- 14.3.1E: ?An article in Industrial Quality Control (1956, pp. 5–8) describes...
- 14.3.2E: ?An engineer suspects that the surface finish of metal parts is inf...
- 14.3.3E: ?In the book Design and Analysis of Experiments, 8th edition (2012,...
- 14.3.4E: ?An experiment was conducted to determine whether either firing tem...
- 14.3.5E: ?An article in Technometrics [“Exact Analysis of Means with Unequal...
- 14.3.6E: ?Johnson and Leone (Statistics and Experimental Design in Engineeri...
- 14.3.7E: ?An article in the IEEE Transactions on Electron Devices (November ...
- 14.3.8E: ?An article in the Journal of Testing and Evaluation (1988, Vol. 16...
- 14.3.9E: ?Consider a two-factor factorial experiment. Develop a formula for ...
- 14.3.10E: ?14-10. An article in Journal of Chemical Technology and Biotechnol...
- 14.3.11E: ?An article in Bioresource Technology [“Quantitative Response of Ce...
Solutions for Chapter 14.3: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
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.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
See Control chart.
Another name for factors that are arranged in a factorial experiment.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
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.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.