The weighted arithmetic mean is similar to an ordinary arithmetic mean, except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.
In reliability engineering, the term availability has the following meanings:
Unavailability, in mathematical terms, is the probability that an item will not operate correctly at a given time and under specified conditions. It opposes availability.
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success. In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution.
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The term is used for repairable systems while mean time to failure (MTTF) denotes the expected time to failure for a non-repairable system.
In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival?
Annualized failure rate (AFR) gives the estimated probability that a device or component will fail during a full year of use. It is a relation between the mean time between failure (MTBF) and the hours that a number of devices are run per year. AFR is estimated from a sample of like components—AFR and MTBF as given by vendors are population statistics that can not predict the behaviour of an individual unit.
Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering.
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time.
In systems engineering and requirements engineering, a non-functional requirement (NFR) is a requirement that specifies criteria that can be used to judge the operation of a system, rather than specific behaviours. They are contrasted with functional requirements that define specific behavior or functions. The plan for implementing functional requirements is detailed in the system design. The plan for implementing non-functional requirements is detailed in the system architecture, because they are usually architecturally significant requirements.
High availability (HA) is a characteristic of a system that aims to ensure an agreed level of operational performance, usually uptime, for a higher than normal period.
Black's Equation is a mathematical model for the mean time to failure (MTTF) of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement (movement) in the solid phase caused by an electromagnetic field.
Probabilistic design is a discipline within engineering design. It deals primarily with the consideration and minimization of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects studied and optimized are related to quality and reliability. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor. Probabilistic design is used in a variety of different applications to assess the likelihood of failure. Disciplines which extensively use probabilistic design principles include product design, quality control, systems engineering, machine design, civil engineering and manufacturing.
A prediction of reliability is an important element in the process of selecting equipment for use by telecommunications service providers and other buyers of electronic equipment, and it is essential during the design stage of engineering systems life cycle. Reliability is a measure of the frequency of equipment failures as a function of time. Reliability has a major impact on maintenance and repair costs and on the continuity of service.
Availability is the probability that a system will work as required when required during the period of a mission. The mission could be the 18-hour span of an aircraft flight. The mission period could also be the 3 to 15-month span of a military deployment. Availability includes non-operational periods associated with reliability, maintenance, and logistics.
Maintenance Philosophy is the mix of strategies that ensure an item works as expected when needed.
Operational availability in systems engineering is a measurement of how long a system has been available to use when compared with how long it should have been available to be used.
High-temperature operating life (HTOL) is a reliability test applied to integrated circuits (ICs) to determine their intrinsic reliability. This test stresses the IC at an elevated temperature, high voltage and dynamic operation for a predefined period of time. The IC is usually monitored under stress and tested at intermediate intervals. This reliability stress test is sometimes referred to as a lifetime test, device life test or extended burn in test and is used to trigger potential failure modes and assess IC lifetime.
Mean Time to Dangerous Failure. In a safety system MTTFD is the portion of failure modes that can lead to failures that may result in hazards to personnel, environment or equipment.
