# Main structure to 1220 years and made it practical to

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main structure to 12–20 years, and made it practical to incorporate power assistance for steering, brakes, window operation, soft top operation, etc. Other everyday engineering artefacts (e.g. washing machines, dish washers, freezers) have similarly benefited. What is Reliability Theory? Reliability theory suggests that biological systems start their adult life with a high load of initial damage. Reliability theory is a general theory about systems failure. It allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. Reliability theory predicts that even those systems that are entirely composed of non-aging elements (with a constant (c) UPES, Not for Reproduction/ Sale
UNIT 17: Reliability Fundamental Theories Notes ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ failure rate) will also deteriorate (fail more often) with age, if these systems are redundant in irreplaceable elements. Aging, therefore, is a direct consequence of systems redundancy. Reliability theory also predicts the late-life mortality deceleration with subsequent levelling-off, as well as the late-life mortality plateaus, as an inevitable consequence of redundancy exhaustion at extreme old ages. The theory explains why mortality rates increase exponentially with age (the Gompertz law) in many species, by taking into account the initial flaws (defects) in newly formed systems. It also explains why organisms “prefer” to die according to the Gompertz law, while technical devices usually fail according to the Weibull (power) law. Reliability theory allows specifying conditions when organisms die according to the Weibull law: organisms should be relatively free of initial flaws and defects. The theory makes it possible to find a general failure law applicable to all adult and extreme old ages, where the Gompertz and the Weibull laws are just special cases of this more general failure law. The theory explains why relative differences in mortality rates of compared populations (within a given species) vanish with age (compensation law of mortality), and mortality convergence is observed due to the exhaustion of initial differences in redundancy levels. Reliability theory is developed apart from the mainstream of probability and statistics. It was originally a tool to help nineteenth century maritime insurance and life insurance companies compute profitable rates to charge their customers. Even today, the terms “failure rate” 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.

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