 8.6.1.2.1: Show that the matrix Q defined by equation (8.133) is a DTMC matrix.
 8.6.1.2.2: Show that with condition (8.135), Q is an aperiodic matrix.
 8.6.1.2.3: Perform steadystate analysis of the CTMC model in Example 8.23 (Fi...
 8.6.1.2.4: Apply the power method to the CTMC of Figure 8.P.4 to obtain an exp...
 8.6.1.2.5: Suppose that we are interested in computing the derivative d/d with...
 8.6.1.2.6: Show that the GaussSeidel iteration matrix for the CTMC of Figure 8...
Solutions for Chapter 8.6.1.2: Successive Overrelaxation (SOR).
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications  2nd Edition
ISBN: 9781119285427
Solutions for Chapter 8.6.1.2: Successive Overrelaxation (SOR).
Get Full SolutionsChapter 8.6.1.2: Successive Overrelaxation (SOR). includes 6 full stepbystep solutions. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427. This expansive textbook survival guide covers the following chapters and their solutions. Since 6 problems in chapter 8.6.1.2: Successive Overrelaxation (SOR). have been answered, more than 1033 students have viewed full stepbystep solutions from this chapter.

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

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

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

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

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.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

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

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

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

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Error variance
The variance of an error term or component in a model.

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.

Experiment
A series of tests in which changes are made to the system under study

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

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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