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# Solutions for Chapter 14: Statistical Process Control

## Full solutions for Elementary Statistics | 12th Edition

ISBN: 9780321836960

Solutions for Chapter 14: Statistical Process Control

Solutions for Chapter 14
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##### ISBN: 9780321836960

This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. Since 10 problems in chapter 14: Statistical Process Control have been answered, more than 199275 students have viewed full step-by-step solutions from this chapter. Chapter 14: Statistical Process Control includes 10 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• Bimodal distribution.

A distribution with two modes

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• 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.

• Confounding

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.

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• Contrast

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.

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Discrete distribution

A probability distribution for a discrete random variable

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Error of estimation

The difference between an estimated value and the true value.

• Error sum of squares

In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.

• Exponential random variable

A series of tests in which changes are made to the system under study

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

• Hat matrix.

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 .

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