- 5.1.1: Consider a fault-tolerant multiprocessor computer system with two p...
- 5.1.2: Consider again the problem of 1M (1-megabyte) RAM chips supplied by...
- 5.1.3: Consider the operation of an online file updating system [MEND 1979...
- 5.1.4: X1 and X2 are independent random variables with Poisson distributio...
- 5.1.5: Let the execution times X and Y of two independent parallel process...
Solutions for Chapter 5.1: Introduction
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
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 attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
The probability of an event given that the random experiment produces an outcome in another event.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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.
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.
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 model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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.
A property of a collection of events that indicates that their union equals the sample space.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .
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