- 184.108.40.206.1: Show that the matrix Q defined by equation (8.133) is a DTMC matrix.
- 220.127.116.11.2: Show that with condition (8.135), Q is an aperiodic matrix.
- 18.104.22.168.3: Perform steady-state analysis of the CTMC model in Example 8.23 (Fi...
- 22.214.171.124.4: Apply the power method to the CTMC of Figure 8.P.4 to obtain an exp...
- 126.96.36.199.5: Suppose that we are interested in computing the derivative d/d with...
- 188.8.131.52.6: Show that the GaussSeidel iteration matrix for the CTMC of Figure 8...
Solutions for Chapter 184.108.40.206: Successive Overrelaxation (SOR).
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.
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
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).
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
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.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
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.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
An expression sometimes used for nonlinear regression models or polynomial regression models.
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).
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
A subset of a sample space.
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.
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 random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.