Application of probability in daily life and in civil engineering

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Statistics and ProbabilityUse of Statistics In Civil

Engineering And In Real Life

Presented by:Engr Habib ur Rehman Chandio

Statistics and Probability

Department of Civil EngineeringWah Engineering College (WEC)

University of Wah, Wah Cantt.

Statistics• the practice or science of collecting and analyzing numerical data in large

quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

OR• A collection of methods for planning experiments, obtaining data, and then then

organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Use of Statistics in Real Life

Let's look at some examples Daily Life Weather Forecasts • Do you watch the weather forecast sometime during the day? How do you use

that information? Have you ever heard the forecaster talk about weather models? These computer models are built using Statistics that compare prior weather conditions with current weather to predict future weather.

Emergency Preparedness • What happens if the forecast indicates that a hurricane is imminent or that

tornadoes are likely to occur? Emergency management agencies move into high gear to be ready to rescue people. Emergency teams rely on Statistics to tell them when danger may occur


Psychology:• Although this is attached to both the science and medical field, success in

psychology would impossible without the systematic study of human behavior, often analyzing results Statistically.

Stock Market: • Another topic that you hear a lot about in the news is the stock market. Stock

analysts also use Statistical computer models to forecast what is happening in the economy


Predicting Disease:• Lots of times on the news reports, Statistics about a disease are reported. If

the reporter simply reports the number of people who either have the disease or who have died from it, it's an interesting fact but it might not mean much to your life. But when Statistics become involved, you have a better idea of how that disease may affect you.For example, studies have shown that 85 to 95 percent of lung cancers are smoking related. The Statistics should tell you that almost all lung cancers are related to smoking and that if you want to have a good chance of avoiding lung cancer, you shouldn't smoke


Education:• Teachers are encouraged to be researchers in their classrooms, to see what

teaching methods work on which students and understand why. They also should evaluate test items to determine if students are performing in a Statistically expected way. At all levels of education and testing there are Statistical reports about student performance, from kindergarten to an SAT or GRE.


Genetics:• Many people are afflicted with diseases that come from their genetic make-up

and these diseases can potentially be passed on to their children. Statistics are critical in determining the chances of a new baby being affected by the disease

Political Campaigns: • Whenever there's an election, the news organizations consult their models

when they try to predict who the winner is. Candidates consult voter polls to determine where and how they campaign. Statistics play a part in who your elected government officials will be.


Quality Testing:• Companies make thousands of products every day and each company must

make sure that a good quality item is sold. But a company can't test each and every item that they ship to you, the consumer. So the company uses Statistics to test just a few, called a sample, of what they make. If the sample passes quality tests, then the company assumes that all the items made in the group, called a batch, are good.


Statistics in Banking• Banks use Statistics for a great number of the services they offer. A bank works

on the idea that someone will deposit their money and not withdraw all of it later on. They earn their profit by lending money to others with interest, and the money they use is the money other people deposit.• Bankers use Statistical approaches to estimate the number of people who will

be making deposits compared to the number of people requesting loans. A great example of Statistics used in banking is the FDIC’s own quarterly publication called


Statistics in Business• If you’re a business major, you’re familiar with the role Statistics plays in your

field. However, if you haven’t gotten to that point yet, here’s some information on Statistics in the business field. Statistics involves making decisions, and in the business world, you often have to make a quick decision then and there. Using Statistics, you can plan the production according to what the customer likes and wants, and you can check the quality of the products far more efficiently with Statistical methods. In fact, many business activities can be completed with Statistics including deciding a new location, marketing the product, and estimating what the profit will be on a new product.


Insurance:• You know that in order to drive your car you are required by law to have car

insurance. If you have a mortgage on your house, you must have it insured as well. The rate that an insurance company charges you is based upon Statistics from all drivers or homeowners in your area

Consumer Goods:• Wal-Mart, a worldwide leading retailer, keeps track of everything they sell and

use Statistics to calculate what to ship to each store and when. From analyzing their vast store of information, for example, Wal-Mart decided that people buy strawberry Pop Tarts when a hurricane is predicted in Florida! So they ship this product to Florida stores based upon the weather forecast


Management and Administration• A nation’s government runs on Statistics. They use Statistical data to make

their decisions regarding any number of things. Most federal and provincial budgets are designed upon Statistical data because it’s the most accurate data available when estimating expected expenditures and revenue.• Another great example of Statistics in the government is figuring out whether

or not to raise the minimum wage due to a rise in the cost of living. Statistical data gives the government the best idea regarding whether or not the cost of living will continue to rise


Medical Studies: • Scientists must show a Statistically valid rate of effectiveness before any drug

can be prescribed. Statistics are behind every medical study you hear about Large Companies• Every large company employs its own Statistical research divisions or firms

to research issues related to products, employees, customer service, etc. Business success relies on knowing what is working and what isn't.


Natural and Social Sciences• Biology, physics, chemistry, meteorology, sociology, communication, and even

information technology all use Statistics. For many of these categories, the use of Statistics in that field involves collecting data, analyzing it, coming up with a hypothesis, and testing that hypothesis.• In biology, the use of Statistics within that field is known as bio-Statistics,

biometry, or biometrics. Bio-Statistics often involves the design of experiments in medicine, , agriculture, and fishery. It also involves collecting, summarizing, and analyzing the data received from those experiments as well as the decided results. Medical bio-Statistics is a separate branch that deals mainly with medicine and health Physics uses probability theory and Statistics dealing mainly with the estimation of large populations. In fact, the phenomenological results of thermodynamics were developed using the mechanics of Statistics.


• There are further examples of Statistics in these sciences fields including analytical chemistry, which involves the presentation of problems in data analysis and demonstrating steps to solve them. Meteorology uses Statistics in stochastic-dynamic prediction, weather forecasting, probability forecasting, and a number of other fields.• Sociology uses Statistics to describe, explain, and predict from data

received. Like many of the sciences, communication uses Statistical methods to communicate data received. Information technology also uses Statistics to predict particular outcomes.


The Role of Statistics in Astronomy• It is impossible to take out a ruler and measure the distance of the Earth from

the sun. Unless, of course, you somehow manage to invent a suit that can survive the temperatures of the sun and design a ruler long enough to measure such a distance. However, it would likely take you a very long time to measure such a distance anyway.• Instead, astronomers use estimates and mathematical theories to devise their

best guess to just how far items in the universe are away from each other. This is why when you read a news report that a star will likely be going supernova “any day now,” you have to understand that “any day now” could mean tomorrow, a year from now, or even ten thousand years from now.


Applications of Statistics in Civil Engineering•The following situations are examples from the field of civil

engineering where variation occurs and Statistical method either are or could be applied. In some instances the current practice may not be very sound based on Statistical theory. These applications are useful for analyzing and discussing the use of Statistics in the practice of civil engineering.

Applications of Statistics in Civil Engineering

Sanitary Engineering • Given: A series of samples of wastewater ("water" from a sewer) and results of

biological oxygen demand (BOD) tests Find: The design BOD, which is the value that corresponds to a certain probability of not being exceeded. This value would be used to design the wastewater treatment plant. Commentary: A deterministic approach would use the mean BOD and apply some factor of safety.


Traffic/Transportation Engineering • Given: An intersection between a residential street and a major artery in a suburban

community. The residential street has a stop sign, but the artery does not. • An access road for a new recreation area is to have a toll booth. The distribution of

vehicles per minute, the time required to process each vehicle, and the length of roadway required for each waiting vehicle are given.

• Find: The probability that a vehicle stopped at the stop sign will have to wait more than a specified period before making a left turn onto the artery. • The required "storage area", which is the minimum required length of roadway between

the toll booth and the adjacent highway such that the probability of waiting vehicles extending onto the highway does not exceed a certain value.


• Commentary: The acceptable probability depends on the consequences of being exceeded. For example, if the highway is a busy one-lane road, a very low design value would be used, whereas if it is a low-volume four-lane road, perhaps a higher probability would be acceptable.

• A similar analysis also could be done based on the probability of exceeding some maximum acceptable waiting time. Based on the results of such analyses, we might decided to have more than one toll booth. If so, how often would both booths need to be in service? (study of waiting lines)

• If this probability is too high a traffic signal may be warranted. Traffic engineers perform this kind of analysis to determine where to place traffic signals.


Surveying and Mapping • Given: A series of measurements from the field, each of which is made using an

instrument that has a certain precision. • Commentary: Many measurements in surveying are made using a series of

instrument setups. For example, consider a piece of property whose boundary consists of 8 line segments. The orientation of one of these segments with respect to true north is known to a precision of 20" of arc. A surveyor sets up a "total station" (an instrument that measures angles and distances) at each of the 8 corners, and measures the angles to a precision of 20" and the distances to a precision of 0.01 ft. These measurements are then "adjusted" so that satisfy the rules of geometry. Find: The precision of the computed orientations of the other property lines. It is not 20"!


Coastal and Port Engineering • Given: Anticipated distribution of cargo ship arrivals at a port in the year 2010,

and the mean time required for a ship to occupy a berth. Find: The number of berths required so the probability of a ship having to wait more than a certain number of hours to enter a berth is no more than x. Commentary: A large amount of construction is currently under way at the ports in Long Beach and Los Angeles. Portions of this construction would be based on these kinds of analysis.


Geotechnical Engineering• Given: Four soil samples obtained from a certain stratum of soil and the results

of laboratory consolidation tests on each sample. These test results are used to compute the settlement that will occur if a certain load is placed on this strata. Find: Considering only variations due to the sample locations (i.e., assuming the sampling method, testing, and analysis introduce no uncertainty), compute the probability that the settlement will exceed some specified value. Commentary: I've seen data that indicate COV values of 0.26 to 0.52 from multiple samples obtained from "homogeneous" strata. Thus, analyses based on mean values could produce results that are seriously in error. Related analysis: Given the cost of sampling and testing, how many samples should be taken


Hydrology• Given: Stream flow records for the Santa Ana River near Corona.

Find: The stream flow (ft^3/s) that corresponds to a particular recurrence interval. This flow can then be used to design dams, levees, etc.

• Commentary: After a devastating flood in 1938, the Army Corps of Engineers built Prado Dam to protect Orange County. This dam and its spillway can be seen from the 91 freeway (the spillway has 1776-1976 painted on it). The reservoir behind this dam is normally empty, and is intended to capture the excess flood waters in the event of another major flood, thus keeping the stream flow below the dam at manageable levels. This dam was designed based on the best hydrologic data and analyses then available. However, subsequent analyses performed in the 1970s and 1980s found the flood that corresponds to a certain recurrence interval (200 years?) is much greater than had previously been considered. Such a flood could overtop the dam, causing it to fail, thus producing massive flooding in Orange County. Because of this, the Army Corps of Engineers is currently building a massive flood control project along the Santa Ana River, which includes a new dam upstream of Prado (Seven Oaks Dam), new levees, and the raising of Prado Dam. This is a massive construction project, all of which is based on a Statisticalanalysis of hydrologic data.


Environmental Engineering • Given: A series of groundwater samples obtained at different locations and

depths in an aquifer, and the concentration of a certain chemical in each sample. Find: The probability that the concentration at any point in the aquifer exceeds some specified value.


Earthquake Engineering/Seismology• Given: A proposed dam to be built at a certain site, the probability of

earthquakes of various sizes occurring on faults at various locations, the predicted peak horizontal ground acceleration at the dam site from each of these earthquakes. Find: The design peak ground acceleration, which is the one that corresponds to a certain probability of being exceeded during the design life of the dam.


• Structural Engineering • Given: The Uniform Building Code dictates certain design values for the live load on building

elements (live load is that load induced by furniture, inventory, occupants, moveable objects, etc., as contrasted to dead load (the structure itself), earthquake load, wind load, etc.). For example, the code-specified design load for classrooms is 40 lb/ft^2. Find: The probability that this design load will be exceeded. buildings. I couldn't • Commentary: I've seen some Statistical data on live loads based on actual measurements in

find it in my files, but I think the COV is about 0.10, and the probability of exceeding is about 0.05. A design method called "load and resistance factor design" (LRFD), which our students learn in a junior-level course, uses "load factors" and "resistance factors" that have been developed from extensive reliability analyses. Although design engineer simply uses the specified factors in a typical design, it is important to understand how the building codes developed them.


Thank you …

… for paying attention