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.
Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, a generalization of pigeonhole sort that allows multiple keys per bucket, and is a cousin of radix sort in the most-to-least significant digit flavor. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed.
The Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are:
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
In polymer science the molar mass distribution describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation.
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
An index of qualitative variation (IQV) is a measure of statistical dispersion in nominal distributions. There are a variety of these, but they have been relatively little-studied in the statistics literature. The simplest is the variation ratio, while more complex indices include the information entropy.
An outage management system (OMS) is a computer system used by operators of electric distribution systems to assist in restoration of power.
The constellation model is a probabilistic, generative model for category-level object recognition in computer vision. Like other part-based models, the constellation model attempts to represent an object class by a set of N parts under mutual geometric constraints. Because it considers the geometric relationship between different parts, the constellation model differs significantly from appearance-only, or "bag-of-words" representation models, which explicitly disregard the location of image features.
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 queueing theory, a discipline within, the queue is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a, there are servers, and job service times are exponentially distributed. It is a generalization of which considers only a single server. The model with infinitely many servers is the M/M/∞ queue.
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 Average Service Unavailability Index (ASUI) is a reliability index commonly used by electric power utilities. It is calculated as
A Distribution Transformer Monitor (DTM) is a specialized hardware device that collects and measures information relative to electricity passing into and through a distribution transformer. The DTM is typically retrofitted onto pole top and pad mount transformers. A pole top or pad mount transformer commonly powers anywhere from 5-8 homes in the US and is the last voltage transition in stepping down voltage before it gets to the home or business. Standard positioning of DTM devices occurs at the transformer bushings, but sometimes they are attached directly onto the secondary electricity lines. DTM devices commonly consist of highly accurate non-piercing or piercing sensors, onboard communications modules to transmit information, and a power supply provision. The DTM device reports to a collection engine, and/or existing SCADA/MDM system where relevant transformer data is stored and presented to the user; analytics platforms are often employed to interpret the information being captured and reported by the DTM.
Evaluation measures for an information retrieval (IR) system assess how well an index, search engine or database returns results from a collection of resources that satisfy a user's query. They are therefore fundamental to the success of information systems and digital platforms. The success of an IR system may be judged by a range of criteria including relevance, speed, user satisfaction, usability, efficiency and reliability. However the most important factor in determining a systems effectiveness for users is the overall relevance of results retrieved in response to a query. Evaluation measures may be categorised in various ways including offline or online, user-based or system-based and include methods such as observed user behaviour, test collections, precision and recall, and scores from prepared benchmark test sets.
Reliability index is an attempt to quantitatively assess the reliability of a system using a single numerical value. The set of reliability indices varies depending on the field of engineering, multiple different indices may be used to characterize a single system. In the simple case of an object that cannot be used or repaired once it fails, a useful index is the mean time to failure representing an expectation of the object's service lifetime. Another cross-disciplinary index is forced outage rate (FOR), a probability that a particular type of a device is out of order. Reliability indices are extensively used in the modern electricity regulation.
