 17.17.1.1: Calculate the reliability of the system diagram in Figure 17.8.
 17.17.1.2: Calculate the reliability of the system diagram in Figure 17.9.
 17.17.1.3: (a) If four identical components are placed in series, how large mu...
 17.17.1.4: (a) Three components with reliabilities r1 =0.92, r2 =0.95, and r3 ...
 17.17.1.5: Calculate the reliability of the system diagram in Figure 17.10.
 17.17.1.6: Calculate the reliability of the system diagram in Figure 17.11.
 17.17.2.1: A component has an exponential failure time distribution with a mea...
 17.17.2.2: A component has an exponential failure time distribution with a mea...
 17.17.2.3: Four components with mean times to failure of 125 minutes, 60 minut...
 17.17.2.4: A component has a constant hazard rate of 0.2. (a) What is the prob...
 17.17.2.5: A component has a lognormal failure time distribution with paramete...
 17.17.2.6: A component has a lognormal failure time distribution with paramete...
 17.17.2.7: A component has a Weibull failure time distribution with parameters...
 17.17.2.8: A component has a Weibull failure time distribution with parameters...
 17.17.3.1: A set of n =30 components are tested and their average lifetime is ...
 17.17.3.2: Vibration Robustness of Electrical Circuits The failure times in ho...
 17.17.3.3: Thirty computer chips are tested in a sequential manner. A chip is ...
 17.17.3.4: Virus Survival Times The survival times in hours of a virus under c...
 17.17.3.5: DS 17.3.3 contains a data set of failure times, where an asterisk r...
 17.17.3.6: Customer Churn Customer churn is a term used for the attrition of a...
 17.17.5.1: (a) A set of n identical components with reliabilities 0.90 are pla...
 17.17.5.2: Calculate the reliability of the system diagram in Figure 17.20.
 17.17.5.3: The germination time of a seed in days is modeled as having a const...
 17.17.5.4: The failure time of a light bulb in days is modeled as a Weibull di...
 17.17.5.5: Conveyor Belt Malfunctions The times in hours that a conveyor belt ...
 17.17.5.6: Concrete Stress Test The times in minutes taken by n =25 samples of...
 17.17.5.7: Electric Motor Reliabilities DS 17.5.3 contains a data set of failu...
 17.17.5.8: You now know much more about probability and statistics than you di...
Solutions for Chapter 17: Reliability Analysis and Life Testing
Full solutions for Probability and Statistics for Engineers and Scientists  4th Edition
ISBN: 9781111827045
Solutions for Chapter 17: Reliability Analysis and Life Testing
Get Full SolutionsChapter 17: Reliability Analysis and Life Testing includes 28 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. Since 28 problems in chapter 17: Reliability Analysis and Life Testing have been answered, more than 11778 students have viewed full stepbystep solutions from this chapter.

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

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Conidence level
Another term for the conidence coeficient.

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

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 .

Covariance
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 .

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Discrete distribution
A probability distribution for a discrete random variable

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).

Estimate (or point estimate)
The numerical value of a point estimator.

Event
A subset of a sample space.

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.

False alarm
A signal from a control chart when no assignable causes are present

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.

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

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 .