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Some Continuous Univariate Probability Distributions

Posted by on 14/ 11/ 15

Several continuous PDFs are used frequently in reliability analysis. They in­clude normal, lognormal, gamma, Weibull, and exponential distributions. Other distributions, such as beta and extremal distributions, also are used sometimes.

The relations among the various continuous distributions considered in this chapter and others are shown in Fig. 2.15.

1.6.1 Normal (Gaussian) distribution

The normal distribution is a well-known probability distribution involving two parameters: the mean and variance. A normal random variable having the mean /гх and variance a2 is denoted herein as X ~ N (tx, ax) with the PDF

Подпись: 2Подпись: 1 {x Hx 2 V ax Подпись: for —TO < x < TO (2.58)fN (x | tx, ax2) = —І— exp ■sj2n ax

The relationship between tx and ax and the L-moments are tx = Л1 and

ax = рЯ^2.

The normal distribution is bell-shaped and symmetric with...

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Poisson distribution

Posted by on 14/ 11/ 15

The Poisson distribution has the PMF as

e — vV x

px(x | v) =—;— for x = 0,1,2,… (2.53)

x!

where the parameter v > 0 represents the mean of a Poisson random variable. Unlike the binomial random variables, Poisson random variables have no upper bound. A recursive formula for calculating the Poisson PMF is (Drane et al., 1993)

Px (x | v) = (X) Px (x — 11 v) = Rp (x) Px (x — 11 v) for x = 1,2,… (2.54)

with px(x = 0 | v) = e—v and RP (x) = v/x. When v and p ^ 0 while np = v = constant, the term RB (x) in Eq. (2.52) for the binomial distribution becomes RP (x) for the Poisson distribution. Tietjen (1994) presents a simple recursive scheme for computing the Poisson cumulative probability.

For a Poisson random variable, the mean and the variance are identical to v...

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Wafer Quality Specialist

Posted by on 14/ 11/ 15

If a site lacks water, it is important to deter­
mine the cost of obtaining it. If the site is served by the local municipality, the water company may be able to give you an estimate. If the site is rocky, you may need to excavate trenches by blasting the surrounding rock. If you must drill a well, the neighbors or the local well driller can inform you of the depth of surrounding wells and give you information about water quality. If the site already contains a well, ensure that the submersible pump was manufactured after 1979, or that it is safe. If the

Подпись: у

The American Society of Dowsers Inc., dowsers. org

BioGeometry, biogeometry. com and vesica. org The British Society of Dowsers, geomancy. org The Canadian Society of Dowsers, canadiandowsers. org

The Canadian Society of Questers, ...

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HIGH-OCCUPANCY VEHICLE LANES

Posted by on 14/ 11/ 15

Another method that is being increasingly used to relieve congestion on urban free­ways is the establishment of high-occupancy vehicle (HOV) lanes. Although the first instances of use in California in the early 1970s met with much public resistance, the idea was revisited and accepted more readily during the mid-1980s and continues to grow in acceptance in highly congested urban traffic areas (Ref. 9). The concept is to provide a separate lane or lanes for high-occupancy vehicles such as buses, carpools, vanpools, and other ride-sharing modes of transportation. This, in turn, provides a positive incentive for the general public to seek out ride-sharing transportation modes, both public and private. The overall goal is to move more people in fewer vehicles.

2.13.1 Planning Considerations

T...

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Habitat Builds Barrier-Free Homes

Posted by on 14/ 11/ 15

Habitat Builds Barrier-Free Homes

SIMPLE, SINGLE-STORY HOUSES are

not only inexpensive to build but also lend themselves well to barrier-free (handicap-аccessible) eonstruction.

In addition to the obvious differences that relate to wheelchair accessibility—

4

wider hallways and doorways, a ramp instead of a stairway at the entrvwav—

/ 4 4

many other smaller details help make these homes easier for their owners to use and enjoy.

The key to building or retrofitting a house for wheelchair accessibility is recognizing the modified reach of a seated person. You can start by raising the position of electrical outlets and
lowering the height of light switches, closet poles, shelves, and countertops. These easily made alterations help make day-to-day life more convenient for someone in a wheelchair.

Bathrooms and kitchens req...

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SHINGLE REPAIRS

Posted by on 14/ 11/ 15

To remove wood shingles, use scrap blocks to ele­vate the butt ends of the course above. Work the blade of a chisel into the butt end of the defective shingle, and with twists of your wrist, split the shingle into slivers. Before fitting in a new shin­gle, remove the nails that held the old one. Slide a hacksaw blade or, better, a shingle ripper (also known as a slate hook) up under the course above and cut through the nail shanks as far down as possible. If you use a hacksaw blade, wear a heavy glove to protect your hand.

Wood shingles should have a!4-in. gap on both sides, so size the replacement shingle lA in. narrower than the width of the opening. Tap in the replacement with a wood block...

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SITE PLANNING

Posted by on 14/ 11/ 15

Successful approaches to affordable housing require more efficient utilization of land than has often characterized American home building practices in the past.

In most of the demonstration projects, reducing land cost per housing unit was the biggest single factor in achieving affordability. Lower housing cost is therefore closely linked to greater density of land utilization per acre.

This, in turn, poses challenges in the design and aesthetics of housing and land use to maintain and even improve liveability in the context of increased density.

Following are guidelines for site planning:

• Encourage plans to increase density and maintain open space.

• Avoid development plans with wide streets in grid patterns, large lots, deep setbacks, and low density.

• Encourage open space and pr...

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Permeability Tests of Saturated Soils and Aggregates

Posted by on 14/ 11/ 15

Traditionally in geotechnical engineering, the saturated permeability is estimated in the laboratory in a constant head test for coarse grained soils whereas a falling head test is used for fine grained soils. An oedometer test can also provide a measure of the saturated permeability for fine grained soils in the laboratory. Field tests which provide a measure of the saturated permeability are usually a kind of pumping well test, or injection test.

3.3.1.1 Constant Head Permeability Test

A constant head permeability test is usually used for coarse grained soils. The sam­ple is placed in the permeameter where a constant head drop is applied to the sample and the resulting seepage quantity is measured (see Fig. 3.5).

Подпись: Fig. 3.5 Constant head permeability test Permeability Tests of Saturated Soils and Aggregates

By rearranging and substituting into Eq. 2...

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Binomial distribution

Posted by on 14/ 11/ 15

The binomial distribution is applicable to random processes with only two types of outcomes. The state of components or subsystems in many hydrosystems can be classified as either functioning or failed, which is a typical example of a binary outcome. Consider an experiment involving a total of n independent trials with each trial having two possible outcomes, say, success or failure. In each trial, if the probability of having a successful outcome is p, the probability of having x successes in n trials can be computed as

Px(x) = Cn, xpxqn-x for x = 0,1,2,…,n (2.51)

where Cn, x is the binomial coefficient, and q = 1 – p, the probability of having a failure in each trial. Computationally, it is convenient to use the following recursive formula for evaluating the binomial PMF (Drane et al...

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The Nilometers

Posted by on 14/ 11/ 15

One can readily see that in Egypt, measurement of the flood level has great importance. The management of the irrigation system is based on such measurements, as are the taxes, since the agricultural yield can be deduced almost automatically from the flood level. The level is quantified using graduated scales carved into stone; Strabo calls these [87] [88]

The Nilometers

Figure 3.1 Major hydraulic works in ancient Egypt and Nubia.

scales “nilometers”. The most well-known nilometers[89] are those at the fortified pass of Semma, upstream of the second cataract (around 1800 BC), on Elephantine Island at Aswan, downstream of the first cataract (1800 BC), at the temple of Karnak at Thebes (800 BC), and near Memphis upstream of the delta (Figure 3.1)...

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