- 18.104.22.168: Consider a variation of the two-state availability model (Example 8...
- 22.214.171.124: Consider another variation of the two-state availability model wher...
- 126.96.36.199: Show that the equivalent repair rate eq for the availability model ...
- 188.8.131.52: In the two-component availability model of Figure 8.27, we assumed ...
- 184.108.40.206: For the parallel redundant system with non-zero detection delay (Ex...
- 220.127.116.11: For the WFS example, plot the steady-state, instantaneous, and inte...
- 18.104.22.168: For the preventive maintenance problem (Example 8.20), derive an ex...
- 22.214.171.124: Consider an approximation for the CTMC model of Example 8.21 where ...
Solutions for Chapter 8.4.1: Availability Models
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).
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.
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
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 attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error of estimation
The difference between an estimated value and the true value.
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.
The variance of an error term or component in a model.
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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