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applied statistics and multivariate
Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions
An chart uses samples of size 4.The center line is at 100, and the upper and lower 3-sigma control limits are at 106 and 94, respectively.(a) What is the process ?(b) Suppose the process mean shifts to 96.Find the probability that this shift will be detected on the next sample.(c) Find the ARL to
An X chart uses samples of size 1.The center line is at 100 and the upper and lower 3-sigma limits are at 112 and 88, respectively.(a) What is the process ?(b) Suppose the process mean shifts to 96.Find the probability that this shift will be detected on the next sample.(c) Find the ARL to detect
Use other statistical process control problem-solving tools
Construct and interpret a cumulative sum and exponentially weighted moving average control chart
Calculate the ARL performance for a Shewhart control chart
Calculate and interpret process capability ratios
Construct and interpret control charts for attributes such as P and U charts
Construct and interpret control charts for variables such as , R, S, and individuals charts
Understand the general form of a Shewhart control chart and how to apply zone rules (such as the Western Electric rules) and pattern analysis to detect assignable causes
Understand the different types of variability, rational subgroups, and how a control chart is used to detect assignable causes
Understand the role of statistical tools in quality improvement
An article in the Journal of Quality Technology (Vol. 17, 1985, pp. 198–206) describes the use of a replicated fractional factorial to investigate the effect of five factors on the free height of leaf springs used in an automotive application. The factors are A furnace temperature, B heating
Construct a design in eight runs. What are the alias relationships in this design?
Construct a design in 16 runs. What are the alias relationships in this design?
Construct a design for the problem in Exercise 14-67.Select the data for the eight runs that would have been required for this design. Analyze these data and compare your conclusions to those obtained in Exercise 14-67 for the full factorial.
Construct a design for the problem in Exercise 14-66.Select the data for the eight runs that would have been required for this design. Analyze these runs and compare your conclusions to those obtained in Exercise 14-66 for the full factorial.
An article in the Journal of Radioanalytical and Nuclear Chemistry (2008, Vol. 276, No. 2, pp. 323–328)presented a 284 fractional factorial design to identify sources of Pu contamination in the radioactivity material analysis of dried shellfish at the National Institute of Standards and
Consider the 262 design in Table 14-29.(a) Suppose that after analyzing the original data, we find that factors C and E can be dropped. What type of 2k design is left in the remaining variables?(b) Suppose that after the original data analysis, we find that factors D and F can be dropped. What type
For each of the following designs write down the aliases, assuming that only main effects and two factor interactions are of interest.(a) (b)
Suppose that in Exercise 14-14 only a 1⁄4 fraction of the 25 design could be run. Construct the design and analyze the data that are obtained by selecting only the response for the eight runs in your design.
An article in Quality Engineering [“Designed Experiment to Stabilize Blood Glucose Levels” (1999–2000, Vol. 12, pp. 83–87)] reported on an experiment to minimize variations in blood glucose levels. The factors were: volume of juice intake before exercise (4 or 8 oz), amount of exercise on a
Consider the 26 factorial design. Set up a design to be run in four blocks of 16 runs each. Show that a design that confounds three of the four-factor interactions with blocks is the best possible blocking arrangement.
Construct a 25 design in four blocks. Select the appropriate effects to confound so that the highest possible interactions are confounded with blocks.
Consider the data from the first replicate of Exercise 14-13, assuming that four blocks are required. Confound ABD and ABC (and consequently CD) with blocks.(a) Construct a design with four blocks of four observations each.(b) Analyze the data.
Construct a 25 design in two blocks. Select the ABCDE interaction to be confounded with blocks.
Consider the data from Exercise 14-18.(a) Construct the design that would have been used to run this experiment in two blocks of eight runs each.(b) Analyze the data and draw conclusions.
Consider the data from the first replicate of Exercise 14-13.(a) Construct a design with two blocks of eight observations each, with ABCD confounded.(b) Analyze the data.
Consider the data from the first replicate of Exercise 14-12.(a) Suppose that these observations could not all be run under the same conditions. Set up a design to run these observations in two blocks of four observations each, with ABC confounded.(b) Analyze the data.
Use response surface methodology for process optimization experiments
Test for curvature in two-level factorial designs by using center points
Design and conduct two-level fractional factorial designs
Understand how two-level factorial designs can be run in blocks
Know how to use the two-level series of factorial designs
Assess model adequacy with residual plots
Understand how the ANOVA is used to analyze the data from these experiments
Know how to analyze and interpret main effects and interactions
Design and conduct engineering experiments involving several factors using the factorial design approach
Suppose that five normal populations have common variance 2 100 and means 1 175, 2 190, 3 160, 4 200, and 5 215.How many observations per population must be taken so that the probability of rejecting the hypothesis of equality of means is at least 0.95? Use 0.01.
Suppose that four normal populations have common variance 2 25 and means 1 50, 2 60, 3 50, and 4 60.How many observations should be taken on each population so that the probability of rejecting the hypothesis of equality of means is at least 0.90? Use 0.05.
(a) Apply Fisher’s LSD method to the data on protein content of milk in Exercise 13-13.Which diets differ? Use(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Apply Fisher’s LSD method to the domain spacing data in Exercise 13-12.Which cross-linker levels differ?Use(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Apply Fisher’s LSD method to the air void experiment described in Exercise 13-11.Using 0.05, which treatment means are different?(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Apply Fisher’s LSD method with 0.05 to the superconducting material experiment described in Exercise 13-10.Which preparation methods differ?(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with 0.01 to analyze the five means for the coating types described in Exercise 13-7.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with to analyze the mean amounts of radon released in the experiment described in Exercise 13-8.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with 0.05 to analyze the mean compressive strength of the four mixing techniques in Exercise 13-5.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with 0.01 to analyze the mean response times for the three circuits described in Exercise 13-6.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with 0.05 to analyze the means of the five different levels of cotton content in Exercise 13-3.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
(a) Use Fisher’s LSD method with 0.05 to analyze the means of the three types of chocolate in Exercise 13-4.(b) Use the graphical method to compare means described in this section and compare your conclusions to those from Fisher’s LSD method.
Design and conduct experiments involving the randomized complete block design
Understand the blocking principle and how it is used to isolate the effect of nuisance factors
Estimate variance components in an experiment involving random factors
Understand the difference between fixed and random factors
Make decisions about sample size in single-factor experiments
Use multiple comparison procedures to identify specific differences between means
Assess model adequacy with residual plots
Understand how the analysis of variance is used to analyze the data from these experiments
Design and conduct engineering experiments involving a single factor with an arbitrary number of levels
Exercise 12-5 introduced the hospital patient satisfaction survey data. One of the variables in that data set is a categorical variable indicating whether the patient is a medical patient or a surgical patient. Fit a model including this indicator variable to the data, using all three of the other
An article in the Journal of the American Ceramics Society (1992, Vol. 75, pp. 112–116) describes a process for immobilizing chemical or nuclear wastes in soil by dissolving the contaminated soil into a glass block. The authors mix CaO and Na2O with soil and model viscosity and electrical
Tables 12-23 and 12-24 present statistics for the Major League Baseball 2005 season (source: The Sports Network).(a) Consider the batting data. Use model-building methods to predict Wins from the other variables. Check that the assumptions for your model are valid.(b) Repeat part (a) for the
A multiple regression model was used to relate y viscosity of a chemical product to x1 temperature and x2 reaction time. The data set consisted of n 15 observations.(a) The estimated regression coefficients were and . Calculate an estimate of mean viscosity when x1 100°F and x2 2 hours.(b) The
Consider the electronic inverter data in Exercise 12-98 and 12-99.Define the response and regressors variables as in Exercise 12-99, and delete the second observation in the sample.(a) Use all possible regressions to find the equation that minimizes Cp.(b) Use all possible regressions to find the
Consider the jet engine thrust data in Exercise 12-96 and 12-97.Define the response and regressors as in Exercise 12-97.(a) Use all possible regressions to select the best regression equation, where the model with the minimum value of MSE is to be selected as “best.’’(b) Repeat part (a) using
The data shown in Table 12-22 represent the thrust of a jet-turbine engine (y) and six candidate regressors: x1 =primary speed of rotation, x2 secondary speed of rotation, x3 fuel flow rate, x4 pressure, x5 exhaust temperature, and x6 ambient temperature at time of test.(a) Fit a multiple linear
A sample of 25 observations is used to fit a regression model in seven variables. The estimate of 2 for this full model is MSE 10.(a) A forward selection algorithm has put three of the original seven regressors in the model. The error sum of squares for the three-variable model is SSE 300.Based on
We have used a sample of 30 observations to fit a regression model. The full model has nine regressors, the variance estimate is and .(a) Calculate the F-statistic for testing significance of regression. Using = 0.05, what would you conclude?(b) Suppose that we fit another model using only four of
Consider the data in Exercise 12-75.Use all the terms in the full quadratic model as the candidate regressors.(a) Use forward selection to identify a model.(b) Use backward elimination to identify a model.(c) Compare the two models obtained in parts (a) and (b).Which model would you prefer and
When fitting polynomial regression models, we often subtract from each x value to produce a “centered’’regressor . This reduces the effects of dependencies among the model terms and often leads to more accurate estimates of the regression coefficients. Using the data from Exercise 12-72, fit
Consider the gas mileage data in Exercise 12-7.Build regression models for the data from the numerical regressors using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models obtained. Which model would
Consider the arsenic data in Exercise 12-12.Use arsenic in nails as the response and age, drink use, and cook use as the regressors. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward
Use the football data in Exercise 12-17 to build regression models using the following techniques:(a) All possible regressions. Find the equations that minimize MSE and that minimize Cp.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the various models
Consider the NHL data in Exercise 12-18.Build regression models for these data with regressors GF through FG using the following methods:(a) All possible regressions. Find the minimum Cp and minimum MSE equations.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Which model
Consider the stack loss data in Exercise 12-16.Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models obtained. Which model would you prefer? Why?(f) Remove any
Consider the nisin extraction data in Exercise 12-14.Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models obtained. Which model would you prefer? Why?
Consider the grey range modulation data in Exercise 12-15.Use the useful range as the response. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models obtained.
Consider the wire bond pull strength data in Exercise 12-8.Build regression models for the data using the following methods:(a) All possible regressions. Find the minimum Cp and minimum MSE equations.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-13.Use density as the response. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment
Consider the electric power data in Exercise 12-6.Build regression models for the data using the following techniques:(a) All possible regressions. Find the minimum Cp and minimum MSE equations.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models
Consider the X-ray inspection data in Exercise 12-11.Use rads as the response. Build regression models for the data using the following techniques:(a) All possible regressions.(b) Stepwise regression.(c) Forward selection.(d) Backward elimination.(e) Comment on the models obtained. Which model
Consider the surface finish data in Example 12-15.Test the hypothesis that two different regression models (with different slopes and intercepts) are required to adequately model the data. Use indicator variables in answering this question.
Consider the gasoline mileage data in Exercise 12-7.(a) Discuss how you would model the information about the type of transmission in the car.(b) Fit a regression model to the gasoline mileage using cid, etw, and the type of transmission in the car as the regressors.(c) Is there evidence that the
Consider the arsenic concentration data in Exercise 12-10.(a) Discuss how you would model the information about the person’s sex.(b) Fit a regression model to the arsenic in nails using age, drink use, cook use, and the person’s sex as the regressors.(c) Is there evidence that the person’s
The diagonal elements of the hat matrix are often used to denote leverage—that is, a point that is unusual in its location in the x-space and that may be influential. Generally, the ith point is called a leverage point if its hat diagonal hii exceeds 2p/n, which is twice the average size of all
Consider the regression model for the NHL data from Exercise 12-18.(a) Fit a model using GF as the only regressor.(b) How much variability is explained by this model?(c) Plot the residuals versus and comment on model adequacy.(d) Plot the residuals from part (a) versus PPGF, the points scored while
Consider the semiconductor HFE data in Exercise 12-9.(a) Plot the residuals from this model versus . Comment on the information in this plot.(b) What is the value of R2 for this model?(c) Refit the model using log HFE as the response variable.(d) Plot the residuals versus predicted log HFE for the
Fit a model to the response PITCH in the heat treating data of Exercise 12-10 using new regressors x1 SOAKTIME SOAKPCT and x2 DIFFTIME DIFFPCT.(a) Calculate the R2 for this model and compare it to the value of R2 from the original model in Exercise 12-10.Does this provide some information about
Consider the bearing wear data in Exercise 12-19.(a) Find the value of R2 when the model uses the regressors x1 and x2.(b) What happens to the value of R2 when an interaction term x1x2 is added to the model? Does this necessarily imply that adding the interaction term is a good idea?
Consider the stack loss data in Exercise 12-16.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot the residuals versus and versus each regressor, and comment on model
Consider the regression model fit to the grey range modulation data in Exercise 12-15.Use the useful range as the response.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c)
Consider the regression model fit to the nisin extraction data in Exercise 12-14.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot the residuals versus and versus each
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-13.Use density as the response.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot
Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot the residuals versus and versus
Consider the regression model fit to the arsenic data in Exercise
Consider the regression model fit to the X-ray inspection data in Exercise 12-11.Use rads as the response.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot the residuals
Consider the regression model for the heat treating data in Exercise 12-10.(a) Calculate the percent of variability explained by this model.(b) Construct a normal probability plot for the residuals.Comment on the normality assumption.(c) Plot the residuals versus and interpret the display.(d)
Consider the regression model for the NFL data in Exercise 12-17.(a) What proportion of totalvariability is explained by this model?(b) Construct a normal probability plot of the residuals. What conclusion can you draw from this plot?(c) Plot the residuals versus and versus each regressor, and
Consider the electric power consumption data in Exercise 12-6.(a) Calculate R2 for this model. Interpret this quantity.(b) Plot the residuals versus and versus each regressor.Interpret this plot.(c) Construct a normal probability plot of the residuals and comment on the normality assumption.
Consider the gasoline mileage data in Exercise 12-7.(a) What proportion of total variability is explained by this model?(b) Construct a normal probability plot of the residuals and comment on the normality assumption.(c) Plot residuals versus and versus each regressor. Discuss these residual
Consider the NHL data in Exercise 12-18.(a) Find a 95% confidence interval on the regression coefficient for the variable GF.(b) Fit a simple linear regression model relating the response variable W to the regressor GF.(c) Find a 95% confidence interval on the slope for the simple linear regression
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