- 13.3.34E: An article in the Journal of the Electrochemical Society [1992, Vol...
- 13.3.35E: A textile mill has a large number of looms. Each loom is supposed t...
- 13.3.36E: In the book Bayesian Inference in Statistical Analysis (1973, John ...
- 13.3.37E: An article in the Journal of Quality Technology [1981, Vol. 13(2), ...
- 13.3.38E: Consider the vapor-deposition experiment described in Exercise 13-3...
- 13.3.39E: Consider the cloth experiment described in Exercise 13-35.(a) Estim...
- 13.3.40E: Reconsider Exercise 13-8 in which the effect of different circuits ...
- 13.3.41E: Reconsider Exercise 13-15 in which the effect of different diets on...
Solutions for Chapter 13.3: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
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.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Defects-per-unit control chart
See U chart
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
The amount of variability exhibited by data
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Exponential random variable
A series of tests in which changes are made to the system under study
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on