- 14-7.14-13: An engineer is interested in the effect of cutting speed (A), metal...
- 14-7.14-14: Four factors are thought to influence the taste of a softdrink beve...
- 14-7.14-15: 14-15. Consider the experiment in Exercise 14-14. Determine an appr...
- 14-7.14-16: The data shown here represent a single replicate of a 25 design tha...
- 14-7.14-17: . 14-17. An article in the IEEE Transactions on Semiconductor Manuf...
- 14-7.14-18: An experiment described by M. G. Natrella in the National Bureau of...
- 14-7.14-19: 14-19. An experiment was run in a semiconductor fabrication plant i...
- 14-7.14-20: Consider the data from Exercise 14-13. I suppose that the data from...
- 14-7.14-21: . 14-21. An experiment has run a single replicate of a 24 design an...
- 14-7.14-22: A 24 factorial design was run in a chemical process. The design fac...
Solutions for Chapter 14-7: 2k FACTORIAL DESIGNS
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
`-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 chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
See Arithmetic mean.
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.
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.
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
A probability distribution for a continuous random variable.
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.
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.
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.
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 .
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.
A probability distribution for a discrete random variable
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.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
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.
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 .