 14.1: A random variable whose distribution function is given by F(t) = 1 ...
 14.2: If X and Y are independent random variables having failure rate fun...
 14.3: The lung cancer rate of a tyearold male smoker, (t), is such that...
 14.4: Suppose the life distribution of an item has failure rate function ...
 14.5: A continuous life distribution is said to be an IFR (increasing fai...
 14.6: Show that the uniform distribution on (a, b) is an IFR distribution.
 14.7: For the model of Section 14.3.1, explain how the following figure c...
 14.8: When 30 transistors were simultaneously put on a life test that was...
 14.9: Consider a test of H0 : = 0 versus H1 : _= 0 for the model of Secti...
 14.10: Suppose 30 items are put on test that is scheduled to stop when the...
 14.11: Suppose that 20 items are to be put on test that is to be terminate...
 14.12: Vacuum tubes produced at a certain plant are assumed to have an und...
 14.13: A oneatatime sequential life testing scheme is scheduled to run ...
 14.14: Using the fact that a Poisson process results when the times betwee...
 14.15: From a sample of items having an exponential life distribution with...
 14.16: Verify that the maximum likelihood estimate corresponding to Equati...
 14.17: A testing laboratory has facilities to simultaneously life test 5 c...
 14.18: Suppose that the remission time, in weeks, of leukemia patients tha...
 14.19: In 17, suppose that prior to the testing phase and based on past ex...
 14.20: What is the Bayes estimate of = 1/ in if the prior distribution on ...
 14.21: The following data represent failure times, in minutes, for two typ...
 14.22: Suppose that the life distributions of two types of transistors are...
 14.23: If X is a Weibull random variable with parameters (, ), show that E...
 14.24: Show that if X is a Weibull random variable with parameters (, ), t...
 14.25: If the following are the sample data from a Weibull population havi...
 14.26: Show that if X is a Weibull random variable with parameters (, ), t...
 14.27: If U is uniformly distributed on (0, 1) that is, U is a random numb...
 14.28: If X is a continuous random variable having distribution function F...
 14.29: Let X(i) denote ith smallest of a sample of size n from a continuou...
 14.30: If U is uniformly distributed on (0, 1), show that logU has an expo...
Solutions for Chapter 14: Life Testing
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists  5th Edition
ISBN: 9780123948113
Solutions for Chapter 14: Life Testing
Get Full SolutionsChapter 14: Life Testing includes 30 full stepbystep solutions. Since 30 problems in chapter 14: Life Testing have been answered, more than 3558 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics for Engineers and Scientists, edition: 5. Introduction to Probability and Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780123948113.

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).

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Bimodal distribution.
A distribution with two modes

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

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.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Continuous distribution
A probability distribution for a continuous random variable.

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.

Control limits
See Control chart.

Cook’s distance
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.

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Expected value
The expected value of a random variable X is its longterm 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.

Experiment
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.

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

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.

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
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