Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
An engineer is interested in the effect of cutting speed (A), metal hardness (B), and cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of a 23 factorial design are run. The tool life data (in hours) are shown in the following table. (a)

Applied Statistics and Probability for Engineers 6
Four factors are thought to influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two levels, producing a 24 design. At each run in the design, samples of the beverage are given to a test

Applied Statistics and Probability for Engineers 6
The following data represent a single replicate of a 25 design that is used in an experiment to study the compressive strength of concrete. The factors are mix (A), time (B), laboratory (C), temperature (D), and drying time (E).

Applied Statistics and Probability for Engineers 6
An article in IEEE Transactions on Semiconductor Manufacturing (1992, Vol. 5, pp. 214222) described an experiment to investigate the surface charge on a silicon wafer. The factors thought to influence induced surface charge are cleaning method (spin rinse dry or SRD and spin dry or SD) and the positi

Applied Statistics and Probability for Engineers 6
An article in Oikos: A Journal of Ecology [Regulation of Root Vole Population Dynamics by Food Supply and Predation: A Two-Factor Experiment (2005, Vol. 109, pp. 387395)] investigated how food supply interacts with predation in the regulation of root vole (Microtus oeconomus Pallas) population dynami

Applied Statistics and Probability for Engineers 6
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, large), \(B=\) exposure time (\(20 \%\) below nominal, \(20 \%\) above nominal), \(C=\) development

Applied Statistics and Probability for Engineers 6
An experiment described by M. G. Natrella in the National Bureau of Standards Handbook of Experimental Statistics (1963, No. 91) involves lame-testing fabrics after applying fire-retardant treatments. The four factors considered are type of fabric (A), type of ire-retardant treatment (B), laundering

Applied Statistics and Probability for Engineers 6
Consider the data from Exercise 14-14. Suppose that the data from the second replicate were not available. Analyze the data from replicate I only and comment on your findings.

Applied Statistics and Probability for Engineers 6
A \(2^{4}\) factorial design was run in a chemical process. The design factors are \(A=\) time, \(B=\) concentration, \(C=\) pressure, and \(D=\) temperature. The response variable is yield. The data follow: (a) Estimate the factor effects. Based on a normal probability plot of the effect

Applied Statistics and Probability for Engineers 6
An experiment has run a single replicate of a 24 design and calculated the following factor effects: (a) Construct a normal probability plot of the effects. (b) Identify a tentative model, based on the plot of effects in part (a). (c) Estimate the regression coefficients in this model, assumi

Applied Statistics and Probability for Engineers 6
A two-level factorial experiment in four factors was conducted by Chrysler and described in the article Sheet Molded Compound Process Improvement by P. I. Hsieh and D. E. Goodwin (Fourth Symposium on Taguchi Methods, American Supplier Institute, Dearborn, MI, 1986, pp. 1321). The purpose was to reduc

Applied Statistics and Probability for Engineers 6
Problem 25E Consider a 22 factorial experiment with four center points. The data are (1) = 21, a = 125, b = 154, ab = 352, and the responses at the center point are 92, 130, 98, 152. Compute an ANOVA with the sum of squares for curvature and conduct an F-test for curvature. Use ? = 0.05.

Applied Statistics and Probability for Engineers 6
Consider the experiment in Exercise 14-16. Suppose that a center point with five replicates is added to the factorial runs and the responses are 2800, 5600, 4500, 5400, 3600. Compute an ANOVA with the sum of squares for curvature and conduct an \(\text { F-test }\) for curvature. Use \(\alpha=0.05\)

Applied Statistics and Probability for Engineers 6
Consider the experiment in Exercise 14-19. Suppose that a center point with five replicates is added to the factorial runs and the responses are 45, 40, 41, 47, and 43. (a) Estimate the experimental error using the center points. Compare this to the estimate obtained originally in Exercise 14-19 by

Applied Statistics and Probability for Engineers 6
An article in Talanta (2005, Vol. 65, pp. 895899) presented a \(2^3\) factorial design to ind lead level by using lame atomic absorption spectrometry (FAAS). The data are in the following table. The factors and levels are in the following table. (a) Construct a normal probabi

Applied Statistics and Probability for Engineers 6
An experiment to study the effect of machining factors on ceramic strength was described at www.itl.nist.gov/div898/handbook/. Five factors were considered at two levels each: \(A=\) Table Speed, \(B=\) Down Feed Rate, \(C=\) Wheel Grit, \(D=\) Direction, \(E=\) Batch. The response is the average of

Applied Statistics and Probability for Engineers 6
Consider the following computer output for a \(2^{3}\) factorial experiment. (a) How many replicates were used in the experiment? (b) Use the appropriate equation to calculate the standard error of a coefficient. (c) Calculate the entries marked with ? in the output. Equation Transcrip

Applied Statistics and Probability for Engineers 6
Consider the following computer output for one replicate of a \(2^{4}\) factorial experiment. (a) What effects are used to estimate error? (b) Calculate the entries marked with ? in the output. Equation Transcription: Text T

Applied Statistics and Probability for Engineers 6
An article in Bioresource Technology (Influence of Vegetable Oils Fatty-Acid Composition on Biodiesel Optimization, (2011, Vol. 102(2), pp. 10591065)] described an experiment to analyze the influence of the fatty-acid composition on biodiesel. Factors were the concentration of catalyst, amount of met

Applied Statistics and Probability for Engineers 6
An article in Analytica Chimica Acta [Design-of-Experiment Optimization of Exhaled Breath Condensate Analysis Using a Miniature Differential Mobility Spectrometer (DMS) (2008, Vol. 628(2), pp. 155161)] examined four parameters that affect the sensitivity and detection of the analytical instruments us