrices only depend on the models forms and assumptions about where prediction will be requested.d.
Which is correct and most complete?a. The EIMSE cannot compare the expected accuracies associated with RSM designs prior to experimentation.b. The moment matrices (μi,j) can only be calculated knowing DOE array.c. X1 and X2 could be the design matrices associated with f1 and f2 respectively.d. All
Which is correct and most complete?a. In calculating the EIMSE, one must know the true values of fitted coefficients.b. The true level of bumpiness likely affects derived prediction errors.c. In calculating the EIMSE, one assumes something about the random errors.d. All of the above are correct.e.
The σestimate = 0.5.d. All of the above are correct.e. All of the above are correct except (a) and (d).
Which of the following is correct and most complete?a. Using the central limit theorem, one can estimate the error of estimates.b. Monte Carlo generally gives expected values with no errors.c. If four simulation runs give, 0, 1, 0, and
Which of the following is correct and most complete?a. Data from a thought experiment proves a factor affects system average outputs.b. If there is no true effect, finding significance in t-testing is a Type I error.c. Type II errors are only possible if there is no true difference.d. All of the
Which of the following is correct and most complete?a. If applied correctly, t-testing cannot result in undesirable declarations.b. If a hypothesis testing method derives appropriate results 95 times out of 100 simulated tests, then an MC estimate for the error probability is 0.05.c. If random
Which of the following is correct and most complete?a. If X is uniform[10, 12], then Pr{X < 11.5} = 0.25 or 25%.b. If X is uniform[10, 12], then the inverse cumulative for X is F-1(u) =10 + 2u.c. Generating random numbers rarely starts with generating U[0,1]deviates.d. All of the above are
Which of the following is correct and most complete?a. Recursive sequences of numbers can seem random to the untrained eye.b. The pseudo-random number generation procedure in the text involves generating two sequences, integer seeds and approximately continuous numbers.c. Slopes of the cumulative
Which of the following is correct and most complete?a. Method evaluation criteria can include subjective judgments about ease of use.b. Many quantitative properties of methods including Type I error rates can be calculated using the assumption that there is a true average difference and
Which of the following is correct and most complete?a. Random variables are numbers whose values are known at time of planning.b. Probabilities can generally be written as expected values of indicator functions.c. Probability theory and simulation can generate information of interest to people
Perform an experiment involving four factors and one or more responses using standard screening using fractional factorials or responses surface methods.The experimental system studies should permit building and testing individual prototypes requiring less than $5 and 10 minutes time.
Which of the following is correct and most complete?a. RSM should have been used in the rubber experiment to focus on shot size and humidity since everyone knew these mattered most.b. A regression analysis of on-hand data could conceivably have suggested that shot size was causing the sticking
Which is correct and most complete?a. Using an EIMSE optimal design, the snap tab study could have been done with 20 runs or fewer.b. The LCRSM approach used could have generated a less accurate prediction model than any of the standard RSM approaches in Chapter 13.c. By dropping fixing factor C,
Which is correct and most complete?a. As is usual in DOE recommendations, they should recommend the settings corresponding to the best run in their DOE.b. If RSM was applied to computer simulations, errors from the DOE modeling process and the simulation could cause poor real world confirmation
Which is correct and most complete?a. Starting with standard screening using fractional factorials is natural because interactions are modeled.b. They could reasonably use a single, standard Box Behnken array with four factors.c. A reasonable recommendation is to perform two Box Behnken DOEs, one
Which is correct and most complete?a. A reasonable first step is to return the process to the documented settings.b. They could study four factors with eight batches of units according to a regular FF.c. A list of factors to study should come from engineers and operators.d. Lenth’s method with
Which is correct and most complete (according to this book)?a. With experts in-the-loop, it is rarely (if ever) critical to consult SOP settings.b. They likely made some Type I errors by assuming that all factors mattered.c. They could have used 12 batches based on a Plackett Burman (PB)array and
Which is correct and most complete (according to this book)?a. The engineers have a high level of evidence, and the settings should work.b. Randomness and interactions could have confused them. Yield might be worse.c. The cost of low first-pass yield is almost all direct payments to operators.d.
Which is correct and most complete (according to the chapter)?a. The paper helicopter example involves four controllable design parameters.b. People might choose different alternatives because of personal differences.c. Maximum likelihood estimation can be used in discrete choice modeling.d.
Which is correct and most complete (according to the chapter)?a. Discrete choice modeling is effectively a subset of logistic regression.b. Linear regression is a natural alternative to discrete choice modeling.c. The functions that predict the underlying utility must be first order.d. Probit
Which is correct and most complete in relation to artificial neural nets(ANNs)?a. RSM arrays cannot be used in neural net fitting.b. The Excel solver can be used in fitting ANNs.c. Often, so-called “back propagation” algorithms are used in fitting ANNs.d. Rules of thumb exist for estimating the
Which is correct and most complete?a. Artificial neural nets are only relevant for predicting categorical responses.b. At least two hidden layers are generally needed for accurate prediction.c. The fittable parameters in neural nets are often called weights.d. The fitting objective in neural nets
Which is correct and most complete based on the data in Table 16.1 with the last response value changed to 200?a. A kriging model prediction would be yest(x1=4.5) = 101.5.b. The kriging models in the text are based on the assumption σ0 = 0.0.c. The maximum log-likelihood value for θ1 is less than
Which is correct and most complete based on the data in Table 16.1?a. A kriging model prediction would be yest(x1=4.5) = 101.5.b. Kriging model predictions could not pass through x1 = 3 and y1 = 70.c. FEM experiments necessarily involve random errors.d. Kriging models cannot be used for the same
Analyze the real estate data in Table 15.14 and make recommendations to a real estate developer about where to build and what type of house to build for profitability. A good analysis will typically include one or two models, reasons for selecting that model, estimates of the errors of the model,
Analyze the box office data in Table 15.13 and make recommendations to the extent possible for a vice president at a major movie studio. A good analysis will typically include one or two models, reasons for selecting that model, estimates of the errors of the model, and interpretation for the
Which is correct and most complete according to the chapter?a. Editing models involves adding terms to regression models.b. If only a single acceptability check is possible, PRESS might be the best.c. If the response is fraction nonconforming, large batch sizes can help make residuals more normally
Calculate the following:a. Create a first order regression prediction model from the data.b. Create a second order regression prediction model from the data.c. Calculate R2 adjusted for a first order model.d. Calculate the PRESS for a first order model.e. Calculate the R2 prediction for a first
Which is correct and most complete with regard to the regression flowchart in Figure 15.5?a. Acceptability checks cannot include residuals plots.b. Models of on-hand data must be used with caution.c. Adding or removing model terms cannot address outliers.d. The initial model must be a first order
Consider a first order regression using all of the factors including x3 with the sales response. Which is correct and most complete?a. Since “Service type” is a three level categorical factor, the coefficient calculations could be aided by creating two “contrasts” or dummy factors.b. All of
Which of the following is correct and most complete (for a model without x3)?a. The regression estimate for sigma based on a first-order model is 0.944.b. The SSR for a first order model is 6637.55.c. The SSE for a first order model is 396.45.d. There are no obvious outliers on a normal plot of
Which of the following is correct and most complete (for a model without x3)?a. The data derive from an application of standard response surface methods.b. No outliers appear in the upper right of the normal probability plot of residuals.c. The PRESS value for a first-order model in this case is
Which of the following is correct and most complete (for a model without x3)?a. Including the optional scaling, VIF1 = VIF2 = 1.08.b. One of the values on the normal probability plot of residuals is–1.7, –2.4 .c. In general, Φ–1[s] = – Φ–1[–s].d. The input pattern is clearly not
Which of the following is correct and most complete?a. The optional first step involving scaling can affect VIF values.b. Least squares coefficient estimates minimize the sum of squared residuals.c. VIFs are not influenced by outliers unless the points are removed.d. Changing the last input in
Which is correct and most complete with regard to regression diagnostics?a. Generally, several acceptability tests must be passed for proof to follow.b. VIFs are directly useful for spotting outliers in the response data.c. Normal probability plotting does not involve any subjectivity.d.
Consider the data in Table 15.1, which is correct and most complete?a. Analysts are almost always given data in a format that make analysis easy.b. Making up data can never increase the believability of analysis results.c. The missing data point in Table 15.1 (a) could be worth saving to produce
Considering the example in Section 15.2.2, which is correct and most complete? a. X'X = 5 25 25 135 b. Best is a 2 x 2 matrix. c. Best [22 34]' minimizes the sum of squares error. d. An optimization solver could not be used to derive least squares estimates. e. All of the above are correct. f. All
A new product is released in two medium-sized cities. The demands in Month 1 were 37 and 43 units and in Month 2 were 55 and 45 units. Which of the following is correct and most complete?a. A first order regression forecast for Period 3 is 70 units.b. One of the residuals is -2 and another one is
(Advanced) Extend RDPM to drop the assumption that Dr = 0 for all r.
List two advantages of Taguchi Methods compared with RDPM.
List two advantages of RDPM compared with Taguchi Methods.
Assume that z1 and z2 have means μ1 and μ2 and standard deviations σ1 and σ2 respectively. Also, assume their covariance is zero. What isin terms of μ 1 and μ2, standard deviations σ1 and σ2, and no matrices? Var[(c+x'C)z]=Var Z Z 2 5 2 Z X2 28
Which is correct and most complete in relation to extended Taguchi Methods?a. Taguchi SNR ratios emphasize quality potentially at the expense of profits.b. ETC factors generally cost less to change than HTC factors.c. Taguchi product arrays call for direct observation of control factor setting
Which is correct and most complete in relation to extended Taguchi Methods?a. Marginal plotting is somewhat similar to regression without controlby-control factor interactions.b. Taguchi Methods necessarily involve using formal optimization.c. Taguchi product arrays always result in higher costs
Which is correct and most complete in relation to extended Taguchi Methods?a. If responses for a control factor combination are: 2, 3, 5, and 3, SNRL = 10.1.b. If responses for a control factor combination are: 2, 3, 5, and 3, SNRS = 2.7.c. A common goal in applying Taguchi methods is to maximize
Which is correct and most complete in relation to extended Taguchi Methods?a. These methods are based on central composite designs.b. The choice of signal-to-noise ratio depends on the number of control factors.c. The methods are called “extended” because they can be used when multiple
What is the relationship between TOC from Chapter 2 and RDPM?
Which is correct and most complete?a. If there are three control factors and four noise factors, Cr is 3 × 4.b. Not every quadratic polynomial can be expressed by Equation (14.1).c. The first diagonal element in Br is a control-by-noise factor interaction.d. The first diagonal element in Br is a
Which is correct and most complete?a. Robustness opportunities are always present in systems.b. Large control-by-noise factor interactions can cause robustness opportunities.c. Noise-by-noise interactions are sometimes neglected in robust engineering.d. Total variation of quality characteristics
Which is correct and most complete?a. Noise factor variation rarely (if ever) causes parts to fail to conform to specifications.b. Quality characteristics can be responses in applying RDPM experimentation.c. The fraction nonconforming cannot be a function of control factors.d. All of the above are
Which is correct and most complete (according to the text)?a. Expected prediction errors cannot be predicted before applying RSM.b. Box Behnken designs often foster more accurate prediction models than CCDs.c. Predictions about the accuracy of RSM depend on beliefs about the system.d. All of the
Which is correct and most complete based on how the designs are constructed?a. Central composite designs do not, in general, contain center points.b. A BBD design with seven factors contains the run -1, -1, -1, -1, -1, -1,-1.c. Central composite designs contain Resolution V fractional factorials.d.
Which is correct and most complete?a. In two stage RSM, interactions are never in the fitted model form.b. In two stage RSM, finding lack of fit indicates more runs should be performed.c. Two stage RSM cannot terminate with a full quadratic fitted model in all factors.d. In two stage RSM, lack of
Which is correct and most complete (within the implied uncertainty)?a. F0 = 29 and lack of fit is detected.b. F0.05,1,nC – 1 = 3.29.c. F0 = 19.d. All of the above are correct.e. All of the above are correct except (a) and (d).
Which is correct and most complete (within the implied uncertainty)?a. Adjusted R2 calculated is 0.99 a high fraction of the variation is unexplained.b. Adjusted R2 calculated is 0.99 a high fraction of the variation is explained.c. Surface plots are irrelevant since the interaction coefficient is
Which is correct and most complete (within the implied uncertainty)?a. A full quadratic polynomial cannot be fitted since (X′X)–1X′ is undefined.b. RSM fitted coefficients are 5.88, 1.83, 0.19, 0.25, 0.06, and 2.75.c. RSM fitted coefficients are 5.88, 2.83, 0.19, 0.25, 1.06, and 2.75.d. All
Which is correct and most complete?a. With three factors, two-step RSM cannot save costs compared with one-shot.b. In general, blocks in experimentation are essentially levels of the factor time.c. The original sequential RSM can be viewed as an optimization method.d. By repeating factor
Which is correct and most complete?a. If you only have enough money for a few runs, using screening without RSM might be wise.b. In general, factors in a DOE must be uncontrollable during experimentation.c. Adjusted R2 is not relevant for evaluating whether data are reliable.d. The number of runs
Which is correct and most complete?a. If X is n × k with n > k, X′ (the transpose) is n × k.b. If RSM is applied, (X′X)–1X′ cannot be calculated for quadratic model forms because X′X is a singular matrix.c. Often, EIMSE designs are not available with fewer runs than CCDs or BBDs.d.
According to the chapter, which is correct and most complete?a. EIMSE designs are an example of optimal or computer generated designs.b. Some EIMSE designs are available that have fewer runs than CCDs or BBDs.c. Both the choice of DOE matrix and of factor ranges affect design matrices.d. One shot
How many factors and levels are involved in the paper airplane example?
Which is correct and most complete?a. With m = 3, f7(x) = x2x3.b. This model form contains pure quadratic terms.c. With m = 4, f6(x) = x1 2.d. With m = 5, f2(x) = 1.e. All of the above are correct.f. All of the above are correct except (a) and (e).
Which is correct and most complete?a. Response surface methods cannot model interactions.b. In standard RSM, all factors must be continuous.c. Pure quadratic terms are contained in full quadratic models.d. All of the above are correct.e. All of the above are correct except (a) and (d).
Which is correct and most complete?a. The model form in (c) in Table 13.19 contains one interaction term.b. Using the design matrix and model in (a) and (b) in Table 13.19, X′X is diagonal.c. Using the design matrix and model in (a) and (c) in Table 13.19, X′X is diagonal.d. All of the above
Which is correct and most complete?a. A design matrix based on (a) and (b) in Table 13.19 would be 9 × 4.b. A design matrix based on (a) and (c) in Table 13.19 would be 9 × 4.c. A design matrix based on (a) and (d) in Table 13.19 would be 10 × 6.d. All of the above are correct.e. All of the
Which is correct and most complete?a. In a design matrix, there is a row for every run.b. Functional forms fitted in RSM are not polynomials.c. Linear regression models cannot contain terms like β1 x1 2.d. Linear regression models are linear in all the factors (x’s).e. All of the above are
Which is correct and most complete?a. RSM is mainly relevant for finding which factor changes affect a response.b. Central composite designs have at most three distinct levels of each factor.c. Sequential response surface methods are based on central composite designs.d. All of the above are
Consider the columns of the experimental planning matrix as A, B, C, D, E, F, G, and H. Which of the following is correct and complete?a. For the design in Table 12.2, AB = E.b. For the design in Table 12.2, AB = D.c. For the design in Table 12.4, none of the columns can be obtained by multiplying
Which of the following is correct and most complete?a. A regular fractional factorial with 20 runs is available in the literature.b. A PB design with 16 runs is available in the literature.c. A PB desing with 20 runs is available in the literature.d. All of the above are correct.e. All of the above
Which of the following is correct and most complete?a. The design in Table 12.14 is a regular fractional factorial.b. The design in Table 12.15 is a regular fractional factorial.c. The design in Table 12.14 is a full factorial.d. All of the above are correct.e. All of the above are correct except
Give one generator for the experimental design in Table 12.15.
Illustrate the application of standard screening using a real example.Experimentation can be based on the paper helicopter design implied by the manufacturing SOP in Chapter 2 in Example 2.6.1.a. Include all the information mentioned in Figure 12.1. Define your response explicitly enough such that
Assume n is the number of runs and m is the number of factors. Which is correct and most complete?a. Normal probability plots are often used instead of Lenth’s method for analysis.b. A reason not to use 3 level designs for screening might be that 2 level designs give a relatively high chance of
Suppose that a person experiments using five factors and the eight run regular array. βest = {82.9, –1.125, –0.975, –1.875, 9.825, 0.35, 1.85, 0.55}.a. No factor has a significant effect on the average response with α =0.05.b. One fails to find the 4h factor has a significant effect using
Which is correct and most complete?a. The design in Table 12.14 is a regular fractional factorial.b. In applying DOE, factors of interest are controllable during testing.c. Sometimes, a good mental test of the factors and levels is the experimenter being honestly unsure about which combination in
Standard screening using regular FFs is used and all responses are close together. Which is correct and most complete?a. Likely users did not vary the factors over wide enough ranges.b. The exercise could be useful because likely none of the factors strongly affect the response. That information
Which is correct and most complete?a. People almost never make design decisions using FF experiments.Instead, they use results to pick factors for RSM experiments.b. Lenth’s method is designed to find significance even when interactions exist.c. DOE matrices are completely random collections of
Which is correct and most complete?a. Most software do not print out runs in randomized order.b. If no factors have significant effects, main effects plots are rarely (if ever) useful.c. Sometimes a response of interest can be an average of three individual responses.d. The usage of all runs to
Which is correct and most complete?a. Often, the wider the level spacing, the greater the chance of finding significance.b. Often, the more data used, the greater the chance of finding significance.c. Sometimes finding significance is actually helpful in an important sense.d. All of the above are
Which is correct and most complete?a. It can be reasonable to adjust factor settings of factors not proven to have significant effects using judgment.b. Changing factor x4 does not significantly affect outputs α = 0.05 using IERs.c. Changing factor x6 cannot affect any possible responses of the
Which of the following is correct (within the applied uncertainty)?a. tLenth,5 = 0.97, and we fail to find significance with α = 0.05 even using IERs.b. tLenth,5 = 1.37, and we fail to find significance with α = 0.05 even using IERs.c. tLenth,2 = 4.57, which is significant with α = 0.05, using
Assume m is the number of factors. Which is correct and most complete?a. Regular fractional factorials all have at least one generator.b. The model plotted in an optional step is a highly accurate prediction of outputs.c. The IER takes into account that multiple tests are being done
Which is correct and most complete based on the above table?a. Changing factor x2 over the levels in the experiment can be proven to make a significant difference with IER and α = 0.05.b. In standard screening, a new set of test prototypes is needed for each response.c. Changes in different
Which of the following is correct and most complete based on Table 12.14?a. There are five factors, and the most standard, conservative analysis uses EER.b. Even if four factors had been used, the same A matrix would be applied.c. The matrix used is part of a matrix that can handle as many as 11

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Introduction To Engineering Statistics And Six Sigma 1st Edition Theodore T. Allen - Solutions

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