- 17.17.1: Consider X1,X2,...,Xn independent Poisson random variables with par...
- 17.17.2: Consider the following data taken on subgroups of size 5. The data ...
- 17.17.3: Suppose for Review Exercise 17.2 that the buyer has set specication...
- 17.17.4: For the situation of Review Exercise 17.2, give numerical estimates...
- 17.17.5: Consider the data of Table 17.1. Suppose that additional samples of...
- 17.17.6: Consider an in-control process with mean = 25 and =1 .0. Suppose th...
- 17.17.7: Consider the situation of Example 17.2. The following data are take...
- 17.17.8: Samples of size 50 are taken every hour from aprocess producing a c...
- 17.17.9: For the situation of Review Exercise 17.8, suppose that additional ...
- 17.17.10: A quality control eort is being undertaken for a process where larg...
Solutions for Chapter 17: Statistical Quality Control
Full solutions for Probability and Statistics for Engineers and the Scientists | 9th Edition
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
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.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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.
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 .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Another name for factors that are arranged in a factorial experiment.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
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.
Fraction defective control chart
See P chart
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.