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Reliability theory
 
 
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Reliability theory developed apart from the mainstream of probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
 and statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
. It was originally a tool to help nineteenth century maritime insurance
Marine insurance

Marine Insurance covers the loss or damage of ships, cargo, terminals, and any transport or property by which cargo is transferred, acquired, or held between the points of origin and final destination....
 and life insurance
Life insurance

Life insurance or life assurance is a contract between the policy owner and the insurance, where the insurer agrees to pay a sum of money upon the occurrence of the insured individual's or individuals' death or other event, such as terminal illness or critical illness....
 companies compute profitable rates to charge their customers. Even today, the terms "failure rate
Failure rate

Failure rate is the frequency with which an engineered system or component failure, expressed for example in failures per hour. It is often denoted by the Greek alphabet ? and is important in reliability theory....
" and "hazard rate" are often used interchangeably.

The failure of mechanical devices such as ships, trains, and cars, is similar in many ways to the life or death of biological organisms. Statistical models appropriate for any of these topics are generically called "time-to-event" models.






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Reliability theory developed apart from the mainstream of probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
 and statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
. It was originally a tool to help nineteenth century maritime insurance
Marine insurance

Marine Insurance covers the loss or damage of ships, cargo, terminals, and any transport or property by which cargo is transferred, acquired, or held between the points of origin and final destination....
 and life insurance
Life insurance

Life insurance or life assurance is a contract between the policy owner and the insurance, where the insurer agrees to pay a sum of money upon the occurrence of the insured individual's or individuals' death or other event, such as terminal illness or critical illness....
 companies compute profitable rates to charge their customers. Even today, the terms "failure rate
Failure rate

Failure rate is the frequency with which an engineered system or component failure, expressed for example in failures per hour. It is often denoted by the Greek alphabet ? and is important in reliability theory....
" and "hazard rate" are often used interchangeably.

The failure of mechanical devices such as ships, trains, and cars, is similar in many ways to the life or death of biological organisms. Statistical models appropriate for any of these topics are generically called "time-to-event" models. Death or failure is called an "event", and the goal is to project or forecast the rate of events for a given population or the probability of an event for an individual.

When reliability is considered from the perspective of the consumer of a technology or service, actual reliability measures may differ dramatically from perceived reliability. One bad experience can be magnified in the mind of the customer, inflating the perceived unreliability of the product. One plane crash where hundreds of passengers die will immediately instill fear in a large percentage of the flying consumer population, regardless of actual reliability data about the safety of air travel.

See also


  • Actuarial science
    Actuarial science

    Actuarial science is the discipline that applies mathematics and statistics methods to Risk assessment in the insurance and finance industries. Actuary are professionals who are qualified in this field through education and experience....
  • Availability
    Availability

    In telecommunications and reliability theory, the term availability has the following meanings:1. The degree to which a system, subsystem, or equipment is operable and in a committable state at the start of a mission, when the mission is called for at an unknown, i.e., a random, time....
  • Catastrophe modeling
    Catastrophe modeling

    Catastrophe modeling is the process of using computer-assisted calculations to estimate the losses that could be sustained by a portfolio of properties due to a catastrophic event such as a hurricane or earthquake....
  • Extreme value theory
    Extreme value theory

    File:1755 Lisbon earthquake.jpgExtreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions....
  • Failure rate
    Failure rate

    Failure rate is the frequency with which an engineered system or component failure, expressed for example in failures per hour. It is often denoted by the Greek alphabet ? and is important in reliability theory....
  • Fault tree
  • Gompertz law
    Benjamin Gompertz

    Benjamin Gompertz , was a autodidact mathematician, denied admission to university because he was Jewish. Nevertheless he was made Fellow of the Royal Society in 1819....
  • Gompertz-Makeham law of mortality
    Gompertz-Makeham law of mortality

    The Gompertz-Makeham law states that death rate is a sum of age-independent component and age-dependent component , which increases exponentially with age....
  • Reliability
    Reliability

    In general, reliability is the ability of a person or system to perform and maintain its functions in routine circumstances, as well as hostile or unexpected circumstances....
  • Reliability engineering
    Reliability engineering

    Reliability engineering is an engineering field, that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time....
  • Reliability theory of aging and longevity
    Reliability theory of aging and longevity

    Reliability theory of aging and longevity is a scientific approach aimed to gain theoretical insights into mechanisms of biological aging and species survival patterns by applying a general theory of systems failure, known as reliability theory....
  • Survival analysis
    Survival analysis

    Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems.This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology....
  • Weibull distribution
    Weibull distribution

    In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is often called the Rosin?Rammler distribution when used to describe the size distribution of Granular material....


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