 147.1413: An engineer is interested in the effect of cutting speed (A), metal...
 147.1414: Four factors are thought to influence the taste of a softdrink beve...
 147.1415: 1415. Consider the experiment in Exercise 1414. Determine an appr...
 147.1416: The data shown here represent a single replicate of a 25 design tha...
 147.1417: . 1417. An article in the IEEE Transactions on Semiconductor Manuf...
 147.1418: An experiment described by M. G. Natrella in the National Bureau of...
 147.1419: 1419. An experiment was run in a semiconductor fabrication plant i...
 147.1420: Consider the data from Exercise 1413. I suppose that the data from...
 147.1421: . 1421. An experiment has run a single replicate of a 24 design an...
 147.1422: A 24 factorial design was run in a chemical process. The design fac...
Solutions for Chapter 147: 2k FACTORIAL DESIGNS
Full solutions for Applied Statistics and Probability for Engineers  3rd Edition
ISBN: 9780471204541
Solutions for Chapter 147: 2k FACTORIAL DESIGNS
Get Full SolutionsChapter 147: 2k FACTORIAL DESIGNS includes 10 full stepbystep solutions. Since 10 problems in chapter 147: 2k FACTORIAL DESIGNS have been answered, more than 18427 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Average
See Arithmetic mean.

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Continuous distribution
A probability distribution for a continuous random variable.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Discrete distribution
A probability distribution for a discrete random variable

Error propagation
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .