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Solutions for Chapter 15.6: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers  6th Edition
ISBN: 9781118539712
Solutions for Chapter 15.6
Get Full SolutionsThis textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Chapter 15.6 includes 10 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 10 problems in chapter 15.6 have been answered, more than 162350 students have viewed full stepbystep solutions from this chapter. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Addition rule
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).

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

Coeficient of determination
See R 2 .

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.

Conditional mean
The mean of the conditional probability distribution of a random variable.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Density function
Another name for a probability density function

Dependent variable
The response variable in regression or a designed experiment.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

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.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials