- 220.127.116.11: Consider a variation of the two-state availability model (Example 8...
- 18.104.22.168: Consider another variation of the two-state availability model wher...
- 22.214.171.124: Show that the equivalent repair rate eq for the availability model ...
- 126.96.36.199: In the two-component availability model of Figure 8.27, we assumed ...
- 188.8.131.52: For the parallel redundant system with non-zero detection delay (Ex...
- 184.108.40.206: For the WFS example, plot the steady-state, instantaneous, and inte...
- 220.127.116.11: For the preventive maintenance problem (Example 8.20), derive an ex...
- 18.104.22.168: 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 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
`-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).
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
A distribution with two modes
Bivariate normal distribution
The joint distribution of two normal random variables
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
A matrix that provides the tests that are to be conducted in an experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete random variable
A random variable with a inite (or countably ininite) range.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.