The Average Service Unavailability Index (ASUI) [1] is a reliability index commonly used by electric power utilities. It is calculated as
where is the number of customers and is the annual outage time (in hours) for location . ASUI can be represented in relation to SAIDI (where annual SAIDI is given in hours) as
In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius.
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 mathematics, particularly in linear algebra, a skew-symmetricmatrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition
A numerically-controlled oscillator (NCO) is a digital signal generator which creates a synchronous, discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digital-to-analog converter (DAC) at the output to create a direct digital synthesizer (DDS).
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating the negative continuous Laplacian obtained by the finite difference method.
The scaled inverse chi-squared distribution is the distribution for x = 1/s2, where s2 is a sample mean of the squares of ν independent normal random variables that have mean 0 and inverse variance 1/σ2 = τ2. The distribution is therefore parametrised by the two quantities ν and τ2, referred to as the number of chi-squared degrees of freedom and the scaling parameter, respectively.
In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight.
The System Average Interruption Duration Index (SAIDI) is commonly used as a reliability index by electric power utilities. SAIDI is the average outage duration for each customer served, and is calculated as:
The System Average Interruption Frequency Index (SAIFI) is commonly used as a reliability index by electric power utilities. SAIFI is the average number of interruptions that a customer would experience, and is calculated as
The Customer Average Interruption Duration Index (CAIDI) is a reliability index commonly used by electric power utilities. It is related to SAIDI and SAIFI, and is calculated as
The digital root of a natural number in a given radix is the value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For example, in base 10, the digital root of the number 12345 is 6 because the sum of the digits in the number is 1 + 2 + 3 + 4 + 5 = 15, then the addition process is repeated again for the resulting number 15, so that the sum of 1 + 5 equals 6, which is the digital root of that number. In base 10, this is equivalent to taking the remainder upon division by 9.
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including function approximation, time series prediction, classification, and system control. They were first formulated in a 1988 paper by Broomhead and Lowe, both researchers at the Royal Signals and Radar Establishment.
The Momentary Average Interruption Frequency Index (MAIFI) is a reliability index used by electric power utilities. MAIFI is the average number of momentary interruptions that a customer would experience during a given period. Electric power utilities may define momentary interruptions differently, with some considering a momentary interruption to be an outage of less than 1 minute in duration while others may consider a momentary interruption to be an outage of less than 5 minutes in duration.
The Customer Average Interruption Frequency Index (CAIFI) is a popular reliability index used in the reliability analysis of an electric power system. It is designed to show trends in customers interrupted and helps to show the number of customers affected out of the whole customer base.
In quantum mechanics, and especially quantum information theory, the purity of a normalized quantum state is a scalar defined as
Krippendorff's alpha coefficient, named after academic Klaus Krippendorff, is a statistical measure of the agreement achieved when coding a set of units of analysis. Since the 1970s, alpha has been used in content analysis where textual units are categorized by trained readers, in counseling and survey research where experts code open-ended interview data into analyzable terms, in psychological testing where alternative tests of the same phenomena need to be compared, or in observational studies where unstructured happenings are recorded for subsequent analysis.
The Average Service Availability Index (ASAI) is a reliability index commonly used by electric power utilities. ASAI is calculated as
The PM NowCast is a weighted average of hourly air monitoring data used by the United States Environmental Protection Agency (USEPA) for real-time reporting of the Air Quality Index (AQI) for PM (PM10 or PM2.5).
The Customer Total Average Interruption Duration Index (CTAIDI) is a reliability index associated with electric power distribution. CTAIDI is the average total duration of interruption for customers who had at least one interruption during the period of analysis, and is calculated as:
Evaluation measures for an information retrieval system are used to assess how well the search results satisfied the user's query intent. Such metrics are often split into kinds: online metrics look at users' interactions with the search system, while offline metrics measure relevance, in other words how likely each result, or search engine results page (SERP) page as a whole, is to meet the information needs of the user.
