- 3.8.1: Given n random numbers u1, u2,...,un, derive an expression for a ra...
- 3.8.2: Compare the TMR/simplex reliability with two-component and three-co...
- 3.8.3: Repeat problem 2 for two and three component parallel redundant sys...
- 3.8.4: Show that the reliability expression (3.78) for k-out-of-n system r...
- 3.8.5: Using equation (3.80) obtain an explicit expression for the reliabi...
Solutions for Chapter 3.8: Distribution Of Sums
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
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.
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.
The mean of the conditional probability distribution of a random variable.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
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 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
An expression sometimes used for nonlinear regression models or polynomial regression models.
Defects-per-unit control chart
See U chart
A subset of effects in a fractional factorial design that deine the aliases in the design.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A series of tests in which changes are made to the system under study
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.
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 .