 4.12.1E: Vendor A supplies parts, each of which has probability 0.03 of bein...
 4.12.2E: There are two competing designs for a certain semiconductor circuit...
 4.12.3E: Rectangular plates are manufactured whose lengths are distributed N...
 4.12.4E: A cable is made up of four wires. The breaking strength of each wir...
 4.12.5E: The lifetime of a laser (in hours) is lognormally distributed with ...
 4.12.6E: Estimating the value of ?. The following figure suggests how to est...
 4.12.7E: Application to mobile computer networks. Computer scientists often ...
 4.12.8E: Refer to Example 4.81 (page 310). In order to increase the lifetime...
 4.12.9E: A system consists of components A and B connected in series, as sho...
 4.12.10E: A system consists of two subsystems connected in series, as shown i...
 4.12.11E: (Continues Exercise 20 in Section 4.11.) The age of an ancient piec...
 4.12.12E: A random sample will be drawn from a normal distribution, for the p...
 4.12.13E: A random sample of size 8 is taken from a Exp (?) distribution, whe...
Solutions for Chapter 4.12: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists  4th Edition
ISBN: 9780073401331
Solutions for Chapter 4.12
Get Full SolutionsSince 13 problems in chapter 4.12 have been answered, more than 243183 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Chapter 4.12 includes 13 full stepbystep solutions.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Biased estimator
Unbiased estimator.

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

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.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

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

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

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

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Fraction defective control chart
See P chart

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Generator
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 mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .