- 3.7.1: A system with three independent components works correctly if at le...
- 3.7.2: A multiprocessor system has n processors. Service time of a process...
- 3.7.3: Consider a series system consisting of n independent components. As...
- 3.7.4: Consider a random access memory card consisting of d VLSI chips, ea...
- 3.7.5: The memory requirement distribution for jobs in a computer system i...
- 3.7.6: Redo the above example assuming that the memory requirement distrib...
- 3.7.7: A series system has n independent components. For i = 1, 2,...,n, t...
- 3.7.8: Consider a system with n independent components each having the mod...
- 3.7.9: Repeat problem 8 above with the defective exponential distribution ...
Solutions for Chapter 3.7: Order Statistics
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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 study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A distribution with two modes
Bivariate normal distribution
The joint distribution of two normal random variables
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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 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.
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.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
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.
Another name for factors that are arranged in a factorial experiment.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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).
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .