
Maximum Likelihood Estimation (MLE) is a statistical technique used to estimate the parameters of a model by maximizing the likelihood function, which measures how likely the observed data is under specific parameter values.
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by Semion Gengrinovich Leave a Comment

Maximum Likelihood Estimation (MLE) is a statistical technique used to estimate the parameters of a model by maximizing the likelihood function, which measures how likely the observed data is under specific parameter values.
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Reducing Fugitive Dust at Red Dog Mine
A 2000 National Park Service study discovered elevated concentrations of metals in tundra along the road and near the port that served the Red Dog Mine in Alaska. The elevated concentrations led to concerns about potential effects on both the general population in the area and the environment.
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The Kansas City Walkway Collapse.
On July 17, 1981, during a tea dance in the vast atrium at the Hyatt Regency Hotel in Kansas City, two elevated walkways collapsed onto the people celebrating in the lobby, killing 114 of them and injuring more than 200.
The determination of what happened focused on the design and construction of the walkways. The 40-story complex featured a unique main lobby design consisting of a 117-foot by 145-foot atrium that rose to a height of 50 feet. Three walkways spanned the atrium at the second, third, and fourth floors.
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On March 3, 1974, Turkish Airlines Flight 981 took off from Orly International Airport in Paris on its way to London’s Heathrow Airport with 346 people on board. After taking off under good flight conditions, the DC-10 jet was cleared to ascend. At 11,000 feet, the rear cargo door opened and detached from the aircraft. The pressure difference between the passenger and cargo areas caused the cabin floor to buckle, trapping the pitch controls in the nose-down position. A minute later the plane crashed in a forest near the town of Senlis, France. There were no survivors.
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In 2001, Whirlpool Corporation, the world’s leading manufacturer and marketer of major home appliances, voluntarily recalled about 1,800,000 Whirlpool, KitchenAid, and Kenmore brand “over the range” microwave-hood combinations.
Working in cooperation with the U.S. Consumer Product Safety Commission (CPSC), Whirlpool recalled the units because they had received seven complaints of fire and did not want to risk customer injury or property damage. The CPSC helps protect the general public from unreasonable risks of serious injury or death from consumer products under the agency’s jurisdiction. More often than not, manufacturers of such products work with the CPSC to voluntarily recall products from the market that may pose a risk to individuals.
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How safe is the modern roller coaster? Media attention to amusement park injuries and fatalities have led to concerns about passenger safety and potential brain injuries resulting from faster, more complex rides that may cause greater stress on the rider.
West European ice slides, popular in the 16th and 17th centuries, are the earliest ancestors of the present-day roller coaster. Ice blocks were fashioned into sleds, and sand created friction to slow down the sled at the end of the ride. As popularity increased, wooden sleds were built with iron runners to increase the speed and intensity of the ride.
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On November 24, 2000, PacifiCorp experienced a massive generator failure at its Hunter Power Plant in Castle Dale, Utah. Post-event inspection of the generator revealed a serious failure of the stator core—a cylindrical structure nearly 19 feet long and more than 16 feet across—which had partially melted. At the time, the generator was operating at its maximum capacity of 415 megawatts. Sparks and heavy arcing were observed before the unit tripped automatically, shutting the system down within 55 minutes.
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On September 11, 2001, terrorists crashed two hijacked commercial jets into the Twin Towers of New York City’s World Trade Center in a coordinated attack on this symbol of American financial power and influence. Remarkably, both towers survived the initial impact of Boeing 767 jets traveling at speeds in excess of 400 mph, and remained standing long enough for most occupants below the impact floors to escape.
The 110-story Twin Towers of the World Trade Center embodied many engineering advances. They were the first major structures to be designed using wind tunnel testing and digital computers, the first to use structural dampers, and, at the time, the tallest ever built.
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EPRI: The Electric Power Research Institute
How safe and reliable are America’s electric power plants?
In 1973 the United States Senate held hearings on the lack of research and development in the power industry. In response, U.S. electric utilities dedicated resources to develop a nonprofit center for research—The Electric Power Research Institute (EPRI). EPRI was mandated with gathering technical experts and members of the electric power industry to work collaboratively on solutions to the challenges of the electric power industry. Among EPRI’s first priorities was an assessment of the reliability of nuclear power facilities with respect to their design, operation, and maintenance.
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On April 13, 1992, water tore a 20-foot long hole through the wall of a tunnel 20 feet below the bed of the Chicago River, some 50 feet below downtown Chicago. Over 200 million gallons of water surged through an extensive series of underground tunnels, affecting over 30 major buildings including City Hall and the financial markets. Lower levels of major office high-rises held up to 40 feet of water, and the city center was evacuated out of fear that electrical or utility connection failures could endanger lives.
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On August 12, 1983, the crankshaft of one of the three emergency diesel generators at the yet-unopened Shoreham Nuclear Power Station snapped during testing. Inspections revealed cracks in the crankshafts of the two other diesels as well as other defects. Permission to perform low-power tests had been granted before the failure of the crankshaft, and two more years of subsequent analysis passed before permission was again granted. By the late 1980s, a conflict over the emergency evacuation plan was still delaying an operating license for the plant.
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With the 1980 X-Car series, General Motors introduced a new generation of front-wheel drive, fuel-efficient compact passenger cars. The letter X designated a generic chassis type that was manufactured into a particular model through styling and features. All X-Cars were tested and met all Federal Motor Vehicle Safety Standards, but during the development of the vehicles it was found that certain manual transmission X-Cars required more aggressive rear brake shoes to meet parking brake standards.
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The Hindenburg disaster, which occurred on May 6, 1937, at Naval Air Station Lakehurst in New Jersey, marked the end of the golden age of airship travel. This catastrophic event not only claimed 36 lives but also exposed significant design flaws and reliability issues in what was once considered a marvel of engineering.
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In Part 2 of Beyond the Numbers, I explored how human reliability principles can be integrated into traditional reliability artefacts such as Reliability Block Diagrams (RBDs), Fault Tree Analysis (FTA) and Failure Modes, Effects and Criticality Analysis (FMECA). Those tools help us understand how systems fail and how different failure paths interact.
But reliability engineering does not end with failure analysis.
In practice, the outputs of FMECA flow directly into the Reliability Centred Maintenance (RCM) process, where failure modes are translated into maintenance strategies such as inspections, condition monitoring, restorations or replacements.
If assumptions about human performance are simplified during reliability analysis, those assumptions do not disappear. They are carried forward, and often amplified, when maintenance requirements are defined.
Maintenance is where reliability modelling becomes an operational commitment.
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In the automotive industry, safety is paramount. Yet, even giants like Ford Motor Company can stumble when it comes to addressing critical safety concerns. The recent saga of Ford’s brake system issues serves as a stark reminder of the importance of corporate responsibility and the potential consequences of overlooking serious defects.
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